Black-Scholes formula

The Concepts and Practice of Mathematical Finance
by Mark S. Joshi
Published 24 Dec 2003

Index N, 65 N(0, 1), 57 N(µ, a2), 98 or-field, 458 accreting notional, 429 admissible exercise strategy, see exercise strategy, admissible almost, 257 almost surely, 99 American, 10 American option, see option, American amortising notional, 429 annualized rates, 302 annuity, 308 .anti-thetic sampling, 192 arbitrage, 19-20, 27-29,429 and bounding option prices, 29-39 arbitrage-free price, 45, 46 arbitrageur, 12-13, 18 Arrow-Debreu security, 152 at-the-forward, 31 at-the-money, 30, 66 auto cap, 429 bank, 12 barrier option, see option, barrier basis point, 429 basket option, 261 Bermudan option, see option, Bermudan Bermudan swaption, see swaption, Bermudan BGM, 429 implementation of, 450-453 BGM model, 322-355 automatic calibration to co-terminal swaptions, 342 long steps, 337 running a simulation, 337-342 BGM/J, 429 BGM/J model, see BGM model bid-offer spread, 21 Black formula, 173, 310-311 approximate linearity, 356 approximation for swaption pricing under BGM model, 341 Black-Scholes formula, see option, call, Black-Scholes formula for Black-Scholes density, 188 Black-Scholes equation, 69, 160, 161 for options on dividend-paying assets, 123 higher-dimensional, 271 informal derivation of, 114-116 rigorous derivation, 116-119 solution of, 119-121 with time-dependent parameters, 164 Black-Scholes formula, 65 Black-Scholes model, 74, 113, 430 Black-Scholes price, 19 Black-Scholes model, 76 bond, 4 6, 430 callable, 301 convertible, 7, 430 corporate, 7 government, 1 premium, 2 riskless, 5, 7 zero-coupon, 5, 24-26, 28, 302, 433 Brownian bridge, 230 Brownian motion, 97-100, 101, 107, 142, 260, 430 correlated, 263 higher-dimensional, 261-263 Buffett, Warren, 2 bushy tree, see tree, non-recombining calibration to vanilla options using jump-diffusion, 377 call, 301 call option, see option, call callable bond, see bond, callable cap, 309, 430 caplet, 309-311, 430 strike of, 309 caption, 326, 430 cash bond, 26, 430 Central Limit theorem, 56, 60 Central Limit Theorem, 64 Central Limit theorem, 278,463 central method, 238 533 Index 534 CEV, see constant elasticity of variance chain rule, 106 for stochastic calculus, 109 characteristic function, 408 Cholesky decomposition, 227 cliquet, 425, 430 call, 425 optional, 426 put, 425 CMS, see swap, constant maturity co-initial, 317, 340 co-terminal, 317, 340 commodities, 123 complete market, 152, 430 compound optionality, 426 conditional probability, 460 consol, 430 constant elasticity of variance, 113 constant elasticity of variance process, 355 constant maturity swap, see swap, constant maturity contingent claim, 152, 430 continuously compounding rate, 25, 26 control variate and pricing of Bermudan swaptions, 351 on a tree, 288 convenience yield, 123 convexity, 35-37, 81 as a function of spot price in a log-type model, 383 correlation, 466 between forward rates, 321, 335 correlation matrix, 268, 466 cost of carry, 123 coupon, 4, 301, 430 covariance, 466 covariance matrix, 466 and implementing BGM, 343 crash, 10, 86 credit default swap, 23 credit rating, 316, 430 cumulative distribution function, 461 cumulative normal function, 65, 435, 437 default, 1 deflated, 168 Delta, 76, 80,430 and static replication, 246, 248 Black-Scholes formula for call option, 80 integral expression for, 189 Delta hedging, see hedging, Delta dependent, 461 derivative, 10, 430 credit, 11 weather, 11 Derman-Kani implied tree, 381 deterministic future smile, 244, 426 digital, 430 digital option, see option, digital dimensionality, 224, 438 dimensionality reduction, 229 discount curve, 431 discretely compounding money market account, 324 displaced diffusion model, 355 distribution log-normal, see log-normal distribution diversifiable risk, 431 diversification, 8 dividend, 7, 431 scrip, 25 dividend rate, 25 dividends and the Black-Scholes equation, 121-123 drift, 60, 111 of a forward rate under BGM, 330 real-world, 64 Dupire model, 381 dynamic replication, see replication, dynamic early exercise, 68 equivalent martingale measure for a tree with jumps, 363 equivalent probability measures, see probability measure, equivalence European, 10 European contingent claim, 116 exercise, 10 exercise boundary, 289 exercise region, 289 exercise strategy admissible, 286 expectation, 431, 462 conditional, 155 fat tails, 85, 431, 464 Feynman-Kac theorem, 161 fickle, 377 filtration, 143, 154, 162 first variation, see variation, first fixed leg, 306 fixed rate, 431 floating, 300 floating leg, 306 floating rate, 431 floating smile, see smile, floating floor, 309,431 floorlet, 309, 431 floortion, 326, 431 forward contract, 9, 22, 181, 431 and risk-neutrality, 137 value of, 26 forward price, 26, 31 forward rates, 303-305 forward-rate agreement, 23, 304, 431 Fourier transform, 395, 408 FRA, see forward-rate agreement free boundary value problem, 290 Gamma, 77, 80, 431 and static replication, 246, 248 Black-Scholes formula for a call option, 80 non-negativity of, 384 Index Gamma distribution, 402 Gamma function, 402 incomplete, 405 Gaussian distribution, 57, 103 Gaussian random variable synthesis of, 191 gearing, 300 geometric Brownian motion, 111, 114 gilt, 314 Girsanov transformation, 214 Girsanov's theorem, 158, 166, 210-213, 368, 390, 431 higher-dimensional, 267-271 Greeks, 77-83, 431 and static replication, 246, 248 computation of on a tree, 186 of multi-look options, 236-238 heat equation, 119, 120-121 Heath, Jarrow & Morton, 322 hedger, 12-13, 18 hedging, 4, 8, 11, 67-68, 431, 441 and martingale pricing, 162-164 Delta, 18-19, 68, 73, 76, 115, 118, 162 exotic option under jump-diffusion, 535 Ito's Lemma, 106-110 application of, 111-114 multi-dimensional, 264 joint density function, 464 joint law of minimum and terminal value of a Brownian motion with drift, 213 without drift, 208 jump-diffusion model, 87, 364-381 and deterministic future smiles, 244 and replication of American options, 293 price of vanilla options as a function of jump intensity, 374 pricing by risk-neutral evaluation, 364-367 jump-diffusion process, 361 jumps, 86-88 jumps on a tree, 362 Kappa, 79 knock in, 202 knock out, 202 knock-in option, see option, barrier knock-out option, see option, barrier kurtosis, 85, 432, 464 375 Gamma, 77 in a one-step tree, 44-45 in a three-state model, 49 in a two-step model, 51 of exotic options, 424 vanilla options in a jump-diffusion world, 372 Vega, 79 hedging strategy, 17-18, 44, 76 stop-loss, 143 hedging, discrete, 76 HJM model, 322 homogeneity, 274, 281, 383 implied volatility, see volatility, implied importance sampling, 193 in-the-money, 30 incomplete, 431 incomplete market, 50, 361, 367-375, 389, 390 incomplete model, 89 incremental path generation, see path generation, incremental independent, 461 information, 2, 4, 113, 140-145, 162, 401 conditioning on, 145 insider trading, 3 insurance, 12 inverse cumulative normal function, 192, 435, 436 inverse floater, 359 Ito, 97 Ito calculus higher-dimensional, 261, 263-266 Ito process, 106, 154 law of large numbers, 69, 191, 462 law of the minimum of a Brownian motion drift, 215, 216 law of the unconscious statistician, 463 Leibniz rule, 110 leveraging, 300 LIBID, 432 LIBOR, 302, 315, 432 LIBOR market model, 322 LIBOR-in-arrears, 312-313 LIBOR-in-arrears caplet pricing by BGM, 326 LIBOR-in-arrears FRA pricing by BGM, 326 likelihood ratio, 195, 237 liquidity, 21 Lloyds, 6 log-normal distribution, 61 log-normal model, 58 approximation by a tree, see tree, approximating a log-normal model for stock price movements, 112 log-type model, 382-385 long, 21, 432 low-discrepancy numbers, 193 the pricing of exotic options, 445-447 lucky paths, 369 marginal distribution, 465 Margrabe option, see option, Margrabe market efficiency, 2-4 weak, 3, 4, 99 market maker, 74 market model, 432 market price of risk, 89, 112 Index 536 Markov property, 3, 98, 99 strong, 210 martingale, 129, 145, 432 and no arbitrage, 146 continuous, 154-160 discrete, 146 higher-dimensional, 267 martingale measure, 148 choice of, 376 uniqueness, 150 martingale pricing and time-dependent parameters, 164-165 based on the forward, 172-175 continuous, 157-160 discrete, 145-154 equivalence to PDE method, 161-162 with dividend-paying assets, 171 martingale representation theorem, 162 maturity, 5 maximal foresight, 296 mean-reverting process, 390 measure change, 368 model risk, 244 moment, 432 moment matching, 193 and pricing of Asian options, 231-233 money-market account, 26, 114, 430 moneyness, 385 monotonicity theorem, 27 Monte Carlo simulation, 69, 462 and price of exotic options using a jump-diffusion model, 379 and pricing of European options, 191 computation of Greeks, 194-195 variance reduction, 192 Moro, 435 mortgage, 301 multi-look option, see option, multi-look Name, 6 natural payoff, 330 NFLWVR, 132, 135 no free lunch principle, 19 no free lunch with vanishing risk, see NFLWVR no-arbitrage, 45 non-recombining tree, see tree, non-recombining normal distribution, see Gaussian distribution, 461 notional, 304 numeral e, 168, 174, 310, 312, 314, 324 change of, 167 numerical integration and pricing of European options, 187-190 option, 9-12 American, 68, 144, 284, 429 boundary conditions for PDE, 290 lower bounds by Monte Carlo, 293-295 PDE pricing, 289-291 pricing on a tree, 287-289 replication of, 291-293 seller's price, 297 theoretical price of, 287 upper bounds by Monte Carlo, 295-297 American digital, 219 American put, 219 Asian, 222, 429 pricing by PDE or tree, 233-234 static replication of, 249-251 barrier, 69, 429 definition, 202-204 price of down-and-out call, 217, 218 basket, 261, 429 Bermudan, 284,429 binary, 429 call, 10, 181, 430 American, 32 Black-Scholes formula for, 65, 160 down-and-in, 202 down-and-out, 202 formula for price in jump-diffusion model, 366, 367 pay-off, 29 perpetual American, 299 pricing under Black-Scholes, 114 chooser, 294 continuous barrier expectation pricing of, 207-208, 216-219 PDE pricing of, 205-207 static replication of, 244-247, 252-256 static replication of down-and-out put, 244-246 continuous double barrier static replication, 246-247 digital, 83, 257 call, 83 put, 83 digital call, 181 Black-Scholes formula for price of, 183 digital put, 181 Black-Scholes formula for price of, 183 discrete barrier, 222 static replication of, 247-249 double digital, 130 European, 431 exotic, 10, 87 Monte Carlo, 444445 pricing under jump-diffusion, 379-381 knock-in, 431 knock-out, 69, 432 Margrabe, 260, 273-275 model-independent bounds on price, 29-39 multi-look, 223 Parisian, 432 path-dependent, 223 and risk-neutral pricing, 223-225 static replication of, 249-251 power call, 182 put, 10, 181,432 Black-Scholes formula for, 65 pay-off, 30 Index quanto, 260, 275-280 static replication of up-and-in put with barrier at strike, 251-252 trigger, 433 vanilla, 10 with multiple exercise dates, 284 out-of-the-money, 30 path dependence weak, 225 path generation, 226-230 incremental, 228 using spectral theory, 228 path-dependent exotic option, see option, path-dependent pathwise method, 195, 236 PDE methods and the pricing of European options, 195-196 Poisson process, 364 positive semi-definite, 467 positivity, 7, 28 predictable, 162 predictor-corrector, 340 present valuing, 302 previsible, 370 pricing arbitrage-free, 22 principal, 5, 301 probability risk-neutral, see risk-neutral probability probability density function, 461 probability measure, 458 equivalence, 147 product rule for Ito processes, 110 pseudo-square root, 468 put option, see option, put put-call parity, 30, 65, 67 put-call symmetry, 252-256 quadratic variation, 100, see variation, quadratic quanto call, 277 quanto drift, 276 quanto forward, 277 quanto option, see option, quanto quasi Monte Carlo, 194 Radon-Nikodym, 214 Radon-Nikodym derivative, 213 random time, 88, 143 random variable, 459 real-world drift, see drift, real-world recombining trees implementing, 443 reflection principle, 208-210 replication, 23, 116 and dividends, 122 and the pricing of European options, 196-198 classification of methods, 257 dynamic, 198, 257 in a one-step tree, 48-49 537 in a three-state model, 50 semi-static and jump-diffusion models, 381 static, 198 feeble, 257 mezzo, 257 strong, 243, 257 weak, 243, 257 repo, 315 restricted stochastic-volatility model, see Dupire model reverse option, 320 reversing pair, 319 Rho, 79 rho, 432 risk, 1-2, 8, 9 diversifiable, 8-9 purity of, 9 risk neutral, 19 risk premium, 46, 60, 64, 111, 119,432 risk-neutral distribution, 64 risk-neutral density as second derivative of call price, 137 in Black-Scholes world, 139 risk-neutral expectation, 64 risk-neutral measure, 148, 432 completeness, 166 existence of, 129 uniqueness, 166 risk-neutral pricing, 64 65, 140 higher-dimensional, 267-271 risk-neutral probability, 47, 52, 54, 59, 128 risk-neutral valuation, 59 in a one-step tree, 45-48 in a three-state model, 50 in jump models, 86 two-step model, 52 riskless, 1 riskless asset, 28 Rogers method for upper bounds by Monte Carlo, 295, 350 sample space, 458 self-financing portfolio, 28, 116-117, 128, 163, 369 dynamic, 28 share, 6-7, 432 share split, 57 short, 432 short rate, 25, 433 short selling, 21 simplex method, 295 skew, 433, 464 smile, 74-77 displaced-diffusion, 356,420 equity, 421 floating, 88, 385, 407, 413-414 foreign exchange, 413 FX, 424 interest-rate, 355-357, 424 jump-diffusion, 378, 415 sticky, 88, 413-414 sticky-delta, 413 538 smile (cont.) stochastic volatility, 398, 416 time dependence, 414-415 Variance Gamma, 406,417 smile dynamics Deiman-Kani, 420 displaced-diffusion, 420 Dupire model, 420 equity, 421 FX, 424 interest-rate, 424 jump-diffusion, 415 market, 413-415 model, 415-421 stochastic volatility, 416 Variance Gamma, 417 smoothing operator, 120 spectral theory, 228 speculator, 12, 18 split share, see share split spot price, 31 square root of a matrix, 467 standard error, 191 standard deviation, 463 static replication, see replication, static stepping methods for Monte Carlo, 439 stochastic, 433 stochastic calculus, 97 stochastic differential equation, 105 for square of Brownian motion, 107 stochastic process, 102-106, 141 stochastic volatility, 88, 389 and risk-neutral pricing, 390-393 implied, 400 pricing by Monte Carlo, 391-394 pricing by PDE and transform methods, 395-398 stochastic volatility smiles, see smile, stochastic volatility stock, 6-7, 433 stop loss hedging strategy, 18 stopping time, 143, 286, 346 straddle, 182, 257 Index lower bound via local optimization, 347 lower bounds by BGM, 345-349 pricing by BGM, 325 upper bounds by BGM, 349-352 cash-settled, 327 European, 310 price of, 313-314 payer's, 309,432 pricing by BGM, 323 receiver's, 309, 432 swaptions rapid approximation to price in a BGM model, 340 Taylor's theorem, 67, 80, 108 term structure of implied volatilities, 334 terminal decorrelation, 339, 352 Theta, 79, 433 and static replication, 246, 248 time homogeneity, 33, 333 time value of money, 24-26 time-dependent volatility and pricing of multi-look options, 235 Tower Law, 155 trading volatility, see volatility, trading of trading volume, 401 transaction costs, 21, 76, 90, 91 trapezium method, 188 tree with multiple time steps, 50-55 and pricing of European options, 183-186 and time-dependent volatility, 184 approximating a log-normal model, 60-68 approximating a normal model, 55-58 higher-dimensional, 277-280 non-recombining, 184 one-step, 44-50 risk-neutral behaviour, 61 trinomial, 184 with interest rates, 58-59 trigger FRA, 318 trigger swap, 325 pricing by BGM, 325 trinomial tree, see tree, trinomial strike, 10, 433 strong static replication, see replication, static, strong sub-replication, 369-375 super-replication, 369-375 swap, 300, 305-309, 433 constant maturity, 328 payer's, 306, 432 pricing by BGM, 323 receiver's, 306, 432 value of, 308 swap rate, 433 swap-rate market model, 340 swaption, 301, 309, 433 Bermudan, 301, 310, 342 and factor reduction, 352-355 lower bound via global optimization, 347 underlying, 10 uniform distribution, 461 valuation risk-neutral, see risk-neutral valuation value at risk, 433 Vanna, 433 VAR, 433 variance, 433, 463 Variance Gamma mean rate, 402 variance rate, 403 Variance Gamma density, 408 Variance Gamma model, 88, 404-407 and deterministic future smiles, 244 Variance Gamma process, 401-403 Index variation, 157, 367 first, 99, 367, 409 quadratic, 368 second, see variation, quadratic Vega, 79, 82, 433 integral expression for, 189 Vega hedging, see hedging, Vega volatility, 60, 65, 66, 73-74, 111 Black-Scholes formula as linear function of, 66 forward, 426 implied, 73, 197 instantaneous curve, 320, 333 539 root-mean-square, 320 time-dependence and tree-pricing, 294 trading of, 73 volatility surface, 363 weak static replication, see replication, static, weak Wiener measure, 141, 142 yield, 5, 24, 433 annualized, 25 yield curve, 319, 433 zero-coupon bond, see bond, zero-coupon 

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Exercise 4.5 A portfolio consisting of a short position in a call option and a long position in a stock is Delta-neutral. Suppose the stock price jumps; how will the value of the portfolio change if the option is priced according to the Black-Scholes formula before and after the jump? Exercise 4.6 Derive simple approximations for at-the-money Vega and Theta. Exercise 4.7 Show that call and put options with the same strike and expiry have the same Vega. Do this without using the Black-Scholes formula. Practicalities 92 Exercise 4.8 In the Black-Scholes model, we have the following parameters: S 100 K 110 r 0.05 sigma 0.1 Ti For a call option, we have value Delta Vega Gamma 2.174 0.343 36.78 0.0367 Find the value, Delta, Vega and Gamma of a put option with the same strike.

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Using the solution of the SDE for a Brownian motion with drift, this is equal to the probability that Soe(' +a212)T+a,ITN(o,1) > K. (6.114) A straightforward computation gives us the first term in the Black-Scholes formula. Risk neutrality and martingale measures 170 To get the second term in the Black-Scholes formula, it is easier to use B as numeraire. Note that this neatly explains the division of the Black-Scholes formula into two terms with coefficients So and e-',T K. Note also that the computation of the first term is made substantially easier by the use of the correct numeraire. O For each complete market, we now have multiple martingales measure each one associated to a choice of numeraire.

Monte Carlo Simulation and Finance
by Don L. McLeish
Published 1 Apr 2005

Then since ln(ZT /Z0 ) has a N ((c − σ2 )T, σ2 T ) distribution 2 we could use the Black-Scholes formula to determine the conditional expected value 268 CHAPTER 5. SIMULATING THE VALUE OF OPTIONS Z E0 [exp{− T rt dt}(ZT − K)+ |rs , 0 < s < T ] (5.18) 0 = EE0 [(S0 e(c−r)T eW − e−rT K)+ |rs , 0 < s < T ], where W has a N (−σ2 T /2, σ 2 T ) (c−r)T = E[BS(S0 e 1 , K, r, T, σ)], with r = T Z 0 Here, r is the average interest rate over the period and the function BS is the Black-Scholes formula (5.2). In other words by replacing the interest rate by its average over the period and the initial value of the stock by S0 e(c−r)T , the Black-Scholes formula provides the value for an option on an asset driven by (5.17) conditional on the value of r.

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The mean is approximately 0 and variance approximately σ 2 when we choose c = −.42278 and ν = .80308/σ and so this distribution is analogous to the 154 CHAPTER 3. BASIC MONTE CARLO METHODS standard normal. However, the skewness is −0.78 and this negative skewness is more typical of risk neutral distributions of stock returns. We might ask whether the Black-Scholes formula is as robust to the introduction of skewness in the returns distribution as to the somewhat heavier tails of the logistic distribution. For comparison with the Black-Scholes model we permitted adding a constant and multiplying the returns by a constant which, in this case, is equivalent to assuming under the risk neutral distribution that ST = S0 eα Y ν , Y is Gamma(2,1) where the constants α and ν are chosen so that the martingale condition is satisfied and the variance of returns matches that in the lognormal case.

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It should be noted that the practice of obtaining implied volatility parameters from options with similar strike prices and maturities is a partial, though not a compete, remedy to the substantial pricing errors caused by using a formula derived from a frequently ill-fitting GENERATING RANDOM NUMBERS FROM NON-UNIFORM CONTINUOUS DISTRIBUTIONS155 Figure 3.17: Relative Error in Black-Scholes formula when Asset returns follow extreme value Black_Scholes model. The Symmetric Stable Laws A final family of distributions of increasing importance in modelling is the stable family of distributions. The stable cumulative distribution functions F are such that if two random variables X1 and X2 are independent with cumulative distribution function F (x) then so too does the sum X1 + X2 after a change in location and scale.

Mathematical Finance: Core Theory, Problems and Statistical Algorithms
by Nikolai Dokuchaev
Published 24 Apr 2007

Then HBS,c(x, K, σ, T, r)=xΦ(d+)−Ke−rTΦ(d−), HBS,p(x, K, σ, T, r)=HBS,c(x, K, σ, T, r)−x+Ke−rT, (5.18) where and where (5.19) This is the celebrated Black-Scholes formula. Note that the formula for put follows from the formula for call from the put-call parity (Corollary 5.51). Numerical calculation via the Black-Scholes formula MATLAB code for Φ(·) function[f]=Phi(x) N=400; eps=abs(x+4)/N; f=0; pi=3.1415; for k=1:N; y=x-eps*(k-1); f=f+eps/sqrt(2*pi)*exp(-y^2/2); end; Here N=400 is the number of steps of integration that defines preciseness. One can try different N=10, 20, 100,…. (See also the MATLAB erf function.) © 2007 Nikolai Dokuchaev Mathematical Finance 96 MATLAB code for Black-Scholes formula (call) function[x]=call(x, K, v, T, r) x=max(0, s-K); if T>0.001 d=(log(s/K)+T*(r+v^2/2))/v/sqrt(T); d1=d-v*sqrt(T); x=s*Phi(d)-K*exp(-r*T)*Phi(dl); end; MATLAB code for Black-Scholes formula (put) function[x]=put(x,K,v,T,r) x=call(x,K,v,T,r)-s+K*exp(-r*T); end; Problem 5.57 Assume that r=0.05, σ=0.07, S(0)=1.

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) © 2007 Nikolai Dokuchaev Mathematical Finance 96 MATLAB code for Black-Scholes formula (call) function[x]=call(x, K, v, T, r) x=max(0, s-K); if T>0.001 d=(log(s/K)+T*(r+v^2/2))/v/sqrt(T); d1=d-v*sqrt(T); x=s*Phi(d)-K*exp(-r*T)*Phi(dl); end; MATLAB code for Black-Scholes formula (put) function[x]=put(x,K,v,T,r) x=call(x,K,v,T,r)-s+K*exp(-r*T); end; Problem 5.57 Assume that r=0.05, σ=0.07, S(0)=1. Write a code and calculate the Black-Scholes price of the call option with the strike price K=2 for three months. (Hint: three-month term corresponds to T=1/4.) 5.10 Dynamic option price process In this section, we consider again the Black-Scholes model with non-random volatility σ and non-random risk-free interest rate r. Definition 5.58 The fair price of the option at time t is the minimal random variable (the initial wealth) X(t) such that there exists an admissible self-financing strategy X(T)≥ψ a.s.

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MATLAB code for the price of an option with payoff F(x)=1+cos(x) function [f]=option(s,r,T,v) N=800; eps=0.01; f=0; pi=3.1415; for k=1:800; x=-4+eps*(k-1); f=f+eps/sqrt(2*pi*T) *exp(-x^2/(2*T))*(1+cos(s*exp((r-v^2/2)*T+v*x))); end; f=exp(-r*T)*f; © 2007 Nikolai Dokuchaev Continuous Time Market Models 95 Problem 5.56 (i) Write your own code for calculation of the fair price for payoff F(S(T)) where F(x)=|sin(4x)|ex. (ii) Let (S(0), T, σ, r)=(2, 1, 0.2, 0.07). Find the option price with payoff F(S(T)). 5.9.5 Black-Scholes formula We saw already that the fair option price (Black-Scholes price) can be calculated explicitly for some cases. The corresponding explicit formula for the price of European put and call options is called the Black—Scholes formula. Let K>0, σ>0, r≥0, and T>0 be given. We shall consider two types of options: call and put, with payoff function ψ where ψ=(S(T)−K)+ or ψ=(K−S(T))+, respectively. Here K is the strike price.

Frequently Asked Questions in Quantitative Finance
by Paul Wilmott
Published 3 Jan 2007

First let me reassure you that you won’t theoretically lose money in either case (or even if you hedge using a volatility somewhere in the 20 to 40 range) as long as you are right about the 40% and you hedge continuously. There will however be a big impact on your P&L depending on which volatility you input. If you use the actual volatility of 40% then you are guaranteed to make a profit that is the difference between the Black-Scholes formula using 40% and the Black- Scholes formula using 20%. V(S,t;σ) - V(S,t;σ̃), where V(S,t;σ) is the Black-Scholes formula for the call option and σ denotes actual volatility and σ̃ is implied volatility. That profit is realized in a stochastic manner, so that on a marked-to-market basis your profit will be random each day. This is not immediately obvious, nevertheless it is the case that each day you make a random profit or loss, both equally likely, but by expiration your total profit is a guaranteed number that was known at the outset.

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There is a difference between the square of the stock price moves and its average value and this gives rise to hedging error, something that is always seen in practice. If you hedge discretely, as you must, then Black-Scholes only works on average. But as you hedge more and more frequently, going to the limit δt = 0, then the total hedging error tends to zero, so justifying the Black-Scholes model. References and Further Reading Andreason, J, Jensen, B & Poulsen, R 1998 Eight Valuation Methods in Financial Mathematics: The Black-Scholes Formula as an Example. Math. Scientist 23 18-40 Black, F & Scholes, M 1973 The pricing of options and corporate liabilities. Journal of Political Economy 81 637-59 Cox, J & Rubinstein, M 1985 Options Markets. Prentice-Hall Derman, E & Kani, I 1994 Riding on a smile.

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The only reason why this is not exactly a Black-Scholes world is because we are hedging at discrete time intervals. The Black-Scholes models prices in the expected value of this expression. You will recognize the from the Black-Scholes equation. So the hedging error is simply This is how much you make or lose between each rebalancing. We can make several important observations about hedging error. • It is large: it is O(δt) which is the same order of magnitude as all other terms in the Black-Scholes model. It is usually much bigger than interest received on the hedged option portfolio • On average it is zero: hedging errors balance out • It is path dependent: the larger gamma, the larger the hedging errors • The total hedging error has standard deviation of total hedging error is your final error when you get to expiration.

My Life as a Quant: Reflections on Physics and Finance
by Emanuel Derman
Published 1 Jan 2004

At first it looked only mildly interesting, a peculiar anomaly we could tolerate. Then, when I thought about it a little more, I realized that the existence of the smile was completely at odds with Black and Scholes's twenty-year-old foundation of options theory. And, if the Black-Scholes formula was wrong, then so was the predicted sensitivity of an option's price to movements in its underlying index, its so-called "delta." In this case, all traders using the Black-Scholes model's delta were hedging their option books incorrectly. But the very essence of Black-Scholes was its prescription for replicating and hedging. The smile, therefore, poked a small hole deep into the dike of theory that sheltered options trading.

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This tentlike surface was a challenge to theorists everywhere. The Black-Scholes model couldn't account for it. Black-Scholes attributed a single volatility at all future times to an index or a stock, and therefore always produced the dull, flat, featureless surface of Figure 14.3a. The best you could do, if you modified the Black-Scholes model to allow future index volatility to be different from today's, was to obtain a surface that slanted in the time direction, as depicted in Figure 14.3b. But the variation in two perpendicular directions, time and strike, was a puzzle. What was wrong with the classic Black-Scholes model? And what new kind of model could possibly explain that surface?

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It is far too easy, in the name of realism, to add complexity to the simple evolution of stock prices assumed by Black and Scholes, but complexity without calibration is pointless. Figure 14.3 Implied volatility surfaces. (a) In the standard Black-Scholes model. (b) In an enhanced Black-Scholes model where volatility varies with time to expiration. Figure 14.4 Simple diffusion in the Black-Scholes model. The shaded regions illustrate the range of possible future prices for a stock whose price is $100 today. The more time passes, the greater the uncertainty in the future price. The darker the shading, the more likely the price will be in that region.

The Rise of the Quants: Marschak, Sharpe, Black, Scholes and Merton
by Colin Read
Published 16 Jul 2012

Through his clever mathematical construct, Merton was able to relax some of the strongest assumptions that offended those most critical of the Black-Scholes formula. Consequently, he was able to increase the generality of the Black-Scholes formula. He demonstrated that dividends and early calls could also be accommodated by his enveloping portfolio. He managed to show that this enveloping portfolio was smooth and hence the differential equation for the enveloping portfolio could be solved. In fact, this enveloping portfolio of an option for an underlying stock that may exhibit jumps and dividends nonetheless follows the same differential equation defined by Black. Merton demonstrated that the Black-Scholes formula is accurate, even if the option may need to be continuously rebalanced at each point in time to accommodate jumps or ex-dividend repricing. 156 The Rise of the Quants We might imagine that there could be great profits to be had if Black, Scholes, and Merton kept their equation secret and started their own investment firm.

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Other Greeks include the vega , the sensitivity of the option price to a one percentage point change in measured volatility, the theta τ, which gives the effect of a one-day reduction in the time until expiration on the option price, and the rho , which gives the effect on the option price for a one percentage point change in the risk-free rate of return. These measures offer financial analysts a language to compare and describe option price dynamics. Of course, they all depend on acceptance of the underlying Black-Scholes model. Subsequent to the publication of the Black-Scholes model, but before the many variants that followed, Stephen A. Ross published in 1976 an entirely different approach to pricing called arbitrage pricing theory (APT). His model will be discussed in greater detail within the context of the efficient market hypothesis in the next volume of this series.

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They were left with the Black-Scholes equation: C(S,t) = SN(d1 ) − Ke− r (t ∗ −t) N(d 2 ) where K is the strike price, d1 ⫽ (ln(S/C) ⫹ (t*⫺t)(r ⫹ v2/2))/(r(t*⫺t)1/2), d2 ⫽ d1 ⫺ v(t*⫺t)1/2, t* is the expiration date, and the optimal hedge ␦C/␦S is simply N(d1). As in Spreckle’s solution and, for that matter, Bachelier’s derivation 70 years earlier, N(d) is the normalized cumulative probability distribution function. Alternative derivations of the Black-Scholes formula Black and Scholes had made a few implicit assumptions in their analysis. First, they assumed that the number of shares outstanding does not change before the settlement date. If so, this would dilute the price of the stock and affect the option price. Similarly, they assumed that no dividends are paid and that the stock evolution follows a log-normal random walk with a constant drift and volatility.

Derivatives Markets
by David Goldenberg
Published 2 Mar 2016

With one more step, we will be in the very fortunate position of being able to simply repeat the European call option calculations we did for shifted ABM without drift, in order to generate the European call option formula for GBM, another name for which is the Black–Scholes formula. This approach unifies the Bachelier model with the Black–Scholes model. This unity shouldn’t be too surprising because GBM is a scaled, exponentiated ABM and, therefore, the ultimate driver of uncertainty in the Black–Scholes model is the ABM. 16.7.2 Preliminaries on Generating Unknown Risk-Neutral Transition Density Functions from Known Ones The derivation is a general result, and is significantly easier if we write down the relationship between the risk-neutral transition density function of the risk-neutralized GBM process and the the risk-neutral transition density function of the shifted ABM to which it is reducible, where the ‘reducing function’ is The risk-neutral transition density function for the shifted ABM reduced process is, The risk-neutral transition density function for the risk-neutralized GBM process will be denoted by pY(T,y;0,Y0), because Yt is the risk-neutralized GBM, where of course y is short form for YT(ω), the random outcome of the YT process at time T.

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The idea behind implied volatility is that the Black–Scholes formula embodies an implicit volatility estimator. If we compare market option prices to Black–Scholes model option prices, we can extract the Black–Scholes implicit volatility estimator. Since option prices incorporate a wide variety of forward views of volatility, implied volatility could be a better estimator of unknown volatility than the historical estimator, which is a backward looking estimator. B. The Implied Volatility Estimator Method Volatility is one of the key parameters in the Black–Scholes formula, but it is unobservable. Why not let the model generate estimates of σ that are consistent with the assumption that the market prices options using the Black–Scholes formula?

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Therefore (GBM 16) is equal to, Now all we have to do is to calculate, This is the definition of d1 in the Black–Scholes formula, where we again used the fact that, Hence, This completes the derivation of the integral in GBM (8a). To get the full European call option price, we have to remember to discount by B(0,T). When we do so, we obtain that our entire European call option formula reduces to, Therefore, the Black–Scholes formula is given by, N(di) is the cumulative normal distribution up to di, i=1,2. Recall that Y0=S0, the initial (t=0) stock price. In the usual Black–Scholes formula, the variable τ=T–t is involved and the formula is given by (Yt=St, the initial (time t) stock price), N(di) is the cumulative normal distribution up to di, i=1,2.

Risk Management in Trading
by Davis Edwards
Published 10 Jul 2014

Using calculus terminology, the delta of an option is the first derivative of the value—the straight line tangent to the curve at a specific point. 207 $25.00 $20.00 $20.00 Price of Underlying Asset $1 10 $1 15 $1 20 $1 05 5 $1 00 0 $9 $8 0 $1 10 $1 15 $1 20 $1 05 $9 $9 5 $1 00 $0.00 0 $0.00 5 $5.00 0 $5.00 $8 Tangent at $100 $10.00 5 $10.00 Tangent at $85 $15.00 $9 $15.00 $8 Option Price $25.00 $8 Option Price Options, Greeks, and Non-Linear Risks Price of Underlying Asset $25.00 Strike Option Price $20.00 Tangent at $115 $15.00 $10.00 $5.00 0 $9 5 $1 00 $1 05 $1 10 $1 15 $1 20 $9 5 $8 $8 0 $0.00 Price of Underlying Asset FIGURE 8.3 Linear Approximations of Option Value BLACK SCHOLES FORMULA A tremendous amount of academic thought has gone into how to correctly price various types of options. Even so, most of that research focuses on unusual or exotic options—exceptional options that are rarely traded. A large majority of options can be valued with a variant of a single formula, called the Black Scholes Formula. Even in cases where Black Scholes can’t appropriately price an option, the intuition behind Black Scholes is often still useful from a risk management perspective. The original Black Scholes model was published in 1973 for non‐dividend paying stocks.

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This is another assumption to simplify the creation of the model. Some of the more common variations of the Black Scholes Formula are: 1. Black Scholes (Stocks without dividends). In the original Black Scholes model, the underlying asset is a common stock that doesn’t pay dividends. Stock is an instrument that is traded at its present value. For an option model, the stock price starts at its present value (a spot price) and its end point is randomly distributed around the present value inflated at the risk‐free rate. 2. Merton (Stocks with continuous dividend yield). The Merton model extends the Black Scholes model by assuming that a dividend is continuously paid to shareholders.

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The original Black Scholes model was published in 1973 for non‐dividend paying stocks. A variety of extensions to the original Black Scholes model have been developed. Collectively, these are referred to as Black Scholes genre option models. The extensions to the Black Scholes formula allow the same mathematical framework to value other financial instruments like dividend paying stocks, commodity futures, and foreign exchange (FX) forwards. The primary difference between these models is how the underlying asset is present valued. Black Scholes genre option models make a number of simplifying assumptions about how financial markets operate. These assumptions are 208 RISK MANAGEMENT IN TRADING made in order to enable an easy‐to‐use framework suitable for pricing a wide variety of options.

A Primer for the Mathematics of Financial Engineering
by Dan Stefanica
Published 4 Apr 2008

Implementation of the Black-Scholes formula. 0(8, t) The Black-Scholes formula P(8, t) The Black-Scholes formulas give the price of plain vanilla European call and 4 put options, under the assumption that the price of the underlying asset ~as lognormal distribution. A detailed discussion of the lognormal assumptlOn can be found in section 4.6. To introduce the Black-Scholes formula, it is enough to assume that, for 1 1 . tl < t , t h e rand om vana . ble S(t2)' any values of tl and t2 WIth S(tl) IS ognorma 2 with parameters (J-L - q - 95 The Black-Scholes Formulas for European Call and Put Options: The Greeks of plain vanilla European call and put options. 3.5 3.5.

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Yield, Duration, Convexity . . 2.7.1 Zero Coupon Bonds. . . . . . . 2.8 Numerical implementation of bond mathematics 2.9 References 2.10 Exercises . 3 Probability concepts. Black-Scholes formula. Greeks and Hedging. 3.1 Discrete probability concepts. . . . . . . . . 3.2 Continuous probability concepts. . . . . . . 3.2.1 Variance, covariance, and correlation 3.3 The standard normal variable 3.4 Normal random variables . . . 3.5 The Black-Scholes formula. . 3.6 The Greeks of European options. 3.6.1 Explaining the magic of Greeks computations 3.6.2 Implied volatility . . . . . . . . . . . . 3.7 The concept of hedging. ~- and r-hedging . 3.8 Implementation of the Black-Scholes formula. 3.9 References 3.10 Exercises. . . . . . . . . . . . . . . . . . . . 4 45 45 48 51 52 56 58 62 64 66 66 67 69 72 73 77 78 81 81 83 85 89 91 94 97 99 103 105 108 110 111 Lognormal variables.

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h(x) = 93 FINANCIAL APPLICATIONS The Black-Scholes formula. CHAPTER 3. PROBABILITY. BLACK-SCHOLES FORMULA. 94 Assume that the price of the underlying asset has lognormal distribution and volatility a, that the asset pays dividends continuously at the rate q, and that the risk-free interest rate is constant and equal to r. Let C (S, t) be the value at time t of a call option with strike K and maturity T, and let P(S, t) be the value at time t of a put option with strike K and maturity T. Then, Implied volatility. The concept of hedging. ~-hedging and r-hedging for options. Implementation of the Black-Scholes formula. 0(8, t) The Black-Scholes formula P(8, t) The Black-Scholes formulas give the price of plain vanilla European call and 4 put options, under the assumption that the price of the underlying asset ~as lognormal distribution.

Mathematics for Finance: An Introduction to Financial Engineering
by Marek Capinski and Tomasz Zastawniak
Published 6 Jul 2003

Proposition 9.1 Denote the European call option price in the Black–Scholes model by C E (S). The delta of the option is given by d E C (S) = N (d1 ), dS where N (x) is the normal distribution function given by (8.10) and d1 is defined by (8.9). Proof The price S = S(0) appears in three places in the Black–Scholes formula, see Theorem 8.6, so the differentiation requires a bit of work, with plenty of nice cancellations in due course, and is left to the reader. Bear in mind that the d C E (S) is computed at time t = 0. derivative dS Exercise 9.1 Find a similar expression for the delta in the Black–Scholes model. d E dS P (S) of a European put option For the remainder of this section we shall consider a European call option within the Black–Scholes model.

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Option Pricing 189 with   1 2 ln S(0) (T − t) X + r + 2σ √ d1 = , σ T −t   1 2 ln S(0) (T − t) X + r − 2σ √ d2 = . (8.11) σ T −t Exercise 8.15 Derive the Black–Scholes formula P E (t) = Xe−r(T −t) N (−d2 ) − S(t)N (−d1 ), with d1 and d2 given by (8.11), for the price of a European put with strike X and exercise time T . Remark 8.2 Observe that the Black–Scholes formula contains no m. It is a property analogous to that in Remark 8.1, and of similar practical significance: There is no need to know m to work out the price of a European call or put option in continuous time. It is interesting to compare the Black–Scholes formula for the price of a European call with the Cox–Ross–Rubinstein formula.

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d E dS P (S) of a European put option For the remainder of this section we shall consider a European call option within the Black–Scholes model. By Proposition 9.1 the portfolio (x, y, z) = (N (d1 ), y, −1), where the position in stock N (d1 ) is computed for the initial stock price S = S(0), has delta equal to zero for any money market position y. Consequently, its value V (S) = N (d1 )S + y − C E (S) does not vary much under small changes of the stock price about the initial value. It is convenient to choose y so that the initial value of the portfolio is equal to zero. By the Black–Scholes formula for C E (S) this gives y = −Xe−T r N (d2 ), 194 Mathematics for Finance with d2 is given by (8.9).

Models. Behaving. Badly.: Why Confusing Illusion With Reality Can Lead to Disaster, on Wall Street and in Life
by Emanuel Derman
Published 13 Oct 2011

The value of the option is the total cost of its manufacture, the cost of all the required trading with borrowed money. The Black-Scholes formula explains how the option value—the estimated cost of trading— depends on the stock price, the interest charged for borrowing, and the riskiness of the stock itself. Just as a weather model makes assumptions about how fluids flow and how heat undergoes convection, just as a soufflé recipe makes assumptions about what happens when you whip egg whites, so the Black-Scholes Model makes assumptions about the riskiness of stock prices, that is, about how stock prices fluctuate. Black-Scholes assumes that stock prices move smoothly but randomly with a definite volatility, a fixed degree of fluctuation.

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In physics the values of the fundamental constants (the gravitational constant G, the electric charge e, Planck’s constant h, the speed of light c) are apparently timeless and universal. I doubt there will ever be a universal value for the risk premium. THE EMM AND THE BLACK-SCHOLES MODEL The best model in all of economics is the Black-Scholes Model for valuing options on stocks, an ingeniously clever extension of the EMM published in 1973 by Fischer Black and Myron Scholes.a I spent my first two years at Goldman Sachs, 1986–1987, working with Fischer Black on an extension of this model to valuing options on bonds,12 and I devoted 1993–1994 to working on an extension of Black-Scholes to stocks with variable volatility.

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Furthermore, because the option must at all times have the same risk premium as the stock, you can replace the option at any instant by an equivalent investment in stock. The Black-Scholes Model tells you exactly how much stock you need to replicate the option’s risk at any instant, and thus, if you know the stock price, what the option is worth at any instant. It’s like a recipe that tells you how to make fruit salad (an option) out of fruit (stocks and bonds) and hence, by the Law of One Price, what the fruit salad is worth. Before Black and Scholes and Merton no one had even guessed that you could manufacture an option out of simpler ingredients. Anyone’s guess for its value was as good as anyone else’s; it was strictly personal. The Black-Scholes Model, even more than the EMM that engendered it, revolutionized modern finance.

Mathematical Finance: Theory, Modeling, Implementation
by Christian Fries
Published 9 Sep 2007

Thus many techniques that are known from the modeling of (also one dimensional) stock price processes may be used out of the box (e.g. finite difference implementations). Depending on the specific model (i.e. the form of µQ and σ) analytic formulas for bond prices or simple European interest rate options may be derived, similar to the Black-Scholes formula for european stock options under a Black-Scholes model. Instead of specifying the model (20.1) of the short process under the real measure P and applying the measure transformation to Q, is is usual to specify the model (20.2) directly under Q and calibrate given model parameters. 20.2. The Market Price of Risk We consider the bond with maturity T .

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S (t) S (T ) Using the functional representation of S we find that P(T ; t) is represented as a functional of x(t) too, namely (t, ξ) 7→ P(T ; t) with P(T ; t, ξ) 1 = EQ ( | {x(t) = ξ}). S (t, ξ) S (T, x(T )) (23.3) 23.2.2. Example: The Black-Scholes Model Let us assume a Markovian driver with constant instantaneous volatility σ(t) = σ. For the Black-Scholes Model we have 1 σBS
S (t, ξ) = S (0) · exp r · t + σ2BS t + ·ξ , 2 σ (23.4) where σBS denotes the (constant) Black-Scholes volatility. Plugging this into (23.3) we find P(T ; t, ξ) = exp(−r(T − t)), so interest rates are indeed deterministic here. This is indeed the Black-Scholes model: From the definition of the Markovian driver we have that σ1 · x(t) = W(t) and thus
1 S (t, x(t)) = S (0) · exp r · t + σ2BS t + σBS · W(t) . 2 In other words the Q dynamics of S is1 dS (t) = rS (t)dt + σ2BS S (t)dt + σBS S (t) · dW Q (t).

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Example: Finite Differences applied to Smooth and Discontinuous Payout . . . . . . . . . . . . . . . . . . . . . . . . . 15.5. Sensitivities by Pathwise Differentiation . . . . . . . . . . . . . . . . 15.5.1. Example: Delta of a European Option under a Black-Scholes Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.5.2. Pathwise Differentiation for Discontinuous Payouts . . . . . . 15.6. Sensitivities by Likelihood Ratio Weighting . . . . . . . . . . . . . . 15.6.1. Example: Delta of a European Option under a Black-Scholes Model using Pathwise Derivative . . . . . . . . . . . . . . . 15.6.2. Example: Variance Increase of the Sensitivity when using Likelihood Ratio Method for Smooth Payouts . . . . . . . . . 15.7.

Tools for Computational Finance
by Rüdiger Seydel
Published 2 Jan 2002

These may be elementary evaluations of functions like the logarithm or the square root such as in the Black-Scholes formula, or may consist of a subalgorithm like Newton’s method for zero finding. There is hardly a purely analytic method. The finite-difference approach, which approximates the surface V (S, t), requires intermediate values for 0 < t < T for the purpose of approximating V (S, 0). In the financial practice one is basically interested in V (S, 0) only, intermediate values are rarely asked for. So the only temporal input parameter is the time to maturity T − t (or T in case the current time is set to zero, t = 0). Recall that also in the Black-Scholes formula, time only enters in the form T − t (−→ Appendix A4).

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So it makes sense to write the formula in terms of the time to maturity τ , τ := T − t , which leads to the compact version of the Black-Scholes formulas (A4.10), 4.8 Analytic Methods   1 S √ + r+ log K σ τ   1 S + r− d2 (S, τ ; K, r, σ) := √ log K σ τ d1 (S, τ ; K, r, σ) :=  # σ2 τ 2  # σ2 τ 2 167 (4.40) VPeur (S, τ ; K, r, σ) = −SF (−d1 ) + Ke−rτ F (−d2 ) VCeur (S, τ ; K, r, σ) = SF (d1 ) − Ke−rτ F (d2 ) (dividend-free case). F denotes the cumulated standard normal distribution function. For dividend-free options we only need an approximation formula for the American put VPam ; the other cases are covered by the Black-Scholes formula. This Section introduces into four analytic methods.

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An immediate candidate for the lower bound V low is the value VPeur provided by the Black-Scholes formula. Thus, VPeur (S, τ ; K) ≤ VPam (S, τ ; K) ≤ VPam (S, τ ; Kerτ ) The latter of the inequalities is the monotonicity with respect to the strike, see Appendix D1. Following [Mar78], an American put with strike Kerτ rising exponentially with τ at the risk-free rate is not exercised, so VPam (S, τ ; Kerτ ) = VPeur (S, τ ; Kerτ ) , 168 Chapter 4 Standard Methods for Standard Options which serves as upper bound. This allows to apply the Black-Scholes formula (4.40) to the European option and provides the upper bound to VPam (S, t; K).

Principles of Corporate Finance
by Richard A. Brealey , Stewart C. Myers and Franklin Allen
Published 15 Feb 2014

Risk and Option Values Summary Further Reading Problem Sets Finance on the Web 21 Valuing Options 21-1 A Simple Option-Valuation Model Why Discounted Cash Flow Won’t Work for Options/Constructing Option Equivalents from Common Stocks and Borrowing/Valuing the Apple Put Option 21-2 The Binomial Method for Valuing Options Example: The Two-Step Binomial Method/ The General Binomial Method/The Binomial Method and Decision Trees 21-3 The Black–Scholes Formula Using the Black–Scholes Formula/The Risk of an Option/The Black–Scholes Formula and the Binomial Method 21-4 Black–Scholes in Action Executive Stock Options/Warrants/ Portfolio Insurance/Calculating Implied Volatilities 21-5 Option Values at a Glance 21-6 The Option Menagerie Summary Further Reading Problem Sets Finance on the Web Mini-Case: Bruce Honiball’s Invention 22 Real Options 22-1 The Value of Follow-On Investment Opportunities Questions and Answers about Blitzen’s Mark II/ Other Expansion Options 22-2 The Timing Option Valuing the Malted Herring Option/Optimal Timing for Real Estate Development 22-3 The Abandonment Option Bad News for the Perpetual Crusher/Abandonment Value and Project Life/Temporary Abandonment 22-4 Flexible Production and Procurement Aircraft Purchase Options 22-5 Investment in Pharmaceutical R&D 22-6 A Conceptual Problem?

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It also increases with the time to maturity and the stock’s variability To derive their formula Black and Scholes assumed that there is a continuum of stock prices, and therefore to replicate an option investors must continuously adjust their holding in the stock.12 Of course this is not literally possible, but even so the formula performs remarkably well in the real world, where stocks trade only intermittently and prices jump from one level to another. The Black–Scholes model has also proved very flexible; it can be adapted to value options on a variety of assets such as foreign currencies, bonds, and commodities. It is not surprising, therefore, that it has been extremely influential and has become the standard model for valuing options. Every day dealers on the options exchanges use this formula to make huge trades. These dealers are not for the most part trained in the formula’s mathematical derivation; they just use a computer or a specially programmed calculator to find the value of the option. Using the Black–Scholes Formula The Black–Scholes formula may look difficult, but it is very straightforward to apply.

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The formula is also more accurate and quicker to use than the binomial method. So why use the binomial method at all? The answer is that there are many circumstances in which you cannot use the Black–Scholes formula but the binomial method will still give you a good measure of the option’s value. We will look at several such cases in Section 21-5. 21-4 Black–Scholes in Action To illustrate the principles of option valuation, we focused on the example of Apple’s options. But financial managers turn to the Black–Scholes model to estimate the value of a variety of different options. Here are four examples. Executive Stock Options In fiscal year 2011 Larry Ellison, the CEO of Oracle Corporation, received a salary of $1 million, but he also pocketed another $63 million in the form of stock options.

Handbook of Modeling High-Frequency Data in Finance
by Frederi G. Viens , Maria C. Mariani and Ionut Florescu
Published 20 Dec 2011

See Section 9.2 of Ref. 1 for more details. We should mention that for the classical Black–Scholes model and for any other Black–Scholes models, such as models that take into account stochastic volatility, it follows that C(S, t) ∼ 0 when S ∼ 0 and C(S, t) ∼ S when S is very large. This observation will justify the boundary conditions we will be using later in this section. Namely, the boundary condition for the Black–Scholes model 355 13.2 Method of Upper and Lower Solutions with stochastic volatility should be the same boundary condition used for the classical Black–Scholes model whenever the spatial domain for S is bounded and very large. 13.2.2 A GENERAL SEMILINEAR PARABOLIC PROBLEM The generalized Black–Scholes model with stochastic volatility leads us to study a more general semilinear parabolic problem than the ones given by Equations 13.5 and 13.6.

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See also Maximum likelihood estimation (MLE) Index Bernoulli(p) distribution, 190 Bessel function, 9, 376 Bessel function of the third kind, modified, 166 Best practices, 51 Bias, 253–254 estimated, 258, 259 of the Fourier covariance estimator, 264–266 Bias-corrected estimator, 261 Bid/ask orders, 29 Bid-ask price behavior, 236 Bid-ask spreads, 228, 229, 236, 238–239, 240 Big values, asymptotic behavior for, 338 Binary prediction problems, 48 Black–Litterman model, 68 Black–Scholes analysis, 383–384 Black–Scholes equation, 352, 400 Black–Scholes formula, 114, 115 Black–Scholes model(s), 4, 6–7, 334 boundary condition for, 354–355 in financial mathematics, 352 with jumps, 375 option prices under, 219 volatility and, 400 Black–Scholes PDE, 348. See also Partial differential equation (PDE) methods Board balanced scorecards (BSCs), 51–52, 59. See also Balanced scorecards (BSCs) designing, 59 Board performance, quantifying, 52 Board strategy map, 59–60 Boosting, 47–74 adapting to finance problems, 68 applications of, 68–69 combining with decision tree learning, 49 as an interpretive tool, 67 Boundary value problem, 319, 320 Bounded parabolic domain, 352, 368 Bozdog, Dragos, xiii, 27, 97 Brownian motion, 78, 120, 220 BSC indicators, 52, 53.

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References 115 There are four steps in the construction of this VIX as follows: • Compute the implied volatilities of entire option chain on SP500 and construct an estimate for the distribution of current market volatility. The implied volatility is calculated by applying Black–Scholes formula. • Use this estimated distribution as input to the quadrinomial tree method. Obtain the price of an at-the-money synthetic option with exactly 30-day maturity. • Compute the implied volatility of the synthetic option based on Black–Scholes formula once the 30-day synthetic option is priced. • Obtain the estimated VIX by multiplying the implied volatility of the synthetic option by 100. Please note that the most important step in the estimation is the choice of proxy for the current stochastic volatility distribution.

Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues
by Alain Ruttiens
Published 24 Apr 2013

N(d2) is the probability that the option will be exercised at maturity, more precisely: the risk-neutral probability, under the assumptions of the Black–Scholes model. From Eq. 10.8 and Eq. 10.9 of the genuine Black–Scholes formula, it is easy to verify that, for a call, if S is K, d1, d2 and therefore N(d2) tend to 0 probability of exercising; if S is K, d1, d2 and therefore N(d2) tend to 1 probability of exercising; and conversely for a put. In particular, if that is, the “adjusted forward” price resulting from modeling S according to the Black–Scholes formula (cf. Eq. 8.14, in a risk-neutral world with μ being replaced by the risk-free rate r), Eq. 10.8 becomes: So that, for a strike equal to this “adjusted forward”, N(d2) = 0.5, that is a 50–50 chance that the option will be exercised.

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The moneyness measure is mainly used with respect to the option smile, as developed in Chapter 12, Section 12.1.3. 10.2.5 Beyond the Black–Scholes formula The Black–Scholes formula is an answer to the diffusion equation (cf. Eq. 10.6, for call options) leading to an option valuation subject to the very specific assumptions as set in Section 10.2.1. This formula, and its variants, is called an “analytical” solution to option pricing, since if suffices to replace the variables of the formula by their values relating to the option to be priced. Moreover, the fact remains that the analytic – also called “close form” or “closed-form” – Black–Scholes formula presents the advantage of allowing a straightforward calculation of options sensitivities (cf.

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Chapter 15, Section 15.1), whose sophistication is also synonymous of real difficulties to properly assess correct values to their ingredients. The Black–Scholes formula is applicable to European options only, and provided the underlying financial instrument offers no return during the lifetime of the option: for example, a stock delivering no dividend during such period, or any non-financial commodity. The hypotheses underlying the Black–Scholes formula are as follows: The underlying price is the only stochastic variable and is assumed to follow a geometric (general) Wiener process. This implies a constant drift and volatility of the underlying returns during the lifetime of the option.

In Pursuit of the Perfect Portfolio: The Stories, Voices, and Key Insights of the Pioneers Who Shaped the Way We Invest
by Andrew W. Lo and Stephen R. Foerster
Published 16 Aug 2021

A Black-Scholes–type model focuses on the solution of a particular pricing issue, such as the value of a call option, and requires specific assumptions, such as constant volatility of the underlying security and a constant interest rate, in order for it to be solved. The Black-Scholes model makes these assumptions in order to solve the pricing puzzle in “closed form” by applying mathematical equations. Thus, a model is an abstraction from reality, and a model’s estimates are measured with error, for example, the predicted value of call options. The performance of a model depends on the quality of its assumptions—if the volatility or interest rates change, for example, then the model’s predicted price of a call option will not be exact. Scholes explains that “a model … by definition has an error to it. So, people say the Black-Scholes model doesn’t work, but it depends on the assumptions and how good the assumptions are.”42 Derivatives technology, in contrast to the model, applies mathematical concepts in order to understand hypothetical relationships.

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By 1984, the CBOE was second only to the New York Stock Exchange in terms of the trading value of financial assets.61 Today the CBOE is the largest U.S. options exchange, offering options on individual equities as well as indexes such as the S&P 500, the most active U.S. index option.62 Many of the assumptions in the Black-Scholes model, such as zero trading costs and no restrictions on short selling, were originally unrealistic, but the world was starting to change, and commissions were soon about to dramatically fall. The Black-Scholes model had an almost immediate impact, hitting the emerging options market in its technological sweet spot. The model helped the exchange to overcome the stigma of options trading as gambling by legitimizing the practice as one related to efficient pricing and hedging.

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If not for his untimely death in 1995, Fischer Black would in all likelihood have been part of this esteemed group. The Formula Known everywhere simply as Black-Scholes, the Black-Scholes/Merton option pricing formula has been described by mathematician-author Ian Stewart as one of “17 equations that changed the world.”29 But what does the Black-Scholes formula actually tell us? This world-changing namesake formula describes the correct price of a call option, under certain assumptions. However, to fully understand this accomplishment, a little more explanation is needed. Just as stocks are securities—tradable financial instruments with monetary value—options are also securities.

The Ascent of Money: A Financial History of the World
by Niall Ferguson
Published 13 Nov 2007

Markowitz, a Chicago-trained economist at the Rand Corporation, in the early 1950s, and further developed in William Sharpe’s Capital Asset Pricing Model (CAPM).83 Long-Term made money by exploiting price discrepancies in multiple markets: in the fixed-rate residential mortgage market; in the US, Japanese and European government bond markets; in the more complex market for interest rate swapsbf - anywhere, in fact, where their models spotted a pricing anomaly, whereby two fundamentally identical assets or options had fractionally different prices. But the biggest bet the firm put on, and the one most obviously based on the Black-Scholes formula, was selling long-dated options on American and European stock markets; in other words giving other people options which they would exercise if there were big future stock price movements. The prices these options were fetching in 1998 implied, according to the Black-Scholes formula, an abnormally high future volatility of around 22 per cent per year. In the belief that volatility would actually move towards its recent average of 10-13 per cent, Long-Term piled these options high and sold them cheap.

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Part of the problem was precisely that LTCM’s extraterrestrial founders had come back down to Planet Earth with a bang. Remember the assumptions underlying the Black-Scholes formula? Markets are efficient, meaning that the movement of stock prices cannot be predicted; they are continuous, frictionless and completely liquid; and returns on stocks follow the normal, bell-curve distribution. Arguably, the more traders learned to employ the Black-Scholes formula, the more efficient financial markets would become.97 But, as John Maynard Keynes once observed, in a crisis ‘markets can remain irrational longer than you can remain solvent’.

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Beveridge Report 204-5 biases 316 bill brokers 299 bill-discounting banks 53 billets d’état 139 bills, commercial 54 bills of exchange (cambium per literas) 43-4 Birmingham & Midland 56 Bismarck, Otto von 202 Black, Fisher 320-22 black box see Black-Scholes model ‘Black’ days 164 black (or grey) economic zones 275 ‘Black Mondays’: 1929: 158 1987 see financial crises black people see African-American people Black-Scholes model (black box) 320-4 Blackstone 337 ‘black swans’ 342 ‘Black Thursday’ 158 Blain, Spencer H., Jr. 256-8 Blankfein, Lloyd 1-2 Bleichroeder (Arnhold & S.) 315 Bloch, Ivan 297 Bloomfield, Arthur 305 Blunt, John 155-6 BNP Paribas 272 Bolivia 2 Bolsheviks 107 bonds and bond markets 64 benefits of 3 bond insurance companies 347 boom 332 bundled mortgages see securitization collateral for 94 compared with mortgages (spread) 241-2 compared with stock markets 124-5 cotton-backed 94-6 crises and defaults 73 definitions 65-9 emerging market bonds see emerging markets face value (par) 73 future of 115-16 government see government bonds history 65-7 importance and power of 67-9 inflation and 105 insurance companies and 198 interest rates 67 liquidity 71 and mortgage rates 68 and pensions 67 perpetual bonds 76 Right- and Left-wing critics of 89-90 Rothschilds and 80-91 and savings institutions 116 and taxes 68 vulnerability of 99 war and 69-75 widening access to 100 bonds and bond markets - cont. and First World War 297 Bonn Consensus 312 bookkeeping 44-5 Borges, Jorge Luis 111 borrowing see credit; debt Boston 266 Botticelli, Sandro 42 ‘bottomry’ 185 Brady, Nicholas 165 Brailsford, Henry Noel 298 Brazil 18. see also BRICs Bretton Woods 305-8 Bretton Woods II 334 Briand, Aristide 159 BRICs (Brazil, Russia, India, China: Big Rapidly Industrializing Countries) 284 Britain: and American Civil War 94-5 banknotes 27 banks and industrialization 48-9 business failures 349 colonies see British Empire compared with France 141 compared with Japan 209-11 cost of living 26 cotton industry 94-6 East Indies trade 134; see also East India Company economy 210-11 finances for Napoleonic wars 80-84 financial ignorance 11-12 financial sector’s contribution to GDP 5 fiscal system 75 foreign investment 287 foreign investment in 76 Glorious Revolution 75-6 house prices and property ownership 10.

Capital Ideas: The Improbable Origins of Modern Wall Street
by Peter L. Bernstein
Published 19 Jun 2005

See also Diversification computer-based dart-board efficiency of market mean-variance analysis of optimal options risk trading variance volatility Portfolio insurance Black Monday and Portfolio management by bank trust departments economic policy and equity management and interior decorator approach to intertemporal capital asset pricing model for Ito’s lemma and Liquidity Preference theory of risk calculations “Portfolio Selection” (Markowitz) Portfolio Selection: Efficient Diversification of Investment (Markowitz) Positive sum theory Predictions of stock movement: see Forecasting, Market theories (general discussion) Price(s). See also Capital Asset Pricing Model; Random price fluctuations; specific types of securities arbitrage Black/Scholes formula of: see Black/Scholes formula earnings ratio efficient markets and future of growth stocks information and interest rates and intrinsic value and manipulation risk and security analysis and shadow transfer trends value differentiation zero downside limit on “Price Movements in Speculative Markets: Trends or Random Walks” (Alexander) “Pricing of Options and Corporate Liabilities, The” (Black/Scholes) Probability theory Procter & Gamble Profit maximization Program trading Prospective yield “Proposal for a Smog Tax, A” (Sharpe) Puts: see Options Railroads RAND Random Character of Stock Prices, The (Cootner) “Random Difference Series for Use in the Analysis of Time Series, A” (Working) Random price fluctuations/random walks selection of securities and “Random Walks in Stock Market Prices” (Fama) Rational Expectations Hypothesis “Rational Theory of Warrant Pricing” (Samuelson) Regulation of markets Return analysis: see Risk/return ratios Review of Economics and Statistics Review of Economic Studies, The “RHM Warrant and Low-Price Stock Survey, The” Risk arbitrage calculations diversification and dominant expected return and minimalization portfolio premium return ratios Rosenberg’s model stock prices and of stocks vs. bonds systematic (beta) trade-offs valuation of assets and “Risk and the Evaluation of Pension Fund Performance” (Fama) Risk-free assets Rosenberg Institutional Equity Management (RIEM) “Safety First and the Holding of Assets” (Roy) Samsonite Savings rates Scott Paper Securities analysis Securities and Exchange Commission Security Analysis (Graham/Dodd) Security selection Separation Theorem Shadow prices “Simplified Model for Portfolio Analysis, A” (Sharpe) Singer Manufacturing Company Single-index model Sloan School of Management Standard & Poor’s 500 index “State of the Art in Our Profession, The” (Vertin) Stock(s) cash ratios common expected return on growth income international legal restrictions on market value variance volatility Stock market (general discussion) Black Monday (October, 1987, crash) “Stock Market ‘Patterns’ and Financial Analysis” (Roberts) Supply and demand theory Swaps Tactical asset allocation theory Tampax Taxes.

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Scholes collaborated with Black to unlock the puzzles of option pricing. Their article on the subject was rejected at first as excessively specialized, but thanks to Merton Miller’s intervention it finally appeared just as the Chicago Board Options Exchange opened for business in 1973. The Black-Scholes formula was soon in general use there and has subsequently formed the basis for many investment, trading, and corporate finance strategies. (©1990 photography by Andy Feldman) In 1968, MIT was the only graduate school that would accept Robert Merton, now of Harvard Business School, when he decided to abandon math for economics.

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If the harvest is unexpectedly large, the olive grower will want to hedge against the possibility that he will have no access to the presses when his crop comes in. In light of all these considerations, how does an investor determine whether an option is cheap, expensive, or priced about right? The answer is to use the Black-Scholes formula. The investor knows the current prices of the stock and the option, the price at which the option can be exercised, the time to expiration, and the going rate of interest. With this information, the model will provide an estimate of the stock’s volatility that is implied in the price of the option.

The Quants
by Scott Patterson
Published 2 Feb 2010

In the early seventies, however, the appearance of the Black-Scholes model seemed propitious. A group of economists at the University of Chicago, led by free market guru Milton Friedman, were trying to establish an options exchange in the city. The breakthrough formula for pricing options spurred on their plans. On April 26, 1973, one month before the Black-Scholes paper appeared in print, the Chicago Board Options Exchange opened for business. And soon after, Texas Instruments introduced a handheld calculator that could price options using the Black-Scholes formula. With the creation and rapid adoption of the formula on Wall Street, the quant revolution had officially begun.

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He programmed the formula into his HP computer, and it quickly produced a graph showing the price of a stock option that closely matched the price spat out by his own formula. The Black-Scholes formula was destined to revolutionize Wall Street and usher in a wave of quants who would change the way the financial system worked forever. Just as Einstein’s discovery of relativity theory in 1905 would lead to a new way of understanding the universe, as well as the creation of the atomic bomb, the Black-Scholes formula dramatically altered the way people would view the vast world of money and investing. It would also give birth to its own destructive forces and pave the way to a series of financial catastrophes, culminating in an earthshaking collapse that erupted in August 2007.

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“I realized that the existence of the smile was completely at odds with Black and Scholes’s 20-year-old foundation of options theory,” wrote Emanuel Derman, a longtime financial engineer who worked alongside Fischer Black at Goldman Sachs, in his book My Life as a Quant. “And, if the Black-Scholes formula was wrong, then so was the predicted sensitivity of an option’s price to movements in its underlying index. … The smile, therefore, poked a small hole deep into the dike of theory that sheltered options trading.” Black Monday did more than that. It poked a hole not only in the Black-Scholes formula but in the foundations underlying the quantitative revolution itself. Stocks didn’t move in the tiny incremental ticks predicted by Brownian motion and the random walk theory.

The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street
by Justin Fox
Published 29 May 2009

But the eerie correctness of traded options prices after Black started his volatility service was something else. Black-Scholes wasn’t just predicting options prices. As the house formula of the brand-new options exchange, it was setting them. The Black-Scholes model had become a self-fulfilling prophecy. A basic assumption behind the Black-Scholes model—that stock prices follow a bell curve random walk—was, as already noted, not quite right. This did not in itself render Black-Scholes invalid. As Milton Friedman had argued two decades before, a successful scientific model is invariably “descriptively false in its assumptions.”

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After several years of this, Thorp got the notice in the mail that his secret formula was about to become public. It was a preprint of the Black-Scholes article, sent by Fischer Black, who professed in an introductory letter to be a “great admirer” of Thorp’s work. After some initial puzzlement, Thorp realized that the Black-Scholes formula was the same as his. Not long after that, the easy options money had mostly disappeared. But Thorp displayed an uncanny ability to keep finding new sources of profit—and get out of them before they stopped working. He was also willing to discuss his trades, at least after he’d made his money on them—something few of his black-box imitators have done since.

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After the 1987 crash, put options that were well out of the money (the stock was at $40, say, and the put allowed one to sell it for $10) traded at prices that, according to Black-Scholes, implied a similar crash every few years. Other options on the same stocks, though, continued to trade at prices that implied less extreme volatility. That was the smile—flat in the middle, rising at the edge. The Black-Scholes formula assumed that volatility would be constant, consistent, and normally distributed. That clearly wasn’t the case, and the search for better models of volatility was now on in earnest. One starting point was the statistical framework assembled twenty-five years before by Benoit Mandelbrot. Mandelbrot hadn’t predicted black Monday.

How I Became a Quant: Insights From 25 of Wall Street's Elite
by Richard R. Lindsey and Barry Schachter
Published 30 Jun 2007

He was also a perfectionist to the highest degree. We would write and rewrite chapters endlessly; and each new theorem we added seemed to inspire the need for new chapters. The book went from a proposed hundred-page set of lecture notes into a long, involved project.15 As I was learning about the Black-Scholes formula I was growing increasingly frustrated with the Ginzburg book project. I needed relief. I decided to take everything I was learning about options pricing and write a book on the subject. Now why would I do that? By working with Ginzburg, I had learned to take extremely complicated ideas and explain them clearly and concisely.

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In Toronto, I continued to work on the book with Ginzburg—which we had named Representation Theory and Complex Geometry—and work on mathematics research, but I also began to write a paper on options pricing. Thus, my career as a quant slowly began in Toronto in 1994. I never published that first paper, but I did post it on the Social Sciences Research Network (SSRN.com). It was called “An Options Pricing Formula with Volume as a Variable.” The idea was that the Black-Scholes formula relies on perfect dynamic replication of an option with a portfolio of the underlying stock and a riskless security. My idea was to ask, what if instead of perfect replication you can only replicate with a certain probability? What I did was show that if you could replicate a security with another with an arbitrarily high degree of probability, then you could obtain pricing formulas that had all the good properties associated with perfect replication.

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When I discovered that the counterparty for most of his trades was a subsidiary of Goldman Sachs (such was the trader’s faith in his own models he neither knew nor cared), I put my foot down and got trading halted. The problem was that in order to derive closed-form solutions, one generally has to work in the Black-Scholes framework. Everyone knows that, due to the fatter than lognormal tails in most asset returns, farfrom-the-money options should generally be priced significantly above the Black-Scholes formula price. But these barrier and double barrier options were close to the money, so this problem doesn’t apply, right? Wrong; if a distribution has fat tails then it must have a taller thinner peak to compensate. Thus a formula derived in the Black-Scholes framework must price near-the-money barrier options too expensively.

The Misbehavior of Markets: A Fractal View of Financial Turbulence
by Benoit Mandelbrot and Richard L. Hudson
Published 7 Mar 2006

These combinations are obscure to most people, but perhaps just what the CFO of GM needs to guard against one particular risk that worries him in his company’s yen-based cash-flow. None of this would exist if the original Black-Scholes formula were accurate. Of course, the formula remains important; it is the benchmark to which everyone in the market refers, much the way, say, people talk about the temperature in winter even though whether they actually feel cold also depends on the wind, the snow, the clouds, their clothing, and their health. Citigroup’s options analysts have the Black-Scholes formula in front of them all the time, in spreadsheets. But it is just a starting point. Third mistake: the research department.

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Hundreds of scholarly papers, several textbooks, and scores of financial conferences have been devoted to studying the errors. A wide error range. This diagram, from Schoutens 2003, plots the volatility that the standard Black-Scholes formula would infer from the market prices for one family of options. All the curves here show the same type of option, but with different times, T, to maturity. The “strike” price at which each contract can be exercised is on the bottom scale; the volatility that the Black-Scholes formula infers from the data is on the vertical scale, in standard deviations. If the formula were right, there would be nothing much to see: just one flat line.

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In hindsight, the newspaper appears to have underestimated, and thus under-played, the importance of the exchange’s opening. 72 “The answer came…” From the eulogy of Black, Scholes 1995. The account of their discovery given here is based on the published recollections of the participants, including Black 1989, Scholes 2001, and the autobiographical essays Merton and Scholes 1997. 73 “The Black-Scholes formula permitted…” The Black-Scholes formula looks complex, but working with it is a simple matter of plugging numbers into their proper places in a spreadsheet or calculator. The price of a call option to buy a stock at a specific price and time is: Here, C0 is the price of the call option; S0 is the current stock price; X is exercise price at which the option contract allows you to buy the stock; r is the risk-free interest rate; and T is the time to maturity.

Stock Market Wizards: Interviews With America's Top Stock Traders
by Jack D. Schwager
Published 1 Jan 2001

The problem is that the Almighty is not giving me or anyone else the probability distribution for the price of IBM a month from now. The standard approach, which is based on the Black-Scholes formula, assumes that the probability distribution will conform to a normal curve [the familiar bell-shaped curve frequently used to depict probabilities, such as the probability distribution of IQ scores among the population]. The critical statement is that it "assumes a normal probability distribution." Who ran out and told these guys that was the correct probability distribution? Where did they get this idea? [The Black-Scholes formula (or one of its variations) is the widely used equation for deriving an option's theoretical value.

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Don't other firms such as Susquehanna [a company whose principal was interviewed in The New Market Wizards] also trade on models based on perceived mispricings implied by the standard Black-Scholes model? When I was on the floor of the Philadelphia Stock Exchange, I was typically trading on the other side of firms such as Susquehanna. They thought they had something special because they were using a pricing model that modified the Black-Scholes model. Basically, their modifications were trivial. I call what they were doing TV set—type adjustments. Let's say I have an old-fashioned TV with an aerial. I turn it on, and the picture is not quite right.

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If I understand you correctly, your basic premise is that stock price movements are not random and therefore the assumption that prices are normally distributed, which everyone uses to determine option values, cannot be the accurate mathematical representation of the true market. Does that imply that you've come up with an alternative mathematical option pricing model? Not in the sense that you are probably thinking. It's not a matter of coming up with a one-size-fits-all model that is better than the standard Black-Scholes model. The key point is that the correct probability distribution is different for every market and every time period. The probability distribution has to be estimated on a case-by-case basis. If your response to Bender's last comment, which challenges the core premises assumed by option market participants, could best be summarized as "Huh?

Stigum's Money Market, 4E
by Marcia Stigum and Anthony Crescenzi
Published 9 Feb 2007

However, it has been empirically shown that stock returns follow a distribution that has fatter tails than does a normal distribution. The original Black-Scholes formula also could not price dividend-paying stocks, though this can be done with an assumption that dividends are paid continuously and at a steady rate. Also, the Black-Scholes formula cannot price American put options and other more complicated derivative securities. The Cox-Ross-Rubinstein binomial tree and Monte Carlo simulation can be used in these cases. APPENDIX TO CHAPTER 17 The Black-Scholes Formula The Black-Scholes formula assumes: 1. Frictionless, competitive, continuous markets, and no constraints on short sales. 2.

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Specifically, given the readily available information on an option, the price of the underlying stock, and the risk-free rate, what is the volatility of the underlying stock that would make the Black-Scholes formula true? As discussed above, the price of an option increases with an increase in the volatility of the underlying asset. Because of this fact and the fact that all the variables from the Black-Scholes formula are readily available except the volatility, traders often quote options in terms of implied volatilities. When they buy an option, they are buying volatility. In this sense, options can be thought of as a bet on the future volatility of the underlying stock.

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In this sense, options can be thought of as a bet on the future volatility of the underlying stock. This is why professional options traders are often known as “vol traders.” Can we calculate implied volatility for different options with the same underlying asset? The answer is yes, but the results actually contradict one of the major assumptions of the Black-Scholes formula. The Black-Scholes formula includes the volatility of the underlying asset. This volatility should be constant regardless of the terms of any options that are written on it. However, it is an empirical fact that the implied volatilities of in-the-money and out-of-the-money options are typically higher than the implied volatilities of at-the-money options.

The Physics of Wall Street: A Brief History of Predicting the Unpredictable
by James Owen Weatherall
Published 2 Jan 2013

During 1977 and 1978, Greenbaum, Struve, and a small team of proto-quants worked out a modified Black-Scholes model that took into account things like sudden jumps in prices, which can lead to fat tails. O’Connor was famously successful, first in options and then in other derivatives — in part because the modified Black-Scholes model tended to outperform the standard one. Remarkably, according to Struve, O’Connor was aware of the volatility smile from very early on. That is, even before the crash of 1987, there were small, potentially exploitable discrepancies between the Black-Scholes model and market prices. Later, when the 1987 crash did occur, O’Connor survived.

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(Sherman McCoy, the star-crossed antihero of Tom Wolfe’s novel Bonfire of the Vanities, was an eighties-era bond trader who took himself to be so important, given the changes in the bond markets during the late seventies and early eighties, that he privately called himself a “Master of the Universe.” The name has stuck, now used to refer to Wall Street traders of all stripes.) The success of the Black-Scholes model and other derivatives models during the 1970s inspired some economists to ask whether bonds could be modeled in a similar way to options. Soon, Black and others had realized that bonds themselves could be thought of as simple derivatives, with interest rates as the underlying asset. They began to develop modified versions of the Black-Scholes model to price bonds, based on the hypothesis that interest rates undergo a random walk. Thus, Black arrived on Wall Street at a moment when derivatives, and derivative models, were proving increasingly important, in unexpected ways.

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If extreme market changes are more likely than Osborne’s model predicts, neither Thorp’s model nor the Black-Scholes model will get options prices right. In particular, they should undervalue options that would be exercised only if the market makes a dramatic move, so-called far-out-of-the-money options. A more realistic options model, meanwhile, should account for fat tails. Mandelbrot left finance at the end of the 1960s, but he returned in the early 1990s. One of the reasons was that many financial practitioners were beginning to recognize the shortcomings of the Black-Scholes model. Instrumental in this shift was the Black Monday stock market crash of 1987, during which world financial markets fell more than 20% literally overnight.

A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation
by Richard Bookstaber
Published 5 Apr 2007

This is a point made by John Danaher in the introduction to Brazilian JiuJitsu: Theory and Technique, by Renzo Gracie and Royler Gracie with Kid Peligro and John Danaher (Montpelier, VT: Invisible Cities Press, 2001). 270 bindex.qxd 7/13/07 2:44 PM Page 271 INDEX Accidents/organizations, 159–161 Accountants, failure (reasons), 135 Accounting conventions, problems, 138 Accounting orientation, 137–138 Adaptation, best measure, 232–233 Adverse selection, 191–192 American depositary receipts (ADRs), 68 America Online (AOL), 139 Amex Major Market Index (XMI) futures, 12 Analytically driven funds, 248 Analytical Proprietary Trading (APT), 44–45 initiation, 189 remnant, form, 190 A Programming Language (APL), 43–47 asset, problem, 45 Armstrong, Michael, 130 Arthur Andersen, failure, 135 Artificial markets, 229 Asia Crisis (1997), 3, 115 Asian currency crisis, 114 Asian economies, 118 Asia-Pacific Economic Cooperation (APEC), 63 Assets class, hedge fund classification, 245 direction, hedge fund classification, 246 Asynchronous pricing, 225 AT&T Wireless Services IPO, SSB underwriting, 130 Back-office functions, 39 Bacon, Louis, 165 Bamberger, Gerry, 185–187, 251 Bankers Trust lawsuit, 38 purchase announcement, 75 Bank exposure, 146–147 Bank failures, 146 Bank of Japan, objectives/strategies, 166 Baptist Foundation, restatements/liability, 135 Barings (bank) bankruptcy, 39 clerical trading error, 38–39 derivatives cross-trading, 143 Beard, Anson, 13 Beder, Tanya, 204 Behavior, economic theory, 231 Berens, Rod, 73 Bernard, Lewis, 42, 52 Biggs, Barton, 11 Black, Fischer, 9 Black Monday (1929), 17 Black-Scholes formula, 9, 252 Block desk, 184–185 trading positions, 186 Bond positions, hedging, 30 Booth, David, 29 Breakdowns, explanation, 5–6 Broker-dealer block-trading desk, usage, 184 price setting role, 213–214 Bucket shop era, 177 Buffett, Warren, 62, 99, 181, 198 arb unit closure, 87–88 Bushnell, Dave, 129–131 Butterfly effect, essence, 227 Capital cushions, 106 Capitalism, 250 Cash futures, 251 arbitrageurs, 19, 23 spread, 19 trade, 19 Cerullo, Ed, 41 Cheapest-to-deliver bond, 251 Chicago Board Options Exchange (CBOE), 252 Black-Scholes formula, impact, 9–10 Citigroup Associates First Capital Corporation, 128 consolidation, impact, 132–134 Japanese private banking arm, 133 management change, Fed reaction, 133 organizational complexity/structural uncertainty, 126 Citron, Robert, 38 Coarse behavior benefits, 232–233 consistency, 236–237 271 bindex.qxd 7/13/07 2:44 PM Page 272 INDEX Coarse behavior (Continued) decision rules, 233 in humans, 235–237 measurement of, 238–239 response based on, 236 rules, optimality, 238 Cockroach example, 232–233, 235 Collateral, usage, 218 Collateralized mortgage obligations (CMOs), 71–75, 250 Commercial Credit, Primerica purchase, 126 Competitive prices, 36 Complexity by-product, 143 implications, 156 importance, 144–146 Consumer lending violations, Federal Reserve fine, 132 Control-oriented risk management, 200 Convergence Capital, 80 Convergence trades, 122 Convertible bond (CB) strategy, 57–58 Cooke, Bill, 185–187 Corporate defaults, possibility, 29–30 Corporate political risk, 140 Corrigan, Gerald, 196–198 Countervailing trades, 213 Credit Suisse First Boston, 72–73 Crises, causes, 240 da Vinci, Leonardo, 136 Denham, Bob, 62–63, 99, 195 Derivatives customization, 143 trading strategy, 30 Deterministic nonperiodic flow, 228 Detroit Edison, Fermi-1 experimental breeder reactor, 161–164 Deutsche Bank, investment banking (problems), 72–73 Dimon, Jamie, 77–78, 91, 97–98, 126 Distressed debt, event risk, 248–249 Dow Jones Industrial Average (DJIA), 2, 12 Dynamic hedge, 12, 161 Dynamic system, 228–229 Ebbers, Bernard, 70 Economic catastrophe, 257 Efficient markets hypothesis, 211 Einstein, Albert, 224–226 Emerging market bonds, 71 Enron restatements/liability, 135 U.S.

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Thus the portfolio is hedged when it needs it and is free to take market exposure when there is a buffer between its value and the floor value. Because the hedge increases and decreases over time, it is called a dynamic hedge. The hedging method of portfolio insurance is based on the theoretical work of Fischer Black, Robert Merton, and Myron Scholes. Their work is encapsulated in the Black-Scholes formula, which makes it possible to set a price on an option. No other formula in economics has had as much impact on the world of finance. Merton and Scholes both received the Nobel Prize for it. (Fischer Black had died a few years before the award was made.) The theory and mathematics behind it were readily embraced by the academic community.

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Despite its esoteric derivation, the formula was timely and—a rarity for work on the mathematical edge of economics—was immediately applicable. First, there was a ready market that required such a pricing tool: the Chicago Board Options Exchange (CBOE) opened for business in 1973, the same year both the paper presenting the Black-Scholes formula and a 9 ccc_demon_007-032_ch02.qxd 2/13/07 A DEMON 1:44 PM OF Page 10 OUR OWN DESIGN more complete exposition on option pricing by Merton were published.1 Second, although the formula required advanced mathematics and computing power, it really worked, and it worked in a mechanistic way.

Corporate Finance: Theory and Practice
by Pierre Vernimmen , Pascal Quiry , Maurizio Dallocchio , Yann le Fur and Antonio Salvi
Published 16 Oct 2017

In these conditions, a new type of approach to risk has developed on trading floors: model risk. The notion of model risk arose when some researchers noticed that the Black–Scholes model was biased, since (like many other models) it models share prices on the basis of a log-normal distribution. We have seen empirically that this type of distribution significantly minimises the impact of extreme price swings. To simplify, we can say that the Black–Scholes model does not reflect the risk of a market crash. This has given rise to the notion of model risk, as almost all banks use the Black–Scholes model (or a model derived from it). Financial research has uncovered risks that had hitherto been ignored.

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By multiplying the number of periods or dividing each period into sub-periods, we can obtain a very large number of very small sub-periods until we have a very large number of values for the stock at the option’s maturity date, which is more realistic than the simplified schema that we developed above. Here is what it looks like graphically: 2. The Black–Scholes model In a now famous article, Fisher Black and Myron Scholes (1972) presented a model for pricing European-style options that is now very widely used. It is based on the construction of a portfolio composed of the underlying asset and a certain number of options such that the portfolio is insensitive to fluctuations in the price of the underlying asset. It can therefore return only the risk-free rate. The Black–Scholes model is the continuous-time (the period approaches 0) version of the discrete-time binomial model.

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However, we can simplify for a European-style call option on an underlying share that pays a dividend: the Black–Scholes model is applied to the share price minus the discounted dividend. The formula for valuing the put option is as follows: Of the six criteria of an option’s value, five are “given” (price of the underlying asset, strike price, maturity date, risk-free rate and, where applicable, dividend); only one is unknown: volatility. From a theoretical point of view, volatility would have to be constant for the Black–Scholes model to be applied with no risk of error, i.e. historical volatility (which is observed) and anticipated volatility would have to be equal.

Hedge Fund Market Wizards
by Jack D. Schwager
Published 24 Apr 2012

Since the purchase or sale of warrants combined with delta neutral hedging led to a portfolio with very little risk, it seemed very plausible to me that the risk-free assumption would lead to the correct formula. The result was an equation that was equivalent to the future Black-Scholes formula. I started using this formula in 1967. Did you apply your formula (that is, the future Black-Scholes formula) to identify overpriced warrants and then delta hedge those positions? I didn’t have enough money to have a diversified warrant portfolio and to also place the hedge, since each side of a hedged position required separate margin. I used the formula to identify the most extremely overpriced warrants.

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Thorp along with Sheen Kassouf developed the first known systematic approach to trading warrants and other convertible securities (e.g., options, convertible bonds, convertible preferred stocks) by hedging them with offsetting stock positions, an approach they detailed in their book, Beat the Market.3 He was the first to formulate an option-pricing model that was equivalent to the Black-Scholes model. Thorp had actually used an equivalent form of the formula to very profitably trade warrants and options for years before the publication of the Black-Scholes model. He was the founder of the first market neutral fund. He established the first successful quant hedge fund. He was the first to implement convertible arbitrage. He was the first to implement statistical arbitrage.

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However, the formula was good enough and the warrants were so overpriced that I still broke even on the naked short positions. The formula really proved itself under the most adverse circumstances. As far as I know, the short warrant positions I implemented during 1967 to 1968 were the first actual application of the Black-Scholes formula in the markets. When did Black-Scholes publish their formula? I believe they discovered it in 1969 and published it 1972 or 1973. Did you consider publishing your formula? The option-pricing formula seemed to me to be a big edge on everybody else. So I was happy just to use it. By 1969, I had started my first hedge fund, Princeton Newport Partners, and I thought that if I published the formula, I would lose the edge that was helping my investors.

The Crisis of Crowding: Quant Copycats, Ugly Models, and the New Crash Normal
by Ludwig B. Chincarini
Published 29 Jul 2012

A call and put option give the holder the right to buy or sell a security at a given price, so the higher the security’s volatility, the greater the chance that the security’s price may move above or below the strike price, letting the investor make a profit. That’s why higher volatility means a higher option price. With a formula that relates an option’s price to the underlying security’s volatility, a trader could convert the option’s price into a volatility consistent with that price. This is called implied volatility. The Black-Scholes formula, discovered in 1973, is most commonly used for this purpose. It is named after one of LTCM’s principals, Myron Scholes, and the late Goldman Sachs partner Fischer Black. LTCM made volatility trades in both fixed income and equities. In the fixed-income arena, they noticed in 1998 that the implied volatility of 5-year options (i.e., options with five years to maturity) on German-denominated swaps was trading much lower than actual realized volatility.

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See also Investment banks; specific banks bailouts of basic operations of fees charged by Greek debt exposure as hedge funds housing bubble and leverage and Maughan on provision of emergency credit by runs on trust between trust in Barclays Barclays Global Investors (BGI) Basel Committee: Basel I document Basel II document financial crisis and guidelines of overview of Bear Stearns: bank run on collapse of failure of hedge funds of history and reputation of J.P. Morgan and leverage of LTCM and near-collapse of repo system and window dressing by Begleiter, Steve Benn, Orson Berkshire Hathaway. See also Buffett, Warren Bernanke, Ben Black, Fischer Black-Scholes formula Blankfein, Lloyd Blasnik, Steve Bond arbitrage Born, Brooksley Box trade Brady Plan Brazilian C bonds Brendsel, Leland Broker-dealers Buffett, Warren Buoni del Tesoro Poliennali Buoni Ordinari del Tesoro Bush, George Butler, Angus Butterfly yield curve trades Callan, Erin Capital, contingency Capital adequacy ratio (CAR) Capital markets Capital ratio and leverage Capital-to-asset ratio Carhart, Mark Cash business Cassano, Joseph Caxton macro hedge fund Cayne, James E.

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See also Risk management Basel I and credit risk failure of models of to account for crowding and interconnectedness Freddie, Fannie, and liquidity risk market risk measuring of mortgages reduction of prior to quarterly reports systemic risk tail risk Risk arbitrage trades Risk management: at Bear Stearns at JWMP and PGAM at JWM Partners at Lehman Brothers lessons from financial crisis of 2008 Risk management at LTCM: broad outlines as cause of failure diversification mathematics of framework for operations raw evidence Robertson, Julian Rosenblum, Ira Rosenfeld, Eric Rosengren, Eric Royal Dutch-Shell trade Rubin, Robert Russian government, default on debt by Russian markets Salomon Brothers: arbitrage trading group bond-trading group shutdown copycat positions Traveler’s Group purchase of Schapiro, Mary Scholes, Myron: Banco Nazionale del Lavoro project and Black-Scholes formula career of on diversification on economic system choices on financial models on insurance on Lehman failure LTCM and PGAM and on spreads on VaR Schwartz, Alan SEC (Securities and Exchange Commission) Securities: Agency asset-backed CMBS corporate debt high-yield illiquid liquid mortgage-backed municipal and tax-exempt Securitization Security price volatility Self help status Shadow banking system Sharpe, William Sharpe ratio Shed show Short swap spread trade Shustak, Robert Simon, James Size of firms and “too big to fail,” Slap hands Sloan, Bob Smith Breeden Mortgage Partners Snow, John Solender, Michael Solomon, David Soros, George Sowood Capital Spector, Warren Spoofing Standard & Poor’s Standard quant factors, erratic behavior of State Street Statistical arbitrage (stat arb) funds Steel, Robert Stock price manipulation Stress tests Stub quotes Subprime mortgage market collapse Subprime mortgages Sun, Tong-Sheng Swap business Swap spreads: behavior of longer-term computing returns from zero-coupon returns derivation of approximate returns historical average Italian Japanese mechanics of U.S.

Keeping Up With the Quants: Your Guide to Understanding and Using Analytics
by Thomas H. Davenport and Jinho Kim
Published 10 Jun 2013

However, Black and Scholes performed empirical tests of their theoretically derived model on a large body of call-option data in their paper “The Pricing of Options and Corporate Liabilities.”16 DATA ANALYSIS. Black and Scholes could derive a partial differential equation based on some arguments and technical assumptions (a model from calculus, not statistics). The solution to this equation was the Black-Scholes formula, which suggested how the price of a call option might be calculated as a function of a risk-free interest rate, the price variance of the asset on which the option was written, and the parameters of the option (strike price, term, and the market price of the underlying asset). The formula introduces the concept that, the higher the share price today, the higher the volatility of the share price, the higher the risk-free interest rate, the longer the time to maturity, and the lower the exercise price, then the higher the option value.

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After making revisions based on extensive comments from several famous economists, they resubmitted it to the Journal of Political Economy and finally were able to publish it. Subsequently, Robert Merton, then a professor at MIT, published a paper expanding the mathematical understanding of the Black-Scholes model. Despite the issues with getting the work published, thousands of traders and investors now use this formula every day to value stock options in markets throughout the world. It is easy to calculate and explicitly models the relationships among all the variables. It is a useful approximation, particularly when analyzing the directionality that prices move when crossing critical points.

New Market Wizards: Conversations With America's Top Traders
by Jack D. Schwager
Published 28 Jan 1994

When did you first get involved in trading options? I did a little dabbling with stock options back in 1975-76 on the Chicago Board of Options Exchange, but I didn’t stay with it. I first got involved with options in a serious way with the initiation of trading in futures options. By the way, in 1975 I crammed the Black-Scholes formula into a TI52 hand-held calculator, which was capable of giving me one option price in about thirteen seconds, after I hand-inserted all the other variables. It was pretty crude, but in the land of the blind, I was the guy with one eye. When the market was in its embryonic stage, were the options seriously mispriced, and was your basic strategy aimed at taking advantage of these mispricings? 

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The job was certainly helpful in terms of overall trading experience, but you have to understand that, at the time, equity options trading at Salomon was highly nonquantitative. In fact, when I think back on it now, it seems almost amazing, but I don’t believe anybody there even knew what the Black-Scholes model was [the standard option pricing model]. Sidney would come in on Monday morning and say, “I went to buy a car this weekend and the Chevrolet showroom was packed. Let’s buy GM calls.” That type of stuff. 24 / The New Market Wizard I remember one trader pulling me aside one day and saying, “Look, I don’t know what Sidney is teaching you, but let me tell you everything you need to know about options.

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One thing that helped me a great deal was that I had a background in options when it was new to the marketplace. “He knows options,” they would say. Hell, I didn’t know that much about it, but the point was that no one in foreign exchange knew very much about it either. Their perception was: “He can derive the Black-Scholes model; he must be a genius.” A lot of senior guys in the currency market wanted to meet me simply because their customers wanted to do options, and they needed to get up to speed on the subject quickly. Also, I worked for Salomon Brothers, which at that time provided an element of mystique: “We don’t know what they do, but they make a lot of money.”

Solutions Manual - a Primer for the Mathematics of Financial Engineering, Second Edition
by Dan Stefanica
Published 24 Mar 2011

The凡 from (3.6) and (3.7) , we find that P(X 主 t+s I X 三 t) P((X 三 t+s)n(x 主 t)) P(X 三 t) e 一 α (t+ s) _,"" If ε'-'0 工 e P(X 三 t + s) Problem 6: Use the Black-Scholes formula to price both a put and a call option wit且 strike 45 expiring in six months on an underlying asset with spot price 50 and volatility 20% paying dividends continuously at 2% , if interest rates are constant at 6%. Solution: Input for the Black-Scholes formula: P(X 三 t) S = 50; K = 45; T - t = 0.5;σ= 0.2; q = 0.02; r = 0.06. 一讪-甲- l f(x)g(川三 (l 尸 (x) (l dx )' The Black-Scholes price of the call is C = 6.508363 and the price of the put is P = 0.675920.

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Problem 10: Show that an ATM call on an underlying asset paying dividends continuously at rate q is worth more than an ATM put with the same maturity if and only if q 三飞 where r is the constant risk free rate. Use the Put-Call parity, and then use the Black-Scholes formula to prove this result. For a non-dividend-paying asset , i.e. , for q = 0 , we find that Solution: For at-th e-money options , i.e. , with S = K , the Put-Call parity can be written as (ii) If q = r , the Theta of an ATM call (i.e. , with S = K) is C- P = e-q(T-t) N( -d1 ) δC 歹歹工 vega(C). Therefore , Volga(P)z 73 Alternatively, the Black-Scholes formulas for at-the-money options can be written as Note that θd 1 3.1. SOLUTIONS TO CHAPTER 3 EXERCISES Se-q(T-t) - K e-r(T-t) _ K e-q(T-t) - K e-r(T-t) K e-r(T-t) (e(r-q)(T-t) - 1) Therefore , C ~三 P if and only if e(r-q)(T-t) ;三 1 ， which is equivalent to r 主 q. 8(C) = -Sσe-4-Tke-r(T-t)N(d2)<0. 2 飞/2作 (T - t) Kae-r(T-t) -~ @ ( C ) = - e 2 十 r K e-r(T-t) N( d 1 ) - 2 飞/2作 (T - t) r K e-r(T-t) N( d 2 ) Ke-r(T-t) (r(N(d 1 ) - N(d 2 )) 一 σJ) \2 飞/2汀 (T - tr ) CHAPTER 3.

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γ(N(d1 ) - N(d2 )) 一 σe-4i \2y2作 (T - t) ) In ∞ z d2 JT-t (γ (N(d 1 ) - 飞 N(出))一 JT-t σJ} 2y2作 (T - t) Then ) 口 ' σVT丁I θd 2 1 and , from (3.11) and (3.12) , we conclude that θ2C Problem 12: Show that the price of a plain vanilla European call option is a convex function of the strike of the option , i.e. , show that θ2C 一一=-=δ K2 > O. 一 Se-q(T-t) N'(d 1 ) - Ke-r(T-t) N'(d 2 ). By differentiating the Black-Scholes formula Se-q(T一忖T(d 1 ) - Ke-r(T-t) N(d 2 ) w山w Se-q(T一叫鞋一 Ke-r(T一川也)在一 e-r(T一切(d2 ) _e-r(T-t) N(d 2 ) , (坐 -252} 飞 θKθK } - σK j2作 (T - t) e-r(T-t) e二Ji>O 口 Solution: The input in the Black-Scholes formula for the Gamma of the call is S = K = 50 ， σ= 0.3 , r = 0.05 , q = O. For T = 1/24 (assuming a 30 days per month count) , T = 1/4 , and T = 1, the following values of the Gamma of the ATM call are obtained: with respect to K , we obtain that Se-q(T-t) N'(d 1 ) θ K2 Problem 13: Compute the Gamma of AT l\!

The Devil's Derivatives: The Untold Story of the Slick Traders and Hapless Regulators Who Almost Blew Up Wall Street . . . And Are Ready to Do It Again
by Nicholas Dunbar
Published 11 Jul 2011

By assuming that smart, aggressive traders like Meriwether would snap up any mispriced options and build their own factory to pick them apart again using the mathematical recipe, Black, Scholes, and Merton followed in Miller’s footsteps with a no-arbitrage rule. In other words, you’d better believe the math because, otherwise, traders will use it against you. That was how the famous Black-Scholes formula entered finance. When the formula was first published in the Journal of Political Economy in 1973, it was far from obvious that anyone would actually try to use its hedging recipe to extract money from arbitrage, although the Chicago Board Options Exchange (CBOE) did start offering equity option contracts that year.

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By April 1998, Merton and Scholes were partners at LTCM and making millions of dollars per year, a nice bump from a professor’s salary. By the late 1990s, investment banks were supplanting exchanges as the favored market-making institution for options and other derivatives, but LTCM worked with both. The original mathematics behind the Black-Scholes formula had gone through several generations of upgrades and refinements since 1973 and was gathering acolytes daily. According to Black-Scholes, the cost of manufacturing options increased with market volatility. Traders learned to use the option price as a kind of “fear gauge,” measuring what the market expected future volatility to be.

…

How could arbitrage trades that were immunized from swings in fundamental markets such as equities or interest rates lose $4 billion in a matter of months? How come VAR, the tool that LTCM and all other big trading banks used to control their exposures, broke down, when it had worked like a dream in 1994? These trades were supposedly safe bets because of the no-arbitrage principle. For example, the Black-Scholes formula suggested that buyers of options were being overcharged compared with the replication cost over time (which tracked underlying market volatility). So LTCM sold options and paid the replication costs, earning a profit as the option price converged on the replication cost, as the quants’ calculations said it would.

On the Edge: The Art of Risking Everything
by Nate Silver
Published 12 Aug 2024

The empirical claim is that low-hanging fruit of the tree of statistical analysis has mostly been picked. Baseball teams no longer have an advantage from targeting players with high on-base percentages because it’s been twenty years since Moneyball was published and everyone does that now. The Black-Scholes formula that Thiel mentioned, an equation involving inputs like the risk-free interest rate and the amount of time until the option expires, might once have made you a handsome profit on Wall Street. But when everyone is using Black-Scholes, its flaws start to show—the simplistic assumptions it makes may even have helped traders to rationalize risky trades that contributed to the Global Financial Crisis.

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*8 GPU stands for “graphics processing unit”—a type of computer chip that was originally optimized to display video game graphics, but which is also highly efficient for general mathematical computations. Thus, GPUs are often used for other computationally intensive problems, such as training AI models. *9 Even the Black-Scholes formula for pricing options—though derided by Peter Thiel and others for being too simplistic—is relatively complex as famous formulas go. It’s a partial differential equation that contains six variables—not exactly E = mc2. *10 Isn’t this message encrypted? No. The data on a blockchain isn’t encrypted, although it’s often represented in hexadecimal, a base-16 numbering system that includes ten digits and the letters A through F.

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A B C D E F G H I J K L M N O P Q R S T U V W X Y Z A abstraction, 23–24, 29, 30–31, 130, 477 academia, 26, 27, 28, 294–96 See also Village accelerationists, 31, 250, 411–13, 455–56, 477, 539n accelerators, 405–6, 477 action, 477 adaptability, 235–37, 264 addiction, 164–65, 166, 167, 168–69, 213–14, 321 Addiction by Design: Machine Gambling in Las Vegas (Schüll), 154–55 Adelson, Sheldon, 146 Adelstein, Garrett, 100, 102, 106 Robbi hand, 80–86, 89, 117, 123–29, 130, 444–45, 512n advantage play, 158–61, 478 adverse selection, 478 Aella, 375–77 Age of Em, The (Hanson), 379 agency, 453, 469–70, 478 agents, 478 aggressiveness, 120 AGI (artificial general intelligence), defined, 478 Aguiar, Jon, 199 AI (artificial intelligence) accelerationists, 31, 250, 411–13, 455–56, 477, 539n adaptability and, 236n agency and, 469–70 alignment and, 441–42, 478 Sam Altman and, 406 analogies for, 446, 541n bias and, 440n breakthrough in, 414–15 commercial applications, 452–53 culture wars and, 273 decels, 477 defined, 478 economic growth and, 407n, 463–64 effective altruism and, 21, 344, 348, 355, 359, 380 engineers and, 411–12 excitement about, 409–10 impartiality and, 359, 366 moral hazard and, 261 New York Times lawsuit, 27, 295 OpenAI founding, 406–7, 414 optimism and, 407–8, 413 poker and, 40, 46–48, 60–61, 430–33, 437, 439, 507n poor interpretability of, 433–34, 437, 479 prediction markets and, 369, 372 probabilistic thinking and, 439 randomization and, 438 rationalism and, 353, 355 regulation of, 270, 458, 541n religion and, 434 risk impact and, 91 risk tolerance and, 408 River-Village conflict and, 27 SBF and, 401, 402 sports betting and, 175–76 technological singularities and, 449–50, 497 transformers, 414–15, 434–41, 479, 499 Turing test and, 499 See also AI existential risk AI existential risk accelerationists and, 412–13, 455–56, 539n alignment and, 441 arguments against, 458–60 Bid-Ask spread and, 444–46 commercial applications and, 452–53 Cromwell’s law and, 415–16 determinism and, 297 effective altruism/rationalism and, 21, 355, 456 EV maximizing and, 457 excitement about AI and, 410 expert statement on, 409, 539n Hyper-Commodified Casino Capitalism and, 452–53 instrumental convergence and, 418 interpretability and, 433–34 Kelly criterion and, 408–9 models and, 446–48 Musk and, 406n, 416 optimism and, 413–14 orthogonality thesis and, 418 politics and, 458, 541n prisoner’s dilemma and, 417 reference classes and, 448, 450, 452, 457 societal institutions and, 250, 456–57 takeoff speed and, 418–19, 498 technological Richter scale and, 450–52, 451, 498 Yudkowsky on, 372, 415–19, 433, 442, 443, 446 Alexander, Scott, 353, 354, 355, 376–77, 378 algorithms, 47, 478 alignment (AI), 441–42, 478 all-in (poker), 478 alpha, 241–42, 478 AlphaGo, 176 Altman, Sam, 401 AI breakthrough and, 415 AI existential risk and, 419n, 451, 459 OpenAI founding and, 406–7 OpenAI’s attempt to fire, 408, 411, 452n optimism and, 407–8, 413, 414 Y Combinator and, 405–6 Always Coming Home (Le Guin), 454–55, 541n American odds, 477, 491 American Revolution, 461 analysis, 23, 24, 478 analytics casinos and, 153–54 defined, 23, 478 empathy and, 224 limitations of, 253–54, 259 politics and, 254 sports betting and, 171, 191 venture capital and, 249 anchoring bias, 222n, 478 Anderson, Dave, 219–20, 230, 231 Andreessen, Marc accelerationists and, 411 AI analogies and, 446, 541n AI existential risk and, 446 Adam Neumann and, 281–82 on patience, 260 politics and, 267–68 River-Village conflict and, 295 techno-optimism and, 249, 250–51, 270, 296, 498 VC profitability and, 293, 526n VC stickiness and, 290, 291–92 angles, 192–94, 235–36, 305, 478 angle-shooters, 478 ante (poker), 478 anti-authority attitude, 111–12, 118, 137 See also contrarianism apeing, 479 arbitrage (arb), 171, 172–74, 206, 478, 489, 516n, 517n Archilochus, 236, 263, 485 Archipelago, The, 22, 310, 478 arms race, 478 See also mutually assured destruction; nuclear existential risk art world, 329–30, 331n ASI (artificial superintelligence), 478 Asian Americans, 135–36, 513n See also race asymmetric odds, 248–49, 255, 259, 260–62, 276, 277 attack surfaces, 177, 187, 478 attention (AI), 479 attention to detail, 233–35 autism, 282–84, 363, 525n B back doors, 479 backtesting, 479 bad beats, 479 “bag of numbers,” 433, 479 bank bailouts, 261 Bankman, Joseph, 383–84 Bankman-Fried, Sam (SBF) AI and, 401, 402 angles and, 305 attitude toward risk, 334–35 bankruptcy and arrest of, 298–301, 373–74 cryptocurrency business model and, 308–9 cults of personality and, 31, 338–39 culture wars and, 341n as dangerous, 403–4 disagreeability and, 280 effective altruism and, 20, 340–42, 343, 374, 397–98, 401 as focal point, 334 fraud and, 124, 374 Kelly criterion and, 397–98 moral hazard and, 261 NOT INVESTMENT ADVICE and, 491 personas of, 302 politics and, 26, 341n, 342 public image of, 338 responses to bankruptcy and arrest, 303–5, 383–85, 386–88 risk tolerance and, 334–35, 397–403, 537–38n River and, 299 theories of, 388–96 trial of, 382–83, 385–86, 387, 403 utilitarianism and, 360, 400, 402–3, 471, 498 venture capital and, 337–39 warning signs, 374 bankrolls, 479 Baron-Cohen, Simon, 101n, 283, 284 Barzun, Jacques, 466 baseball, 58–59, 174 See also sports betting base rates, 479 basis points (bips), 479 basketball, 174 See also sports betting Bayesian reasoning, 237, 238, 353, 355, 478, 479, 493–94, 499 Bayes’ theorem, 479 beards, 207–8, 479 See also whales bednets, 479 Bennett, Chris, 177, 178 Bernoulli, Nicolaus, 498 Betancourt, Johnny, 332–33 bet sizing, 396, 479 Bezos, Jeff, 277, 410 Bid-ask spread, 444–46, 479 Biden, Joe, 269, 375 big data, 432–33, 479 Billions, 112 Bitcoin bubble in, 6, 306, 307, 307, 310, 312 creation of, 322–23, 496 vs. Ethereum, 324, 326–27 as focal point, 329, 332 poker and, 109 profitability of, 310 See also cryptocurrency Black, Fischer, 479 blackjack, 131–37, 481 Black-Scholes formula, 479 black swans, 479 blinds (poker), 41, 480 blockchain technology, 322, 323–24, 325–26, 480 blockers, 229, 480 bluffing, 39–40, 51, 64–65, 70–75, 77, 101, 125, 509n board (poker), 41, 480 Boeree, Liv, 347 Bollea, Terry G., 274 bookmakers, 480 See also retail bookmakers Bored Apes, 480 Boredom Markets Hypothesis, 310, 480 Bostrom, Nick, 364, 372, 380, 417, 418, 442, 470, 491, 498 Box, George, 447n Bradley, Derek, 198 Brin, Sergey, 259, 406 Bringing Down the House, 131 Brokos, Andrew, 46, 486–87 Brownhill, Jean, 288–89 Brunson, Doyle on bluffing, 39–40, 51, 64 bracelet wins, 98 on computer applications, 39, 47 independence and, 239 poker history and, 40–41, 43, 506n raise-or-fold attitude and, 230 sports betting and, 194–95 Super/System, 39–40, 45–46 on tight-aggressive strategy, 39, 498 bubble, cryptocurrency, 306–7, 307, 310, 311–18, 317 bubble (poker), 480 Buchak, Lara, 364–66 Buffett, Warren, 344, 431n, 497 bullet (poker), 480 bust out, 480 Buterin, Vitalik, 250, 323–24, 326, 327, 329n button (poker), 480 buy-in, 480 C Calacanis, Jason, 252 calibration, 480 California Gold Rush, 139–40 call (poker), 480 calling stations (poker), 48, 480, 507n call options, 480 canon, 481 capitalism, 28–29, 32, 174, 403 Caplan, Bryan, 447n capped (poker), 481 Cappellazzo, Amy, 329–30 Carlsen, Magnus, 84 cash games, 83–84, 115, 251–52, 481 casinos, 5–8 abuse and, 118, 149 advantage play, 478 agency and, 453 analytics and, 153–54 Archipelago and, 22 blackjack, 131–37, 481 card counting, 131–37, 481 corporatization of, 138, 144, 145 COVID-19 and, 7–8, 10, 10 customer loyalty, 156–58, 515n design of, 162–63, 167–68 Downriver and, 21–22, 374, 483 gender and, 166n house edge, 132, 154–55, 155 hustle and, 134–35, 513n Las Vegas history, 139–45 payout structures, 154–56, 155, 156, 166 poker and, 22 private games at, 83 regulation of, 134, 135, 143–44, 157, 513n, 514n safety of, 128n sports betting in, 174–75, 177–78, 182–83, 185–87 Trump and, 142, 150–52, 514n trust and, 143–44, 514n Steve Wynn’s influence, 146–49, 148 See also gambling; slots catastrophic risk.

Automate This: How Algorithms Came to Rule Our World
by Christopher Steiner
Published 29 Aug 2012

In 1973 Fischer Black and Myron Scholes, both professors at the University of Chicago, published a paper that included what would become known as the Black-Scholes formula, which told its users exactly how much an option was worth. Algorithms based on Black-Scholes would over the course of decades reshape Wall Street and bring a flock of like-minded men—mathematicians and engineers—to the front lines of the financial world. The Black-Scholes solution, quite similar to Peterffy’s, earned Myron Scholes a Nobel Prize in 1997 (Black had died in 1995). Change didn’t happen overnight. The Black-Scholes formula, a partial differential equation, was brilliant. But most traders didn’t peruse academic journals.

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“He was not amused,” Jarecki says. For traders who understood it, Black-Scholes gave them a way to calculate the exact price at which options should be traded. It was like having a cheat sheet for the market. There was money to be made by anybody who could accurately calculate each factor within the Black-Scholes formula and apply it to options prices in real time. Traders using the formula would sell options that were priced higher than the formula stipulated and buy ones that were priced lower than their fair price. Do this enough times with enough securities and a healthy profit was virtually guaranteed.

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Peterffy returned to the pits with a renewed focus. He stuck to his sheets, as always, but with DuPont haunting him, he didn’t make what he called “cowboy bets.” He slowly rebuilt his capital, one grinding day at a time. Sticking to his algorithmic system, he rarely experienced days with substantial losses. Even though the Black-Scholes formula had been published seven years before, it wasn’t moving the markets enough to bother Peterffy or others who were cashing in on its genius. As effective as his algorithms and sheets were, Peterffy was only one man. He needed more people in the pits. So he slowly hired more traders. To prevent losses and keep control of how his traders operated, he trained them to bid and offer only off of values on his sheets, which he would update with fresh numbers from his algorithm every night.

Why Aren't They Shouting?: A Banker’s Tale of Change, Computers and Perpetual Crisis
by Kevin Rodgers
Published 13 Jul 2016

In this way, they argued, you (as market maker) could be sure of having the right hedge at every stage – as the price rose you would buy more shares such that, at maturity, you would be able to deliver shares to the customer if the price was above the strike – and vice versa (sell, and thus hold no shares) if the price fell. From this reasoning, using nifty mathematics after making some simplifying assumptions, they derived an exact formula for the price of options – the famous Black–Scholes formula – which allowed a price to be calculated using a handful of parameters: the asset price, the strike, the option maturity, the volatility and yield of the asset and the interest rate. Their work ushered in a revolution in finance. I sat in the lecture theatre entranced by all this. Afterwards, I gushed to my classmates about how cool it all was!

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There are numerous fascinating, exquisitely detailed and reassuringly expensive books that explain at great length how this is done. My intention now, however, is just to provide a flavour of the process. The risks of having an option position are directly related to the pricing parameters in the Black–Scholes formula. For instance, the asset price (in FX this is the spot price) is vital. Say you sold a call on US dollars versus Deutschmarks to a fund. If the US dollar started to rally the option would become more valuable and you would start to lose money because the option would now be worth more than the premium you initially received.

…

Then Chris’s eyes lit up. ‘What’s interesting is what we could do if computers keep getting faster,’ he speculated, dreamily; ‘that’d open up a world of new possibilities.’ The reason it was practical to offer a relatively simple product like barrier options, he said, was that, just as was the case for the Black–Scholes formula for plain vanilla options, their price and their Greeks were solvable ‘analytically’ or in ‘closed form’. Other more complicated potential products were not so mathematically tractable. Why did this matter? It’s a little like trying to find the roots (the zero points) of quadratic equations, he told me.fn2 This is made easy by the fact that there is a simple, exact, ‘analytic’ formula that gives you the answer – all you need to do is to look it up and plug in the parameters from the quadratic equation you are solving.

Analysis of Financial Time Series
by Ruey S. Tsay
Published 14 Oct 2001

The unobservability of volatility makes it difficult to evaluate the forecasting performance of conditional heteroscedastic models. We discuss this issue later. In options markets, if one accepts the idea that the prices are governed by an econometric model such as the Black–Scholes formula, then one can use the price to obtain the “implied” volatility. Yet this approach is often criticized for using a specific model, which is based on some assumptions that might not hold in practice. For instance, from the observed prices of a European call option, one can use the Black–Scholes formula in Eq. (3.1) to deduce the conditional standard deviation σt . The resulting value of σt2 is called the implied volatility of the underlying stock.

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Continuous-Time Models and Their Applications 6.1 6.2 6.3 6.4 6.5 Options, 222 Some Continuous-Time Stochastic Processes, 222 Ito’s Lemma, 226 Distributions of Stock Prices and Log Returns, 231 Derivation of Black–Scholes Differential Equation, 232 221 ix CONTENTS 6.6 Black–Scholes Pricing Formulas, 234 6.7 An Extension of Ito’s Lemma, 240 6.8 Stochastic Integral, 242 6.9 Jump Diffusion Models, 244 6.10 Estimation of Continuous-Time Models, 251 Appendix A. Integration of Black–Scholes Formula, 251 Appendix B. Approximation to Standard Normal Probability, 253 7. Extreme Values, Quantile Estimation, and Value at Risk 7.1 7.2 7.3 7.4 7.5 7.6 7.7 8. 256 Value at Risk, 256 RiskMetrics, 259 An Econometric Approach to VaR Calculation, 262 Quantile Estimation, 267 Extreme Value Theory, 270 An Extreme Value Approach to VaR, 279 A New Approach Based on the Extreme Value Theory, 284 Multivariate Time Series Analysis and Its Applications 299 8.1 Weak Stationarity and Cross-Correlation Matrixes, 300 8.2 Vector Autoregressive Models, 309 8.3 Vector Moving-Average Models, 318 8.4 Vector ARMA Models, 322 8.5 Unit-Root Nonstationarity and Co-Integration, 328 8.6 Threshold Co-Integration and Arbitrage, 332 8.7 Principal Component Analysis, 335 8.8 Factor Analysis, 341 Appendix A.

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In Section 6.2, we provide a brief introduction of Brownian motion, which is also known as a Wiener process. We then discuss some diffusion equations and stochastic calculus, including the well-known Ito’s lemma. Most option pricing formulas are derived under the assumption that the 221 222 CONTINUOUS - TIME MODELS price of an asset follows a diffusion equation. We use the Black–Scholes formula to demonstrate the derivation. Finally, to handle the price variations caused by rare events (e.g., a profit warning), we also study some simple diffusion models with jumps. If the price of an asset follows a diffusion equation, then the price of an option contingent to the asset can be derived by using hedging methods.

Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street
by William Poundstone
Published 18 Sep 2006

Thorp had not included this because the over-the-counter options he traded did not credit the trader with the short-sale proceeds. The rules were changed when options began trading on the Chicago Board of Exchange. Black and Scholes accounted for this. Otherwise, the formulas were equivalent. The Black-Scholes formula, as it was quickly christened, was published in 1973. That name deprived both Merton and Thorp of credit. In Merton’s case, it was a matter of courtesy. Because he had built on Black and Scholes’s work, he delayed publishing his derivation until their article appeared. Merton published his paper in a new journal that was being started by AT&T, the Bell Journal of Economics and Management Science.

…

“I never thought about credit, actually,” Thorp said, “and the reason is that I came from outside the economics and finance profession. The great importance that was attached to this problem wasn’t part of my thinking. What I saw was a way to make a lot of money.” Man vs. Machine FEW THEORETICAL FINDINGS changed finance so greatly as the Black-Scholes formula. Texas Instruments soon offered a handheld calculator with the formula programmed in. The market in options, warrants, and convertible bonds became more efficient. This made it harder for people like Thorp to find arbitrage opportunities. Of necessity, Thorp was constantly moving from one type of trade to another.

…

In some cases, the funds’ trading is dictated completely by computer printouts, which not only suggest the proper position but also estimate its probable annual return. “The more we can run the money by remote control the better,” Mr. Thorp declares. The Journal linked Thorp’s operation to “an incipient but growing switch in money management to a quantitative, mechanistic approach.” It mentioned that the Black-Scholes formula was being used by at least two big Wall Street houses (Goldman Sachs and Donaldson, Lufkin & Jenrette). The latter’s Mike Gladstein offered the defensive comment that the brainy formula was “just one of many tools” they used. “The whole computer-model bit is ridiculous because the real investment world is too complicated to be reduced to a model,” an unnamed mutual fund manager was quoted as saying.

I.O.U.: Why Everyone Owes Everyone and No One Can Pay
by John Lanchester
Published 14 Dec 2009

The interacting factors of time, risk, interest rates, and price volatility were so complex that they defeated mathematicians until Fischer Black and Myron Scholes published their paper in 1973, one month after the Chicago Board Options Exchange had opened for business. The revolutionary aspect of Black and Scholes’s paper was an equation enabling people to calculate the price of financial derivatives based on the value of the underlying assets. The Black-Scholes formula opened up a whole new area of derivatives trading. It was a defining moment in the mathematization of the market. Within months, traders were using equations and vocabulary straight out of Black-Scholes (as it is now universally known) and the worldwide derivatives business took off like a rocket.

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INDEX accounting, 26, 28, 106, 231 Against the Gods (Bernstein), 149 AIG: bailout of, 39, 76–78 in CDS market, 75–78, 201 aircraft industry, 227 Alternative Mortgage Transaction Parity Act (AMPTA), 100 Animal Spirits (Akerlof and Shiller), 145n Annie Hall, 1–2 Apple, 34 appraisals, 128 arbitrage, 54–55 arms manufacturing, 200 Arthur Andersen, 106 Asano, Yukio, 18 asset price bubble, 176–77 assets, 10, 25–42, 106, 176 in balance sheets, 25–34, 37–38, 70, 120 banks and, 25, 32–42, 70, 74, 120, 194 of businesses, 29–30, 34 derivatives and, 38, 48–50, 52, 57–58, 120, 205–6 housing and, 96, 126, 130, 176–77 intangible, 30 leverage and, 35–36, 41 liquidity and, 28–29 risk and, 37, 146, 165 toxic, 37–38, 42, 75, 165, 189 ATMs, 7–9, 176 Austen Riggs Center, 140–41 automobiles, automobile industry, 1–2, 24, 40, 134, 197, 222 in balance sheets, 27–28 stocks in, 148–49 balance sheets, 25–35 banks and, 25–34, 37–39, 41–42, 70, 120, 205–7 of businesses, 29–34, 37, 106 of individuals, 27–29, 35 Baltimore, Md., 83–86, 127, 129, 163 Bankers Trust, 150 banking, bankers, banks, 19–22, 24–43, 169, 171–78, 216–20, 222–30 assets and, 25, 32–42, 70, 74, 120, 194 ATMs of, 7–9, 176 bailouts of, 32, 39–41, 77, 120, 204, 212, 219–20, 225–26 balance sheets and, 25–34, 37–39, 41–42, 70, 120, 205–7 of Canada, 116, 211–12 central, 36, 40, 52, 92, 102, 142, 167, 172–78, 180–81, 183, 189, 194–95, 206 check-clearing system of, 33 collapses of, 5, 39, 75, 78, 94, 180, 194, 204, 206, 225 credit and, 37, 41, 43, 209, 211 customer deposits of, 25, 27, 31–34, 74, 187, 224 derivatives and, 20, 51–54, 57–58, 63–71, 74–75, 77, 79, 115–17, 120–21, 132, 183–84, 200, 205–6, 211 economic centrality of, 24–26, 41 of Europe, 8, 35–36, 40, 51, 77, 83, 92, 120, 227 financial industry’s ascent and, 20–21 Glass-Steagall Act on, 64–65, 187–88, 200 holding, 40 housing and, 83–84, 86, 89, 91–95, 102, 126–27, 129–31, 174, 177, 194, 216–17 Iceland’s economic crisis and, 9–12, 24, 40 incentives and bonuses of, 19, 37, 76–78, 206–8, 224, 228 interest rates and, 24, 172–78 investment, 19, 39–40, 65, 77–78, 186–87, 163, 190, 200, 224–25, 227–28 lending of, 22, 24, 27, 33–36, 41–42, 58–60, 67, 69–70, 74, 83–84, 91–94, 102, 117, 127, 129–30, 143, 146, 165, 187, 216–17, 229 leverage of, 35–36, 41–42, 70, 190 mathematicization of, 53–54 narrow, 224–25 nationalization of, 39–40, 228–30 nonbank, 22, 201, 205, 224 paying the bill and, 219–20, 223 regulation and, 21, 33, 180–91, 194–96, 199–200, 202, 204–5, 208, 211, 223–27 risk and, 19, 34–37, 41, 133, 135–36, 143, 150–54, 156–57, 160, 165–66, 174, 187–88, 191–95, 202, 204–7, 216, 224, 226, 228, 230 of U.K., 5, 11, 32–36, 38–40, 51–54, 76–77, 89, 94, 120, 146, 180, 194–96, 199, 202, 204–6, 211–12, 217, 227–28 of U.S., 36–37, 39–40, 43, 63–71, 73, 75, 77–78, 84, 116, 120–21, 127, 150, 152, 163, 183, 185, 190, 195, 204, 211–12, 219–20, 225, 227–28 wish list of, 186–87, 195 zombie, 43, 229 banking-and-credit crisis, 192–96, 215–21, 225–28, 231 aftermath of, 215–17 bases of, 201–2 causes of, 182–83, 186, 196, 205–7, 217 economists on, 192–94 failure in forecasting of, 193–94, 211 journalists on, 192–93 profits in, 78, 227–28 and regulation, 182–83, 194–96, 202, 205, 211, 225–26 and risk, 192–95, 202, 205–7, 216 Bank of America, 39 Bank of England, 36, 52, 102, 167, 177–78, 206 and banking-and-credit crisis, 194–95 and interest rates, 178, 180 and regulation, 180–81, 195 Barclays, Barclays Bank, 11, 35–36, 77, 146, 227 Baring, Peter, 52 Barings Bank, 51–52, 54, 180 Barofsky, Neil, 219 Basel rules, 154, 208 derivatives and, 67–68, 120, 183 Bear Stearns, 39, 190 Belair-Edison Community Association, 127 Belgium, 40 Bell, Madison Smartt, 89 bell curve, 154–56, 160 Berlin Wall, fall of, 12, 16, 18, 23 Bernstein, Peter, 149 “Big Bang,” 22, 195–96, 200–201 Bitner, Richard, 124–27, 131 Black, Conrad, 59 Black, Fischer, 45, 47–48, 147 Black-Scholes formula, 48, 54, 116–17, 151 Blank, Victor, 40 BNP Paribas, 36, 77 bond market, bonds, 20, 22–23, 58–59, 73, 107–12 Broad Index Secured Trust Offering (BISTRO), 70–71, 121 corporate, 154, 210 derivatives and, 58, 63–67, 112, 114, 118–19, 210–11 of governments, 29–30, 61–62, 103, 109, 118, 144, 176–77, 208 incentives and, 209–11 investing and, 62–63, 102–3, 107–8, 111, 208–9 investment grade, 62 junk, 42, 62, 208 prices and, 61, 63, 102–3, 108–10, 144 in raising capital, 59, 61–63, 102–3 ratings of, 61–63, 114, 118–19, 208–11 risk and, 61–63, 103, 118, 144, 154, 208 Russia’s default and, 55–56, 162, 164–65 bonuses, 19, 37, 76–78, 207, 218, 224, 228 Bradford & Bingley, 40 Bragason, Valgarður, 10–11 British Airways, 199 Brown, Gordon, 12, 33, 88, 178 Buffett, Warren, 150 credit rating of, 123, 125 derivatives and, 56–57, 78 Bush, George W., 2, 78, 99, 142, 203, 219 regulation and, 19–20, 191, 195 businesses, 15, 58–63, 105–6, 187, 198–99, 221 balance sheets of, 29–34, 37, 106 banks and, 195, 229 bonds and, 59, 61–63, 102–3, 154, 208, 210 derivatives and, 112, 114, 153 lending to, 41–42, 60, 108 offshore, 70, 72 regulation and, 183, 195 risk and, 37, 145, 150–51, 153–54, 195 Canada, banks of, 116, 211–12 capitalism, 12–19, 116 banks and, 19, 25, 182–83, 202, 218, 228, 231 communism vs., 12, 16–17 failure of, 228, 230 free-market, 13–19, 21, 23–24, 96, 105n, 143, 173–75, 184, 192, 196, 202–4, 230–32 in Hong Kong, 13–14 laissez-faire, 142–43, 173, 182–83, 189, 191, 195–96, 202, 211–12 Marxist analysis of, 15–16 regulation and, 182, 192 as secular religion, 202–4 success and spread of, 14–15, 18–19, 21, 23–24 Carville, James, 22–23 cash ratios, 25 Cassano, Joseph, 201 check-clearing systems, 33 Chicago Board Options Exchange, 48 Chicago Mercantile Exchange, 47 China, People’s Republic of, 115, 124 economic boom in, 3–4, 14, 108–9 Hong Kong and, 13–14 U.S. investment of, 109, 176–77 Cisneros, Henry, 99 Citigroup, 120, 163, 219–20, 227 Citron, Robert, 51 City of London, 32, 195–97, 199–202, 217–18 and banking-and-credit crisis, 205–6 and Big Bang, 195–96, 200–201 derivatives and, 56–57, 79, 201 and financial vs. industrial interests, 197, 199 ideological hegemony of, 21–23 Wimbledonization of, 195–96 Civil Justice Network, 85, 128–29, 131 Cleveland, Ohio, 83 Clinton, Bill, 22, 43, 107 housing and, 99–100 regulation and, 19–20 Coggan, Philip, 25 cognitive illusions, 141–42 Cold War, 201–2 end of, 16, 18, 21, 164 collateralized debt obligations (CDOs), 183, 201, 210–12 bonds and, 112, 114, 118–19, 210–11 of CDOs, 119, 206 Gaussian copula function and, 116–17, 157–60, 163 mathematics and, 115–16 mortgages and, 75–76, 112–22, 132, 157, 159–60, 172, 210 risk and, 114–15, 117–22, 158–60, 163, 167, 212 securitization and, 113–14, 11719, 122 shortage of borrowers for, 121–22 tranching and, 117–18, 122 commodities, 227 derivatives and, 47, 49n, 51–52, 184 prices of, 3–4, 107–8, 148–49 Commodity Futures Modernization Act, 184 communism, 12, 16–18, 23 competition, 58, 96, 105n, 203, 226–27 regulation and, 187–88, 226 Confessions of a Subprime Lender (Bitner), 124, 127 Congress, U.S., 77, 100, 204 regulation and, 184–86 risk and, 142–43, 164–66 conservatism, housing and, 98 correlation, correlations: CDOs and, 115–16, 158, 167 risk and, 74, 148–49, 158–59, 165, 167 credit, 8, 169–73 banks and, 24–26, 37, 41, 43, 209, 211 bubbles in, 42, 60, 109, 170, 176, 216–17, 221, 223 CDOs and, 114–15, 119–20, 172 crunch in, 37, 41, 43, 54n, 77, 84–86, 92–93, 94n, 136, 163–64, 169, 171–73, 182, 193, 201–2, 215–16, 218–19 histories and ratings on, 85, 100, 123–26, 158, 163, 165, 208–11 housing and, 84–86, 92–93, 94n, 100, 109, 112, 125, 129–30, 132, 163–64 Iceland’s economic crisis and, 10–12 interest rates and, 172–73, 175, 209 risk and, 136, 158, 165 see also banking-and-credit crisis Crédit Agricole, 36 credit cards, 27, 217 credit ratings and, 123–24 Iceland’s economic crisis and, 9, 11–12 risk and, 158–59, 163 credit default swaps (CDSs), 20, 63, 65–80, 117, 158–59, 183–86 AIG and, 75–78, 201 attractive aspects of, 72–74 examples of, 57–58 Exxon deal and, 67–70, 121 over-the-counter trading of, 184–85, 201 regulation and, 68, 70, 73, 184–86 risk and, 58, 66–70, 72–75, 78–80, 212 securitized bundles of, 69–70, 74 streamlining and industrializing of, 68–69 unfortunate side effect of, 74–75 Credit Suisse, 36, 227 Cuomo, Andrew, 99 Cutter family, 126–27 Darling, Alistair, 172, 220 debt, debts, 27–29, 34, 59–63, 118, 172n, 179, 216, 229 in balance sheets, 27–28, 30–31 benefits of, 59–61 bonds and, 59, 61–63, 208, 210 credit and, 123–26, 221 derivatives and, 52, 67, 69–72 housing and, 93, 100, 132, 176 paying the bill and, 220–22 personal, 221–22 regulation and, 181, 190 Russian default on, 55–56, 162, 164–65 see also collateralized debt obligations default, defaults, default rates, 162–65 CDOs and, 114–15 on mortgages, 159–60, 163, 165, 229 risk and, 154, 159–60, 163 of Russia, 55–56, 162, 164–65 see also credit default swaps Demchak, William, 69 democracy, democracies, 15–18, 108–9, 179, 213 free-market capitalism and, 15, 17, 23 housing and, 87, 98 DePastina, Anthony, 85 Depository Institutions Deregulation and Monetary Control Act (DIDMCA), 100 deregulation, see regulation, deregulation derivatives, 45–58, 63–80, 86, 210–12 in balance sheets, 30–31, 70 banks and, 20, 51–54, 57–58, 63–71, 74–75, 77, 79, 115–17, 120–21, 132, 183–84, 200, 205–6, 211 Black-Scholes formula and, 48, 54, 116–17, 151 bonds and, 58, 63–67, 112, 114, 118–19, 210–11 Buffett and, 56–57, 78 and City of London, 56–57, 79, 201 complexity of, 52–54, 56–57 Enron and, 56, 105–6, 185 futures and, 46–47, 49n, 51–52, 54, 184 Greenspan on, 166, 183–84 in history, 45–48, 147 mathematics and, 47–48, 52–54, 115–17, 166 offshore companies and, 70, 72 options and, 46–47, 50–52, 151, 174, 184 over-the-counter trading of, 184–85, 201, 205–6 prices and, 38, 46–52, 54, 56, 75, 158–59, 166 regulation and, 68, 70, 73, 153, 183–86, 200–201 risk and, 46–47, 49–52, 54–55, 57–58, 66–75, 78–80, 114–15, 117–22, 151, 153, 158–60, 163, 166–67, 184–85, 205, 212 size of market in, 48, 56, 80, 117, 201 see also collateralized debt obligations; credit default swaps Detroit, Mich., 81–82 Deutsche Bank, 36, 77, 83, 227 diversification, 146–48, 177 dividends, 101, 147–48 Doctorow, E.

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INDEX accounting, 26, 28, 106, 231 Against the Gods (Bernstein), 149 AIG: bailout of, 39, 76–78 in CDS market, 75–78, 201 aircraft industry, 227 Alternative Mortgage Transaction Parity Act (AMPTA), 100 Animal Spirits (Akerlof and Shiller), 145n Annie Hall, 1–2 Apple, 34 appraisals, 128 arbitrage, 54–55 arms manufacturing, 200 Arthur Andersen, 106 Asano, Yukio, 18 asset price bubble, 176–77 assets, 10, 25–42, 106, 176 in balance sheets, 25–34, 37–38, 70, 120 banks and, 25, 32–42, 70, 74, 120, 194 of businesses, 29–30, 34 derivatives and, 38, 48–50, 52, 57–58, 120, 205–6 housing and, 96, 126, 130, 176–77 intangible, 30 leverage and, 35–36, 41 liquidity and, 28–29 risk and, 37, 146, 165 toxic, 37–38, 42, 75, 165, 189 ATMs, 7–9, 176 Austen Riggs Center, 140–41 automobiles, automobile industry, 1–2, 24, 40, 134, 197, 222 in balance sheets, 27–28 stocks in, 148–49 balance sheets, 25–35 banks and, 25–34, 37–39, 41–42, 70, 120, 205–7 of businesses, 29–34, 37, 106 of individuals, 27–29, 35 Baltimore, Md., 83–86, 127, 129, 163 Bankers Trust, 150 banking, bankers, banks, 19–22, 24–43, 169, 171–78, 216–20, 222–30 assets and, 25, 32–42, 70, 74, 120, 194 ATMs of, 7–9, 176 bailouts of, 32, 39–41, 77, 120, 204, 212, 219–20, 225–26 balance sheets and, 25–34, 37–39, 41–42, 70, 120, 205–7 of Canada, 116, 211–12 central, 36, 40, 52, 92, 102, 142, 167, 172–78, 180–81, 183, 189, 194–95, 206 check-clearing system of, 33 collapses of, 5, 39, 75, 78, 94, 180, 194, 204, 206, 225 credit and, 37, 41, 43, 209, 211 customer deposits of, 25, 27, 31–34, 74, 187, 224 derivatives and, 20, 51–54, 57–58, 63–71, 74–75, 77, 79, 115–17, 120–21, 132, 183–84, 200, 205–6, 211 economic centrality of, 24–26, 41 of Europe, 8, 35–36, 40, 51, 77, 83, 92, 120, 227 financial industry’s ascent and, 20–21 Glass-Steagall Act on, 64–65, 187–88, 200 holding, 40 housing and, 83–84, 86, 89, 91–95, 102, 126–27, 129–31, 174, 177, 194, 216–17 Iceland’s economic crisis and, 9–12, 24, 40 incentives and bonuses of, 19, 37, 76–78, 206–8, 224, 228 interest rates and, 24, 172–78 investment, 19, 39–40, 65, 77–78, 186–87, 163, 190, 200, 224–25, 227–28 lending of, 22, 24, 27, 33–36, 41–42, 58–60, 67, 69–70, 74, 83–84, 91–94, 102, 117, 127, 129–30, 143, 146, 165, 187, 216–17, 229 leverage of, 35–36, 41–42, 70, 190 mathematicization of, 53–54 narrow, 224–25 nationalization of, 39–40, 228–30 nonbank, 22, 201, 205, 224 paying the bill and, 219–20, 223 regulation and, 21, 33, 180–91, 194–96, 199–200, 202, 204–5, 208, 211, 223–27 risk and, 19, 34–37, 41, 133, 135–36, 143, 150–54, 156–57, 160, 165–66, 174, 187–88, 191–95, 202, 204–7, 216, 224, 226, 228, 230 of U.K., 5, 11, 32–36, 38–40, 51–54, 76–77, 89, 94, 120, 146, 180, 194–96, 199, 202, 204–6, 211–12, 217, 227–28 of U.S., 36–37, 39–40, 43, 63–71, 73, 75, 77–78, 84, 116, 120–21, 127, 150, 152, 163, 183, 185, 190, 195, 204, 211–12, 219–20, 225, 227–28 wish list of, 186–87, 195 zombie, 43, 229 banking-and-credit crisis, 192–96, 215–21, 225–28, 231 aftermath of, 215–17 bases of, 201–2 causes of, 182–83, 186, 196, 205–7, 217 economists on, 192–94 failure in forecasting of, 193–94, 211 journalists on, 192–93 profits in, 78, 227–28 and regulation, 182–83, 194–96, 202, 205, 211, 225–26 and risk, 192–95, 202, 205–7, 216 Bank of America, 39 Bank of England, 36, 52, 102, 167, 177–78, 206 and banking-and-credit crisis, 194–95 and interest rates, 178, 180 and regulation, 180–81, 195 Barclays, Barclays Bank, 11, 35–36, 77, 146, 227 Baring, Peter, 52 Barings Bank, 51–52, 54, 180 Barofsky, Neil, 219 Basel rules, 154, 208 derivatives and, 67–68, 120, 183 Bear Stearns, 39, 190 Belair-Edison Community Association, 127 Belgium, 40 Bell, Madison Smartt, 89 bell curve, 154–56, 160 Berlin Wall, fall of, 12, 16, 18, 23 Bernstein, Peter, 149 “Big Bang,” 22, 195–96, 200–201 Bitner, Richard, 124–27, 131 Black, Conrad, 59 Black, Fischer, 45, 47–48, 147 Black-Scholes formula, 48, 54, 116–17, 151 Blank, Victor, 40 BNP Paribas, 36, 77 bond market, bonds, 20, 22–23, 58–59, 73, 107–12 Broad Index Secured Trust Offering (BISTRO), 70–71, 121 corporate, 154, 210 derivatives and, 58, 63–67, 112, 114, 118–19, 210–11 of governments, 29–30, 61–62, 103, 109, 118, 144, 176–77, 208 incentives and, 209–11 investing and, 62–63, 102–3, 107–8, 111, 208–9 investment grade, 62 junk, 42, 62, 208 prices and, 61, 63, 102–3, 108–10, 144 in raising capital, 59, 61–63, 102–3 ratings of, 61–63, 114, 118–19, 208–11 risk and, 61–63, 103, 118, 144, 154, 208 Russia’s default and, 55–56, 162, 164–65 bonuses, 19, 37, 76–78, 207, 218, 224, 228 Bradford & Bingley, 40 Bragason, Valgarður, 10–11 British Airways, 199 Brown, Gordon, 12, 33, 88, 178 Buffett, Warren, 150 credit rating of, 123, 125 derivatives and, 56–57, 78 Bush, George W., 2, 78, 99, 142, 203, 219 regulation and, 19–20, 191, 195 businesses, 15, 58–63, 105–6, 187, 198–99, 221 balance sheets of, 29–34, 37, 106 banks and, 195, 229 bonds and, 59, 61–63, 102–3, 154, 208, 210 derivatives and, 112, 114, 153 lending to, 41–42, 60, 108 offshore, 70, 72 regulation and, 183, 195 risk and, 37, 145, 150–51, 153–54, 195 Canada, banks of, 116, 211–12 capitalism, 12–19, 116 banks and, 19, 25, 182–83, 202, 218, 228, 231 communism vs., 12, 16–17 failure of, 228, 230 free-market, 13–19, 21, 23–24, 96, 105n, 143, 173–75, 184, 192, 196, 202–4, 230–32 in Hong Kong, 13–14 laissez-faire, 142–43, 173, 182–83, 189, 191, 195–96, 202, 211–12 Marxist analysis of, 15–16 regulation and, 182, 192 as secular religion, 202–4 success and spread of, 14–15, 18–19, 21, 23–24 Carville, James, 22–23 cash ratios, 25 Cassano, Joseph, 201 check-clearing systems, 33 Chicago Board Options Exchange, 48 Chicago Mercantile Exchange, 47 China, People’s Republic of, 115, 124 economic boom in, 3–4, 14, 108–9 Hong Kong and, 13–14 U.S. investment of, 109, 176–77 Cisneros, Henry, 99 Citigroup, 120, 163, 219–20, 227 Citron, Robert, 51 City of London, 32, 195–97, 199–202, 217–18 and banking-and-credit crisis, 205–6 and Big Bang, 195–96, 200–201 derivatives and, 56–57, 79, 201 and financial vs. industrial interests, 197, 199 ideological hegemony of, 21–23 Wimbledonization of, 195–96 Civil Justice Network, 85, 128–29, 131 Cleveland, Ohio, 83 Clinton, Bill, 22, 43, 107 housing and, 99–100 regulation and, 19–20 Coggan, Philip, 25 cognitive illusions, 141–42 Cold War, 201–2 end of, 16, 18, 21, 164 collateralized debt obligations (CDOs), 183, 201, 210–12 bonds and, 112, 114, 118–19, 210–11 of CDOs, 119, 206 Gaussian copula function and, 116–17, 157–60, 163 mathematics and, 115–16 mortgages and, 75–76, 112–22, 132, 157, 159–60, 172, 210 risk and, 114–15, 117–22, 158–60, 163, 167, 212 securitization and, 113–14, 11719, 122 shortage of borrowers for, 121–22 tranching and, 117–18, 122 commodities, 227 derivatives and, 47, 49n, 51–52, 184 prices of, 3–4, 107–8, 148–49 Commodity Futures Modernization Act, 184 communism, 12, 16–18, 23 competition, 58, 96, 105n, 203, 226–27 regulation and, 187–88, 226 Confessions of a Subprime Lender (Bitner), 124, 127 Congress, U.S., 77, 100, 204 regulation and, 184–86 risk and, 142–43, 164–66 conservatism, housing and, 98 correlation, correlations: CDOs and, 115–16, 158, 167 risk and, 74, 148–49, 158–59, 165, 167 credit, 8, 169–73 banks and, 24–26, 37, 41, 43, 209, 211 bubbles in, 42, 60, 109, 170, 176, 216–17, 221, 223 CDOs and, 114–15, 119–20, 172 crunch in, 37, 41, 43, 54n, 77, 84–86, 92–93, 94n, 136, 163–64, 169, 171–73, 182, 193, 201–2, 215–16, 218–19 histories and ratings on, 85, 100, 123–26, 158, 163, 165, 208–11 housing and, 84–86, 92–93, 94n, 100, 109, 112, 125, 129–30, 132, 163–64 Iceland’s economic crisis and, 10–12 interest rates and, 172–73, 175, 209 risk and, 136, 158, 165 see also banking-and-credit crisis Crédit Agricole, 36 credit cards, 27, 217 credit ratings and, 123–24 Iceland’s economic crisis and, 9, 11–12 risk and, 158–59, 163 credit default swaps (CDSs), 20, 63, 65–80, 117, 158–59, 183–86 AIG and, 75–78, 201 attractive aspects of, 72–74 examples of, 57–58 Exxon deal and, 67–70, 121 over-the-counter trading of, 184–85, 201 regulation and, 68, 70, 73, 184–86 risk and, 58, 66–70, 72–75, 78–80, 212 securitized bundles of, 69–70, 74 streamlining and industrializing of, 68–69 unfortunate side effect of, 74–75 Credit Suisse, 36, 227 Cuomo, Andrew, 99 Cutter family, 126–27 Darling, Alistair, 172, 220 debt, debts, 27–29, 34, 59–63, 118, 172n, 179, 216, 229 in balance sheets, 27–28, 30–31 benefits of, 59–61 bonds and, 59, 61–63, 208, 210 credit and, 123–26, 221 derivatives and, 52, 67, 69–72 housing and, 93, 100, 132, 176 paying the bill and, 220–22 personal, 221–22 regulation and, 181, 190 Russian default on, 55–56, 162, 164–65 see also collateralized debt obligations default, defaults, default rates, 162–65 CDOs and, 114–15 on mortgages, 159–60, 163, 165, 229 risk and, 154, 159–60, 163 of Russia, 55–56, 162, 164–65 see also credit default swaps Demchak, William, 69 democracy, democracies, 15–18, 108–9, 179, 213 free-market capitalism and, 15, 17, 23 housing and, 87, 98 DePastina, Anthony, 85 Depository Institutions Deregulation and Monetary Control Act (DIDMCA), 100 deregulation, see regulation, deregulation derivatives, 45–58, 63–80, 86, 210–12 in balance sheets, 30–31, 70 banks and, 20, 51–54, 57–58, 63–71, 74–75, 77, 79, 115–17, 120–21, 132, 183–84, 200, 205–6, 211 Black-Scholes formula and, 48, 54, 116–17, 151 bonds and, 58, 63–67, 112, 114, 118–19, 210–11 Buffett and, 56–57, 78 and City of London, 56–57, 79, 201 complexity of, 52–54, 56–57 Enron and, 56, 105–6, 185 futures and, 46–47, 49n, 51–52, 54, 184 Greenspan on, 166, 183–84 in history, 45–48, 147 mathematics and, 47–48, 52–54, 115–17, 166 offshore companies and, 70, 72 options and, 46–47, 50–52, 151, 174, 184 over-the-counter trading of, 184–85, 201, 205–6 prices and, 38, 46–52, 54, 56, 75, 158–59, 166 regulation and, 68, 70, 73, 153, 183–86, 200–201 risk and, 46–47, 49–52, 54–55, 57–58, 66–75, 78–80, 114–15, 117–22, 151, 153, 158–60, 163, 166–67, 184–85, 205, 212 size of market in, 48, 56, 80, 117, 201 see also collateralized debt obligations; credit default swaps Detroit, Mich., 81–82 Deutsche Bank, 36, 77, 83, 227 diversification, 146–48, 177 dividends, 101, 147–48 Doctorow, E.

Transaction Man: The Rise of the Deal and the Decline of the American Dream
by Nicholas Lemann
Published 9 Sep 2019

By purchasing derivatives, one could protect oneself against the potential losses that a straightforward portfolio of assets inescapably entailed. The Black-Scholes formulas could help determine the price of a derivative in a scientific way, and also the precise mix of assets and derivatives that would most reduce the risk in a portfolio. The cause they felt they were serving was reducing the beta, or volatility, of stock and bond holdings. As complicated as the Black-Scholes formula was, the next and final major breakthrough in financial economics was even more complicated. It was invented by Robert C. Merton, a colleague of Scholes’s at MIT.

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Merton, a colleague of Scholes’s at MIT. Merton adopted techniques developed by a Japanese mathematician named Kiyosi Itô (the only previous practical application of whose work was in plotting the trajectories of rockets) that allowed for “dynamic modeling” of the Black-Scholes formula, meaning that all the elements in a portfolio would be constantly recalculated and readjusted as conditions in the markets changed. By this time, the early 1970s, the power of computers had increased so much that the work of Black, Scholes, and Merton (all of whom later won the Nobel Prize in economics for these discoveries) did not sit on a shelf for years, as had the work of the other pioneer financial economists.

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Berle, Beatrice Bishop; diary entries of; work of Bernanke, Ben Bernard, Lewis Bernstein, Peter beta, as economic term Biden, Joe Big Business (Lilienthal) Big Short, The (Lewis) Bilderberg (conference) Binger, Carl bin Laden, Osama Bishop, Amy Bend Bishop, Cortlandt Black, Fischer black Americans, discrimination faced by; in housing; in policing Black Monday Black Panthers Black-Scholes formula Blackstone Blagojevich, Rod Blankenbeckler, Frank Blankfein, Lloyd blitzscaling Bloom, Ron Bloomberg, Michael Bohac, Ben bonds; as fixed-income; high-risk; in WWI Booth, David Bork, Robert Born, Brooksley Boyce, Neith Brandeis, Louis D.; as anti-bigness; on Other People’s Money; political maneuvering by; revival of ideas of; taxation advocated by Branson, Richard Breyer, Stephen Brin, Sergey broadcasting, regulation of Brody, Ken Bryan, William Jennings Buddhism Buffett, Warren Buick Bullitt, William bureaucrats; accountability to market; as ruling class; suspicion of; see also executives Burke, Edmund Burke, Edward Burnham, James Bush, George H.

The Investopedia Guide to Wall Speak: The Terms You Need to Know to Talk Like Cramer, Think Like Soros, and Buy Like Buffett
by Jack (edited By) Guinan
Published 27 Jul 2009

For example, currency is considered the most liquid asset in the world; thus, currency spreads are very narrow (one-hundredth of a percent). In contrast, less liquid assets such as a small-cap stock will have wider spreads, sometimes as high as 1 to 2% of the asset’s value. Related Terms: • Ask • Market Maker • New York Stock Exchange—NYSE • Bid • Pink Sheets Black Scholes Model What Does Black Scholes Model Mean? A model of price variation over time in financial instruments such as stocks that often is used to calculate the price of a European call option. The model assumes that the price of heavily traded assets follows a geometric Brownian motion with constant drift and volatility.

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The model assumes that the price of heavily traded assets follows a geometric Brownian motion with constant drift and volatility. When applied to a stock option, the model incorporates the constant price variation of the stock, the time value of money, the option’s strike price, and the time to the option’s expiration. Also known as the Black-Scholes-Merton Model. Investopedia explains Black Scholes Model The Black Scholes Model is one of the most important concepts in modern financial theory. It was developed in 1973 by Fisher Black, Robert Merton, and Myron Scholes and is used widely today and regarded as one of the best formulas for determining option prices. Related Terms: • Exercise • Standard Deviation • Strike Price • Option • Stock Option 24 The Investopedia Guide to Wall Speak Blue-Chip Stock What Does Blue-Chip Stock Mean?

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This is due to the common belief that bearish markets are more risky than bullish markets. In addition to known factors such as market price, interest rate, expiration date, and strike price, implied volatility is used in calculating an option’s premium. IV can be derived from a model such as the Black Scholes Model. Implied volatility sometimes is referred to as vols. Related Terms: • Beta • Options • Volatility • Black Scholes Model • Stock Option In the Money What Does In the Money Mean? The state of a call option when its strike price is below the market price of the underlying asset. For put options, it is the state when the strike price is above the market price of the underlying asset.

Escape From Model Land: How Mathematical Models Can Lead Us Astray and What We Can Do About It
by Erica Thompson
Published 6 Dec 2022

The idea that the model itself is not just a tool but an active participant in the decision-making process has been described as ‘performativity’. In later chapters we will meet several examples of performative models, from the Black–Scholes model of option pricing to Integrated Assessment Models of energy and climate. Sociologist Donald MacKenzie described the Black–Scholes model as ‘an engine, not a camera’ for the way that it was used not just to describe prices but directly to construct them. This is a strong form of performativity, more like a self-fulfilling prophecy, where the use of the model directly shapes the real-world outcome in its own image.

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Just as arbitrage in the real world encourages convergence of prices, so the widespread adoption of Black–Scholes option pricing in the 1970s encouraged convergence of the real world with the model. Traders who believed that the Black–Scholes price represented ‘the right price’ for an option would buy contracts under that price, driving the price up, and then sell contracts over that price, driving it down again. Sociologist Donald MacKenzie famously identified the Black–Scholes model as a performative agent – ‘an engine, not a camera’. Rather than being an external representation of market forces, it became in itself a self-fulfilling market force, changing the behaviour of traders and influencing prices. In MacKenzie’s language, the traders’ use of the model actually ‘performed’ the model and caused it to be correct.

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In addition, the 1970s and 1980s were a time when the frictions of transaction were being driven down, directly improving the realism of Black and Scholes’s assumptions. Costs and commissions were being removed, communications improved, and electronic and automatic transactions becoming more common. In the decade leading up to the summer of 1987, the theoretical descriptions of the Black–Scholes model were remarkably close to realised market prices for options. That’s not to say there was only one single theoretical prediction. Because the Black–Scholes equation derives option prices as a function of the observed volatility (variability) of previous share prices, we still have the question of how long a period to use to fit the volatility parameter.

A Man for All Markets
by Edward O. Thorp
Published 15 Nov 2016

These options, like the call options we were already trading, were called American options, as distinguished from European options. European options can be exercised only during a short settlement period just prior to expiration, whereas American options can be exercised anytime during their life. If the underlying stock pays no dividends, the Black-Scholes formula, which is for the European call option, turns out to coincide with the formula for the American call option, which is the type that trades on the CBOE. A formula for the European put option can be obtained using the formula for the European call option. But the math for American put options differs from that for European put options, and—even now—no general formula has ever been found.

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It was as though the sun suddenly winked out or the earth stopped spinning. They described stock prices using a distribution of probabilities with the esoteric name lognormal. This did a good job of fitting historical price changes that ranged from small to rather large, but greatly underestimated the likelihood of very large changes. Financial models like the Black-Scholes formula for option prices were built using the lognormal. Aware of this limitation in academia’s model of stock prices, as part of the indicators project we had found a much better fit to the historical stock price data, especially for the relatively rare large changes in price. So even though I was surprised by the giant drop, I wasn’t nearly as shocked as most.

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Assume you may have an edge only when you can make a rational affirmative case that withstands your attempts to tear it down. Don’t gamble unless you are highly confident you have the edge. As Buffett says, “Only swing at the fat pitches.” 3. Find a superior method of analysis. Ones that you have seen pay off for me include statistical arbitrage, convertible hedging, the Black-Scholes formula, and card counting at blackjack. Other winning strategies include superior security analysis by the gifted few and the methods of the better hedge funds. 4. When securities are known to be mispriced and people take advantage of this, their trading tends to eliminate the mispricing. This means the earliest traders gain the most and their continued trading tends to reduce or eliminate the mispricing.

The Dhandho Investor: The Low-Risk Value Method to High Returns
by Mohnish Pabrai
Published 17 May 2009

The house was civil about taking large losses. The mob wasn’t running the casino. He found that such a casino existed, and it was the New York Stock Exchange (NYSE) and the fledgling options market. Rumor has it that Thorp figured out something along the lines of the Black-Scholes formula years before Black and Scholes did. He decided not to publish his findings. The Black-Scholes formula is, effectively, Basic Strategy for the options market. It dictates what a specific option ought to be priced at. Because he was one of the only players armed with this knowledge, Thorp could buy underpriced options and sell overpriced ones—making a killing in the process.

Money Changes Everything: How Finance Made Civilization Possible
by William N. Goetzmann
Published 11 Apr 2016

The option pricing model is based on the principle of forecasting the range of future outcomes of the stock price by assuming it will follow a random walk that conforms to Regnault’s square-root of time insight. However, the Black-Scholes formula gives a solution to the option price today by mathematically rolling time backward. It reverses entropy. In this, it echoes the most basic trait of finance—it uses mathematics to transcend time. THERMODYNAMICS The Black-Scholes formula was published in 1973, just around the time that the Chicago Board Option Exchange began to trade standardized option contracts. Like Bachelier’s thesis, the path-breaking paper was not at first well received.

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Evidently none knew of Bachelier, and thus they had to retrace the mathematical logic of fair prices and random walks when they began work on the problem of option pricing in the late 1960s. Like Bachelier, they relied on a model of variation in prices—Brownian motion—although unlike Bachelier, they chose one that did not allow prices to become negative—a limitation of Bachelier’s work. The Black-Scholes formula, as it is now referred to, was mathematically sophisticated, but at its heart it contained a novel economic—as opposed to mathematical—insight. They discovered that the invisible hand setting option prices was risk-neutral. Option payoffs could be replicated risklessly, provided one could trade in an ideal, frictionless market in which stocks behaved according to Brownian motion.

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See also Arabic numerals Objectivism, of Ayn Rand, 452 Ohio Company, 388–89 oil income, government investment of, 512 O’Keeffe, Georgia, 468, 475–76, 481 Old Babylonian period, 46, 49, 55–57, 65 Onslow’s Insurance, 370 operations research, 504, 507 opium trade, Chinese, 423, 425–26, 427, 441 Opium Wars, 425–26, 437, 441 option pricing: Bachelier on, 282–83; Black-Scholes formula for, 283–84; Brownian motion and, 276; fractal-based, 287; Lefèvre on, 279–82 options: defined, 280; on Law’s Mississippi Company shares, 357; in seventeenth-century Amsterdam stock market, 317; stock options as compensation, 171 oracle bones, Chinese, 146–47, 271 Ott, Julia, 469–70 owl coins, Athenian, 96–98, 101 Pacioli, Lucca, 246–47 paghe, 291–92 paper instruments, Chinese, 174–75; pawn tickets, 178–79; of Song dynasty, 186–89, 199 paper making and printing, 181–82 paper money: in American colonies, 386–88, 390, 400; Chinese invention of, 139, 168, 174–75, 183–84, 201–2, 400; Chinese nationalization of printing of, 185–86; eighteenth-century comeback of, 382, 399–400; of French revolutionary government, 391–92; of Law’s proposed land bank, 352–53 (see also land banks); Marco Polo’s account of, 191–93; Song dynasty collateral problem with, 387–88; Song dynasty color printing of, 182; of Song dynasty in military crisis, 199.

Smart Money: How High-Stakes Financial Innovation Is Reshaping Our WorldÑFor the Better
by Andrew Palmer
Published 13 Apr 2015

The answer they came up with, expressed as what is now known as the Black-Scholes equation, was based on a simple idea: two things that had identical outcomes ought to cost the same. The price of the option ought to be the same as whatever it cost to construct an investment portfolio that achieved the same end. The Black-Scholes formula enabled the rapid pricing of options and paved the way for explosive growth in derivatives markets. Greek academics have even used it to work out what Thales should have paid for his olive-oil option more than fifteen hundred years ago.25 The third driver was technology. We have seen how a new technology like the railways required finance to adapt in order to provide appropriate financing and screening mechanisms.

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The question of what price to pay for an option was one to which there was no rigorous answer until Black, Scholes, and Merton came along. The answer they came up with, expressed as what is now known as the Black-Scholes equation, was based on the idea that the price of the option ought to be the same as the cost of constructing a perfect hedge for the underlying asset. The Black-Scholes formula, which coincided with the computerization of trading, enabled the rapid pricing of options and paved the way for huge growth in derivatives markets.7 At a time when financial innovation and derivatives have become dirty words, Merton has become practiced at answering the criticisms thrown their way.

Fred Schwed's Where Are the Customers' Yachts?: A Modern-Day Interpretation of an Investment Classic
by Leo Gough
Published 22 Aug 2010

You can now gamble on a huge range of financial derivatives. The future prices of almost anything, from stock indexes to soya beans, are available, and you can construct fantastically complex bets with them. This has come about because of a number of mathematical discoveries, most notably the Black Scholes model, for which its discoverers won a Nobel Prize, which enabled more accurate pricing of these exotic products. The most important thing you should know about derivatives is that they do not represent ‘real’ financial assets that you own. They are contracts – i.e. promises – that are ‘derived’ from real assets, indices or events.

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A Abramovich, Roman 112 accounts, comparing 36–7 AIM (Alternative Investment Market) 70 analysis fundamental analysis 54–5 technical analysis (TA) 40–1 analysts 95, 96 annual reports 36–7 annuities 61 Aristotle 26 Arthur Andersen 53 assets, living off 22–3 astrology, use in predicting share prices 41 Austen, Jane 22 average performance 34–5 average returns 105 B bankers and financial crisis 28–9 banks, merger activity 89 bargains, finding 92–5 Barlow Clowes affair 74, 75 Baruch, Bernard 76 ‘bear raiders’ 82–3 behavioural finance 104–5 benchmarks 35, 87 Bernard, Claude 34 Black Scholes model 32–3 blue chip companies 51, 53 Bogle, John 110 ‘bond washing’ 75 bonds investing in 10–11, 50–2, 53 in the US 80 book value 92 books about the stock market 112–13 booms 18–19 dot.com 30 excessive borrowing in 29 mergers and acquisitions in 88–9 regulators in 85 selling in 76–7 borrowing and the financial crisis 29 British Rail 66–7 Brown, Gordon 18 Buffett, Warren 13, 32, 48, 50, 52, 54, 62, 64, 66, 68, 70, 83, 90, 96, 100, 105, 110 bull markets, new issues in 57 businesses, start-up 106–7 business failure 106 buying high 64–5 C capital raising 24–5 spending 22–3 car manufacturers 67 charting 40–1 China, government bonds 51 ‘churning’ 71– 2 Cisco Systems 90 ‘closed-end’ funds 86 collapses 74–5 collective investment 86–7 companies mergers 88–9 raising capital 24–5 under threat 66–7 compensation for collapses 74–5 compound interest 102 compounding 111 costs of transactions 70–1 counter-cyclical investments 76–7 crashes 28–9 reacting to 108 regulators in 85 credit card debts, during a boom 19 crooks 72–3 see also fraud cycles, economic 19 D debts, during a boom 19 deflationary periods 103 derivatives 32–3, 85 descendants entrusting with money 59 investing for 16–17 Discounted Cash Flow (DCF) 94–5 diversification 48–9 dividend discount model 95 dot.com boom 30 Dow Jones Industrial Average (DJIA) 35 Duttweiler, Rudolph 42 E earnings management 90 Ebbers, Bernard 73 economic cycles 19 economy, growth rate 42–3 Einhorn, David 83 Einstein, Albert 102 Enron 53 equity investment 80–1 estimating returns 80–1 execution-only brokers 71 executives, benefitting from mergers 89 F fact finds 98 false information 72–3, 90, 91 family, building 99 fees, transaction 70–1 Fibonacci numbers 40 figures, ‘managing’ 90–1 financial crisis, who to blame 28–9 financial professionals 96, 98 commissions 72 and investment skills 47, 54–5 risk aversion 58 see also fund managers financial statements 91 Fisher, Irving 56 Fisher, Philip 94, 113 fluctuations in share prices 38–9 Foreman, George 60 Franklin, Benjamin 10 fraud 73, 74–5 and blue chip companies 53 FSA (Financial Services Authority) 14, 74, 83, 84 FTSE 100 64–5 fund managers 35, 54–5, 101 and tracker funds 62 see also financial professionals fundamental analysis 54–5 fundamentals 110 G Garland, Judy 98 ‘gilts’ 50–1 globalisation 78–9 Goldstein, Phil 82 Goldwyn, Sam 40 good stories about companies 42–3 government bonds 10–11, 50–2 in the US 80 Graham, Benjamin 92, 104, 113 growth rate of economies 42–3 Grubman, Jack 73 ‘gurus’ 96–7 H ‘head and shoulders’ pattern 40 hedge funds 33, 82–3, 100–1 Hendrix, Jimi 16 I Icelandic banks 11 income from capital 22–3 index investing 34–5, 62–3, 110, 111 Indonesia 76–7 government bonds 10–11 Industrial Revolution 78 inflation 61 and rate of return 103 Initial Public Offerings (IPOs) 56–7 innovations, investing in 30–1 insurance for investments 74 insurance companies 72 annuities 61 interest calculating 103 on interest 102 rates 11 international diversification 49 international investment 79 internet, investing in 30–1 investment mergers before88–9 collective 86–7 income 10–11 and inflation 61 international 79 long term 16–17, 64–5, 98–9, 102, 111 popular 30–1 risks in 44–5 short term 63 skill in 20–1 trusts 35, 48–9, 58–9, 86 IPOs (Initial Public Offerings) 56–7 J Johnson, Ross 89 K Keynes, J.

Stocks for the Long Run, 4th Edition: The Definitive Guide to Financial Market Returns & Long Term Investment Strategies
by Jeremy J. Siegel
Published 18 Dec 2007

But the theory of options pricing was given a big boost in the 1970s when two academic economists, Fischer Black and Myron Scholes, developed the first mathematical for12 Chapter 16 will discuss a valuable index of option volatility called VIX. 266 PART 4 Stock Fluctuations in the Short Run mula to price options. The Black-Scholes formula was an instant success. It gave traders a benchmark for valuation where previously they used only their intuition. The formula was programmed on traders’ handheld calculators and PCs around the world. Although there are conditions when the formula must be modified, empirical research has shown that the Black-Scholes formula closely approximates the price of traded options. Myron Scholes won the Nobel Prize in Economics in 1997 for his discovery.13 Buying Index Options Options are actually more basic instruments than futures or ETFs.

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.): representative, 326 return, in stock indexes, 46–47 self-attribution, 326 survivorship, 18, 343, 343i Big Board (see New York Stock Exchange [NYSE]) Bikhchandani, S. D., 325n Bill and Melinda Gates Foundation, 7n Bills, interest rates on, 7–9, 9i Birrell, Lowell, 38–39 Black, Fischer, 265, 266n Black-Scholes formula, 266 Blake, Christopher R., 348 Blitzer, David, 107, 108n, 353n Blodget, S., Jr., 7n Blue Chip Economic Indicators, 217, 218 Bodie, Zvi, 35n Bogle, John C., 343n, 348 Bonds: current yield of, 111 equity premium and, 16–18, 17i government, interest rate on, above dividend yield on common stocks, 95–97 inflation-indexed, 35 long-term performance of, 7–9, 9i real returns on, 14–15, 15i return on, correlation with stock returns, 30–32, 31i Russian default on, 88 standard deviation of returns for, 30 stocks’ outperformance of, 26 yields on, stock yields related to, 95–97 (See also Fixed-income assets) Book value, 117 Bos, Roger, J., 353n Bosland, Chelcie C., 82 Boyd, John, 241n BP (British Petroleum), 177, 183 Index BP Amoco, 55 Brealey, Richard A., 171n Bristol Myers, 59n British American Tobacco, 63, 177 Brock, William, 295n, 304n Brown, Stephen J., 18n Browne & Co., 21n Bubbles: stock (see Stock bubbles) technology, 167 Buffett, Warren, 7n, 61, 104, 107, 187q, 268, 359q Bull markets: beginning of, 85–86 from 1982-1999, 14 Bureau of Labor Statistics (BLS), 241 Burns, Arthur, 210n Bush, George W., 69, 75 Business cycle, 207–219, 285 dating of, 208–211 definition of, 209–210 prediction of, 216–219 timing of, gains through, 214–216, 215i turning points of, stock returns around, 211–214, 212i–214i Buy-and-hold returns, 215 Buy and write strategy, 267 Buy programs, 258 Buybacks, 98 CAC index, 238 Calendar anomalies, 305–318 day-of-the-week effects, 316–318, 317i investing strategies for, 318 seasonal, 306–316 California Packing Co., 60i, 62 Calls, 264 Campbell, John Y., 35n, 87, 158 Capital asset pricing model (CAPM), 140, 141 Capital gains taxes: benefits of deferring, 69–70 failure of stocks as long-term inflation hedge and, 204 Capital gains taxes (Cont.): historical, 66, 67i increasingly favorable tax factors for equities and, 72–73 inflation and, 70–72, 71i total after-tax returns index and, 66, 68–69, 68i, 69i Capitalization-weighted indexing, 351–352, 352i fundamentally weighted indexation versus, 353–355 Carnegie, Andrew, 57 Carvell, Tim, 107n Cash flows, from stocks, valuation of, 97–98 Cash market, 257 Cash-settled futures contracts, 257 CBOE Volatility Index, 281–282, 282i Celanese Corp., 60i, 64 Center for Research in Security Prices (CRSP) index, 45, 46i, 141 Central bank policy, 247 (See also Federal Reserve System [Fed]) Chamberlain, Lawrence, 82 Chamberlain, Neville, 78 Channels, 40 technical analysis and, 294 Chartists (see Technical analysis) Chevron, 176i, 177 ChevronTexaco, 55 Chicago Board of Trade (CBOT): closure due to Chicago River leak, 253, 254i, 255 stock market crash of 1987 and, 273 Chicago Board Options Exchange (CBOE), 264–265 Volatility Index of, 281–282, 282i Chicago Gas, 47 in DJIA, 39i, 48 Chicago Mercantile Exchange, stopping of trading on, 276 Index Chicago Purchasing Managers, 244 China: global market share of, 178, 179i, 180, 180i sector allocation and, 177 China Construction Bank, 175 China Mobile, 177, 183 China National Petroleum Corporation, 182 Chrysler, 64 Chunghwa Telecom, 177 Cipsco (Central Illinois Public Service Co.), 48 Circuit breakers, 276–277 Cisco Systems, 38, 57n, 89, 104, 155, 157, 176i on Nasdaq, 44 Citigroup, 144, 175, 176i Clinton, Bill, 75, 227, 238 Clough, Charles, 86 CNBC, 48, 88 Coca-Cola Co., 59i, 61, 64 Cognitive dissonance, 328 Colby, Robert W., 295–296 Colgate-Palmolive, 59i Colombia Acorn Fund, 346 Comcast, 176 Common stock theory of investment, 82 Common Stocks as Long-Term Investments (Smith), 79, 83, 201 Communications technology, bull market and, 88 Compagnie Française des Pétroles (CFP), 184 Conference Board, 244 Conoco (Continental Oil Co.), 57 ConocoPhillips, 176i, 177, 183 Consensus estimate, 239 Consumer choice, rational theory of, 322 Consumer discretionary sector: in GICS, 53 global shares in, 175i, 176 Consumer Price Index (CPI), 245 369 Consumer staples sector: in GICS, 53 global shares in, 175i, 177 Consumer Value Store, 61 Contrarian investing, 333–334 Core earnings, 107–108 Core inflation, 245–246 Corn Products International, 47 Corn Products Refining, 47 Corporate earnings taxes, failure of stocks as long-term inflation hedge and, 202–203 Correlation coefficient, 168 Corvis Corporation, 156–157 Costs: agency, 100 effects on returns, 350 employment, 246 interest, inflationary biases in, failure of stocks as longterm inflation hedge and, 203–204 pension, controversies in accounting for, 105–107 Cowles, Alfred, 42, 83 Cowles Commission for Economic Research, 42, 83 CPC International, 47 Crane, Richard, 61 Crane Co., 59i, 60i, 61 Cream of Wheat, 62 Creation units, 252 Crowther, Samuel, 3 Cubes (ETFs), 252 Currency hedging, 173 Current yield of bonds, 111 Cutler, David M., 224n CVS Corporation, 61 Cyclical stocks, 144 DaimlerChrysler, 176 Daniel, Kent, 326n Dart Industries, 62 Dash, Srikant, 353n Data mining, 326–327 David, Joseph, 21 DAX index, 238 Day-of-the-week effects, 316–318, 317i Day trading, futures contracts and, 261 Dean Witter, 286 De Bondt, Werner, 302–303, 335 Defined benefit plans, 106–107 Defined contribution plans, 105–106 Delaware and Hudson Canal, 22 Deleveraging, 120 Del Monte Foods, 62 Department of Commerce, 203 Depreciation, failure of stocks as long-term inflation hedge and, 203 Deutsch, Morton, 324n Deutsche Post, 177 Deutsche Telekom, 177 Dexter Corp., 21n Diamonds (ETFs), 252 Dilution of earnings, 104 Dimensional Fund Advisors (DFA) Small Company fund, 142n Dimson, Elroy, 18, 19n, 20 Discounts, futures contracts and, 258 Distiller’s Securities Corp., 48 Distilling and Cattle Feeding, 47 in DJIA, 39i, 48 Diversifiable risk, 140 Diversification in world markets, 168–178 currency hedging and, 173 efficient portfolios and, 168–172, 169i–171i private and public capital and, 177–178 sector diversification and, 173–177, 174i The Dividend Investor (Knowles and Petty), 147 Dividend payout ratio, 101 Dividend policy, value of stock as related to, 100–102 370 Dividend yields, 145–149, 146i–149i interest rate on government bonds above, 95–97 ratio of market value to, 120, 120i Dodd, David, 77q, 83, 95q, 139q, 141, 145n, 150, 152, 289q, 304n, 334n Dogs of the Dow strategy, 147–149, 148i, 149i, 336 Dollar cost averaging, 84 Domino Foods, Inc., 47 Dorfman, John R., 147n Double witching, 260–261 Douvogiannis, Martha, 113n Dow, Charles, 38, 290–291 Dow Chemical, 58 Dow Jones & Co., 38 Dow Jones averages, computation of, 39–40 Dow Jones Industrial Average (DJIA), 37, 47 breaks 2000, 85 breaks 3000, 85 breaks 8000, 87 crash of 1929 and, 4 creation of, 38 fall in 1998, 88 firms in, 38–39, 39i following Iraq’s defeat in Gulf War, 85 long-term trends in, 40–41, 41i Nasdaq stocks in, 38 during 1922–1932, 269, 270i during 1980–1990, 269, 270i original firms in, 47–49 original members of, 22 predicting future returns using trend lines and, 41–42 as price-weighted index, 40 Dow Jones Wilshire 5000 Index, 45 Dow 10 strategy, 147–149, 148i, 149i, 336 Dow Theory (Rhea), 290 Index Dow 36,000 (Hassett), 88 Downes, John, 147 Dr.

The Trade Lifecycle: Behind the Scenes of the Trading Process (The Wiley Finance Series)
by Robert P. Baker
Published 4 Oct 2015

Notice that the mathematics does not care what the underlying asset actually is and so option modelling is applicable across asset classes. 346 THE TRADE LIFECYCLE TABLE 26.5 Option outcomes at different final prices Price 0.7 0.8 0.9 1.0 2.0 3.0 Probability Payoff at exercise 0.2 0.2 0.2 0.2 0.1 0.1 0 0 0 100 1100 2100 A more likely distribution of underlying prices is to assume that they are log normal. Then we can use the industry standard Black Scholes formula to calculate the option NPV. Other dependencies An exotics trade such as a knock out single barrier option pays a return conditional on two events:   The underlying price did not reach the barrier at any point in the life of the trade. The option was exercised meaning the spot price was greater than the strike at maturity (for European style options).

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The option was exercised meaning the spot price was greater than the strike at maturity (for European style options). To calculate the NPV the probability of both events must be calculated. Since both are dependent upon the underlying price, we could still use the log normal price distribution and a variant of the Black Scholes formula. Monte Carlo The Black Scholes option pricing formula is an example of a closed form solution – that is, the result can be expressed in some formulaic combination of the input parameters. Many trade pricing functions are closed form or semi-closed form and they work like a black box: input data is fed in, the parameters are set, the button is pushed and results come out.

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Bob Steiner (2012) Mastering Financial Calculations: A Step-by-step Guide to the Mathematics of Financial Market Instruments, Financial Times/Prentice Hall. 377 Index 30/360 date calculation 350–1 ABSs see asset backed securities abusive behaviour, traders 223 acceptance testing see user acceptance testing accounting 161–9 balance sheet 161–4 financial reports 168–9 profit and loss account 164–8 accrual accrual convention 349–50 accrued profit and loss 165 actual/actual date calculation 350 advisory services 269, 370 aggregation of calculations 342 trades 101–2 agricultural commodities 56 algorithms 184 amendment to a trade 108 American options 29, 66 amortising bonds 47, 48 analytics 271–2 see also quantitative analysts animal products 56 application programming interface (API) 270 architects, IT 187 asset backed securities (ABSs) 47 asset classes 33–59 bonds and credit 46–53 commodities 29, 53–8 equities 44–5 foreign exchange 40–4 interest rates 33–40 and products 17 trade matrix 71–2 trading across 58–9 asset holdings see holdings asset managers 10, 168–9 at-the-money options 66 audit 191–2 average trades, exotic options 68 back book trading 132 back office (operations) 183, 227, 316 back testing 317 back-to-back trades 152 bad data 105, 317–20 balance sheet 161–4 banks culture and conduct 203 interbank systems 158 reasons for trading 9–10 retail banks 222 traders’ internal accounts 123 Barclays Capital 219 barrier options 68 base rate, interest rates 35 Basel II 144 Basel III 205 baskets exotic options 68 FX trades 41–2 BCP see business continuity planning bearer securities 124 Bermudan options 66 bespoke trades 69–70 bid/offer spread 310 binary options 68–9 black box (mathematical library) 238, 241, 270 black box testing 301 Black Scholes formula 346 board of directors 193–4 bond basis deltas 175 379 380 bonds 27, 28, 29, 46–53 coupon payments 47, 48, 106–7 RABOND project case study 225–35 sovereign debt 46 tradeflow issues 49 types 46–7 bonuses 220–1 booking of a trade 85, 93–4 bootstrapping 348–9 boundary testing 351 breaches, dealing with 155–6 breaks, settlement 356–7 brokers 5–6, 10, 75 buckets (time intervals) 148–9 bullying behaviour 223 business continuity planning (BCP) 373 calculation process 337–52 see also valuation process bootstrapping 348–9 calibration to market 351 dates 349–51 example 337–8 mark-to-market value 339–40 model integration 352 net present value 338–9, 343–8 risks 352 sensitivity analysis 347–8 calibration process, valuation 351 call options 62, 63 cancellation of a trade 109 capital adequacy ratio (CAR) 144 case studies 225–52 EcoRisk project 235–47 OTTC equity confirmation project 247–52 RABOND project 225–35 cash balance sheet item 162 exchange dates 86 exercise 111 settlement 98, 99 cashflows American options 30 asset holdings 117–24 bank within a bank 123 consolidated reporting 122 custody of securities 123–4 diversification 122–3 realised and unrealised P&L 122 INDEX reconciliation 121 risks 124 treatment of 119–20 value of 120–1 credit default swaps 31 deposits 23 discount curve 38–9 equity spot trades 26 fixed bonds 27, 28 floating bonds 27, 28 foreign exchange swaps 25 future trades 20–1 loans 22 options 27–30, 345–6 post booking 96–7 risks 367 spot trades 19 swap trades 24 unknown, options valuation 345–6 zero bonds 27, 29 CDSs see credit default swaps Central Counterparty Clearing (CCP) 210–12 change coping with 260–1, 284 to a trade 105–10 clearing 210–12 Cliquet (ratchet options) 68 collateral 108, 153–4, 156, 212–13 COM (common object model) 246 commodities 29, 53–8 cash settlement 99 characteristics 55–6 currency 57 definition 55 example 53–5 localised production 57 OTC commodities 56 physical settlement 57–8 profit curve 54–5 time lag 57 tradeflow issues 58 types 56 utility of 57 common object model (COM) 246 communication 188, 197–8, 254–5, 259–60, 305, 371 competition analysis 269 compliance officers 192–3 confirmation of a trade 94–6, 247–52, 355 conflicts and tensions 196–7, 198–9, 360–1 381 Index consolidated reporting 122 consolidation of processes 283–4 control see also counterparty risk control; market risk control people involved in 189–99, 224 of report generation 335 conversion, currency 344 correlation risk 131, 363 counterparties changes to a trade 108 correlation between 364 identification of 85 Counterparty Clearing, Central 210–12 counterparty risk control 147–60, 364–5 activities of department 154–7, 190–1 collateral 153–4, 156 counterparty identification 153 default consequences 148 limit imposition 152–3 management interface 157 measurement of risk 149–52, 155, 156 non-fulfilment of obligations 147–8 payment systems 158–60 quantitative analyst role 268 risks in analysing credit risk 157–8 settlement 356 time intervals 148–9 coupon payments, bonds 47, 48, 106–7 credit default swaps (CDSs) 30–1, 51–2, 65–6, 175, 209 credit exposure 150–1 credit quantitative analysts 274 credit rating companies 231–2 credit risk see also counterparty risk control; credit default swaps; credit valuation adjustment bonds 46–53 default 51 definition 50 documentation 50–1 market data 316 measurement of 209 recovery rate 52–3 risks in analysing 157–8 types of risk 131 credit valuation adjustment (CVA) 207–13 debt valuation adjustment 209 definition 208 funding valuation adjustment 209 measurement of 208 mitigation 210 netting 211–12 portfolio-based 213 rehypothication 212–13 credit worthiness 51–2, 155 creditors, balance sheet item 163 CreditWatch 232 culture of banks 203 currency conversion 344 exposure to 4 precious metals as 57 reporting currency 42 value of holdings 120–1 currency swaps, foreign exchange 41 current (live) market data 79, 314 curves, market data 310–13 custodians 98, 124 customer loyalty 199 CVA see credit valuation adjustment data 307–25 absence of 368 authentic data 368 back testing 317 bad data 105, 317–20 bid/offer spread 310 corrections to 321–2 data feeds 226 expectations 309–10 extreme values 317 implied data 323 integrity of 322–4 internal data 321 interpolation 319 market data 107–8, 180, 292, 308–17 processes 286 risks 324–5, 367–8 sources of 320–1, 323 storage 309 testing 302 time series analysis 320 types of 308–10 validity of 307 vendors 321 data cleaning 320 data discovery 319–20 data engineering 319 databases 250–1, 308 382 dates calculation of 349–51 exercise of trades 111 final settlement 113 internal and external trades 102 relating to a trade 86–7 settlement 101, 113 on trade tickets 102 debt, exposure to 127 debt valuation adjustment (DVA) 209 debtors, balance sheet item 162 default 51, 131, 148 see also credit default swaps delivery versus payment (DvP) 98 delta hedging 133 delta risk 130 deltas 175 deposits 23, 35 derivatives 61–72 see also futures and forwards; options; swaps digital options 68–9 directors, role of 193–4 discount curve, interest rates 38–9 discounting, NPV calculation 343–4, 345 diversification 122–3 dividends 105–6 documentation credit risk 50–1 EcoRisk project case study 240–1 legal documents 84–5 processes 287 risks 356, 374 settlement 98 Dodd–Frank Act 206–7 dreaming ahead 131–2 due diligence 192, 292 duties (fees) 97 DVA (debt valuation adjustment) 209 DVO1, risk measure 138 DvP (delivery versus payment) 98 economic data 84 EcoRisk project, case study 235–47 documentation 240–1 functionality 243–4 Graphical User Interface 237–8 mathematical library 238, 241 solution 238–40 testing 239–40 valuation problem debugging 242–3 INDEX electronic exchanges 6 electronic systems 92 email 92 EMIR (European Markets Infrastructure Regulation) 202–3 employees see people involved in trade lifecycle end of day roll 103, 181–2 end of month reports 182 energy products 56 equal opportunities 219–20 equities 26, 44–5, 247–52 errors confirmation process 95 in data 322 P&L corrections 171 post booking 97 in reports 333–4 European Markets Infrastructure Regulation (EMIR) 202–3 European options 29, 66 exceptions, processes 322 exchange price 75 exchanges 6, 86, 320 execution of a trade 89–93 exercise, option trades 64, 110–12, 357–8 exotic options 67–9, 109, 235–47, 346 expected loss 150 exposure 4, 125–8, 130–2, 150–1, 155, 156 fault logging 302–4 fees 97, 169 finance department 191, 316 financial products 17–31 bonds 27, 28, 29, 46–53, 106–7, 225–35 credit default swaps 30–1, 51–2, 65–6, 175, 209 deposits 23, 35 equities 26, 44–5, 247–52 futures 20–1, 35–6, 40–1, 61, 62, 77, 127, 311, 312 FX swaps 25, 41 loans 21–3 options 27–30, 61–9, 77, 109–12, 127, 235–47, 345–6, 357–8 spot trades 18–19, 40, 127 swaps 23–5, 30–1, 36–7, 41, 107, 312–13 financial reports 168–9 financial services industry 8–10 fixed assets, balance sheet item 161 fixed bonds 27, 28, 47, 48 fixed and floating coupons 127 383 Index fixed for floating swaps 23–4 fixed loans 22 fixing date 86 fixings 107–8 float for fixed/float for float 36 floating bonds 27, 28 floating loans 22 floating rate notes (FRNs) 47 flow diagrams 287 FoP (free of payment) 98 foreign exchange (FX) 40–4 baskets 41–2 FX drift 42–3 reporting currency 42 swaps 25, 41 tradeflow issues 43–4 forward rate agreement (FRA) 37–8 see also futures and forwards free of payment (FoP) 98 FRNs (floating rate notes) 47 front book trading 132 front line support staff 186 front office EcoRisk project, case 235–47 market risk control 142 risks 375–6 fugit 112 fund managers 10 funding valuation adjustment (FVA) 209 futures and forwards 20–1, 35–6, 40–1, 61, 62 gold futures 311, 312 leverage 77 risks 127 FVA (funding valuation adjustment) 209 FX see foreign exchange gamma risk 130 gearing 77–8 gold futures 311, 312 governance 204 Graphical User Interface (GUI) 237–8 hedge funds 10, 168–9, 212–13 hedging strategies 133–4 hedging trades 128 help desks 247 historical market data 314 holdings 117–24 asset types 118 bank within a bank 123 consolidated reporting 122 custody of securities 123–4 diversification 122–3 realised and unrealised P&L 122 reconciliation 121 risks 124 value 120–1 human resources see people involved in trade lifecycle human risks 194–9, 359–61 hybrid trades 69–70 identification details, trades 83–4 illiquid products 140 illiquid trades 339 in person trades 92 in-the-money options 66 incentives 195 industrial metals 56 information technology (IT) architects 187 case studies 225–52 communication 259–60 dependency on 284 EcoRisk project 235–47 equity confirmation project 247–52 infrastructure 186 IT divide 253–66 business functions 255–6 business requirements 261–3 coping with change 260–1 do’s and don’ts 263 IT blockers 258 IT requirements 263–4 misuse of IT 256–7 organisational blockers 257–8 problems caused by 255 project examples 265–6 solution 259–60 language of 254 legacy systems 282 operators 188 project managers 187–8 quality control 260 and quantitative analysts 271–4 RABOND project 225–35 risks 375–6 staff 185–9, 197, 217–18, 253–66 testers 188–9 and traders 258 384 infrastructure, IT 186 instantaneous risk measures 138 insurance 30–1, 50 integration testing 300 interbank systems 158 interbank trading (LIBOR) 39 interest rates 21–3, 33–40 base rate 35 credit effects 39 deltas 175 deposits 35 discount curve 38–9 forward rate agreement 37–8 futures 35–6, 311–12 market participants 34–5 option valuation 67 products 35–8 quantitative analysts 274 swaps 23–5, 36–7 time value of money 33–4 tradeflow issues 39–40 vegas 175 interim delivery of projects 259 internal audit 191–2 International Swaps and Derivatives Association (ISDA) 50 investment banks 9–10 investments, balance sheet item 161 ISDA (International Swaps and Derivatives Association) 50 IT see information technology kappa risk 130 knock in/knock out, barrier options 68 knowledge, risks 359–60 legacy IT systems 282 legal department 189, 293, 316 legal documents 84–5 legal risks 50, 369 leverage 64–6, 76–9 LIBOR (interbank trading) 39 libraries 184–5 lifecycle of a trade see trade lifecycle limit orders 129 limits and credit worthiness 155 imposing 152–3 market risk control 141 line managers 222 INDEX linear derivatives 61, 62 liquidity 73–5, 202, 375 litigation 370 live trading 7 loans 21–3 management see also project management; risk management of changes 109–10 counterparty risk control 157 fees 169 market data usage 317 new products 292 responsibilities of 193–4 risks 374 of teams 229–31 margin payments 156 mark-to-market value 339–40 market data 180, 292, 308–17 business usage 315–17 changes as result of 107–8 curves and surfaces 310–13 sets of 314 market participants 4–5 market risk control 135–45, 190, 363–4 allocation of risk 139 balanced approach 143 controlling the risk 140–1 human factor 143 limitations 142–3 market data usage 316 methodologies 135–9 monitoring of market risk 140 need for risk 139 quantitative analyst role 268 regulatory requirements 143–4 responsibilities 141–2 market sentiment 340 matching of records 94–5 mathematical libraries 238, 241, 270 mathematical models evolution of 343 new products 293 parameters 341 prototypes 238–9 quantitative analyst role 183–5 risks 373 validation team 189–90 maturity of a trade 8, 67, 86, 112–13 MBS see mortgage backed securities 385 Index metal commodities 56, 57 middle office (product control) market data usage 316 new products 293 RABOND project, case study 225–35 role of 180–2 missing data 317 mobile phones 92 models see mathematical models Monte Carlo technique 346–7 mortgage backed securities (MBS) 47 multilateral netting 211–12 NatWest Markets, EcoRisk project 235–47 net present value (NPV) 338–9, 343–8 netting 152, 211–12 new products 289–95 checklist 292–3 evolution of 294 market data 292 market risk control 140 process development/improvement 279–88 risks 194, 294–5, 369 testing 291–2 trial basis for 290–2 new trade types 156 nonlinear derivatives 62–9 nostro accounts 99 NPV see net present value official market data 314 offsetting of risks 128 OIS (overnight indexed swap) 39 operational risks 355–8 operations department 183, 227, 316 operators, IT 188 options 27–30, 61–9 credit default swaps 65–6 exercise 110–12 exotic options 67–9, 109, 235–47, 346 leverage 64–6, 77 risks 127, 357–8 terminology 66 trade process 64–6 valuation 67, 345–6 orders 90–1, 357 OTC see over-the-counter trading OTTC equity confirmation project, case study 247–52 out-of-the-money options 66 over-the-counter (OTC) trading 6–7 clearing 210 commodities 56 price 75 overnight indexed swap (OIS) 39 overnight processes 101–5 P&L see profit and loss parallel testing 301 pay 203, 220–1 payment systems 106–7, 158–60, 357 pension funds 10 people involved in trade lifecycle 177–200 see also working in capital markets back office 183, 227, 316 compliance officers 192–3 conflicts and tensions 196–9, 360–1 control functions 189–99 counterparty risk control department 190–1 finance department 191, 316 human risks 194–9 information technology 185–9, 197, 217–18, 253–66 internal audit 191–2 legal department 189, 293, 316 line managers 222 management 193–4 market risk control department 190 middle office 180–2, 225–35, 293, 316 model validation team 189–90 personality and outlook 194–5, 244–5, 273 programmers 187, 244–5 quantitative analysts 183–5, 267–75 researchers 179–80 revenue generation 177–89 sales department 179, 227, 315, 375 senior managers 126 staffing levels 195 structurers 179 supervisors 204 testers 298–9 traders 125–6, 177–8, 218–23, 226–7, 258, 268, 315, 361 trading assistants 178 trading managers 126, 193 training of staff 193 performance reports 169 personality and outlook 194–5, 244–5, 273 PFE (potential future exposure) 151 physical assets, exercise 111 386 physical commodities, settlement 57–8, 99 planning of processes 282–3 recovery plans 203–4 risks 360 post booking processes 96–7 postal trades 92–3 potential future exposure (PFE) 151 power, abuses of 220, 221–2 pre-execution of a trade 89–91 precious metals 56, 311, 312 premiums 31 price 75–6, 138–9 pricing methods EcoRisk project, case study 235–47 short-term pricing 183 process development/improvement 279–88 coping with change 284 current processes 285–7 evolution of processes 280–1 improving the situation 284–7 inertia 287–8 inventory of current systems 282–4 planning 282–3 timing 288 producers 5 product appetite 4 product control see middle office product development see new products profit curve, commodity trading 54–5 profit and loss (P&L) accounts 164–8 accrued and incidental 165 example 165–6 individual trades 166–7 realised and unrealised 165 responsibility for producing 167 risks associated with reporting 167–8 rogue trading 168 attribution reports 171–6 benefits of 171–2 example 173–6 market movements 173, 175 process 172–3 unexplained differences 173 balance sheet item 163 end of day 182 realised and unrealised 122, 165 programmers 187, 244–5 see also quantitative analysts INDEX project management 225–47, 259, 262 project managers 187–8 proprietary (‘prop’) trading 203 prototypes, IT projects 238–9 provisional trades 89–90, 357–8 put options 62, 63 PVO1, risk measure 138 quality control, IT 260 see also testing quantitative analysts (quants) 183–5, 267–75 and IT professionals 271–4 role of 267–9, 270 seating arrangements 270–1 working methods 269–70 RABOND project, case study 225–35 management 229–31 outcome 233–5 reports 227–9 team management 229–31 traders 226–7 random market data 314 rapid application development (RAD) 260, 281 ratchet options (Cliquet) 68 ratings companies 231–2 raw data 323 raw reporting 331 real world of capital markets see working in capital markets realised P&L 122 receipts 156 reconciliation 121 recovery plans 203–4 recovery rates 52–3, 176 redundancy, processes 282 reform of banks 203 registered securities 123–4 regression testing 302 regulation 201–13, 223–4 authorities 202 Basel II and III 144, 205 credit valuation adjustment 207–13 external 192 internal 224 market risk control 143–4 new products 293 problems 204–5 requirements 202–4 387 Index risk-weighted assets 205–7 risks 369 rehypothication 212–13 remuneration 203, 220–1 reporting currency 42 reports 327–36 accuracy 330–1, 368 calculation process 342 configuration 331–2 consolidated reporting 122 content 328–9 control issues 335 dimensions 333 distribution 329–30, 335, 369 dynamic reports 332–3 end of month reports 182 enhancements 335 errors in 333–4 false reporting 375 financial reports 168–9 frame of reference 333 middle office role 180–1 OTTC equity confirmation project 250, 251 performance reports 169 presentation 329 problems 333–4 profit and loss 167, 171–6 RABOND project 227–9 raw reporting 331 readership 328, 329, 368–9 redundancy of 334–5 requirements 328–33 risks 335–6, 368–70 security issues 335, 368 timing 330 types of 330 reputation, risk to 356, 370 research 268, 375 researchers 179–80 reserve accounts 141 reset date 86 resettable strike, exotic options 68 retail banks 222 revenue generation, people involved in 177–89 rho risk 130 risk 13–16 see also counterparty risk control; market risk control advisory services 370 appetite for 4 business continuity planning 373 calculation process 352 cashflows 124, 367 changes to a trade 110 communication 371 confirmation 95–6, 355 control departments 224 correlation 363 data 324–5, 367–8 definition 13 documentation 356, 374 exercise 112 front office 375–6 human risks 194–9, 359–61 information technology 375–6 instantaneous measures 138 legal risks 369 liquidity 74–5, 375 litigation 370 management risks 374 measures 130, 138, 149–52, 155, 156 model approval 373 new products 140, 194, 294–5, 369 operational risks 355–8 orders 91 origin of risks 126–8 payment systems 357 provisional trades 90, 357–8 quantifying 14 regulation 369 reports 335–6, 368–70 reputation 356, 370 risk-weighted assets 205–7 sales 375 settlement 100, 355–7 short-term thinking 360 straight through processing 357 support activities 376 systematic 202–3, 375–6 testing 304–5, 370–1 types 130–2 unexpected charges 356 unforeseen 16, 353 valuation process 352, 373 risk management 13, 15, 125–34 in absence of trader 128–9 dreaming ahead 131–2 EcoRisk project case study 235–47 hedging strategies 133–4 hedging trades 128 388 risk management (continued) offsetting of risks 128 senior managers 126 traders 125–6, 361 trading managers 126 trading strategies 132 rogue trading 168 sales data 84 sales department 179, 227, 315, 375 SBC Warburg, equity confirmation project, case study 247–52 scenario analysis 136, 198–9, 341 scope creep 187, 264 scrutiny of trades 96 securities, custody of 123–4 security issues 181, 335, 368 semi-static data 309 senior managers 126 sensitivity analysis 138, 347–8 settlement 97–101, 147–8 breaks 101, 356–7 commodities 99 dates 101, 113 nostro accounts 99 quick settlement 101 risks 100, 355–7 shares 44–5 see also equities short selling 65 short-term pricing 183 short-term thinking 195–6, 360 silo approach 257 simple products 70–1 smoke testing 301 sovereign debt 46 speculators 5 spot prices 61, 62, 63, 67, 76–7 spot testing 301 spot trades 18–19, 40, 127 spread of bid/offer 310 spreadsheets 184, 238 staff see people involved in trade lifecycle stale data 105, 318 Standard & Poor’s (S&P) ratings 231–2 static data 309 stop-loss hedging 133–4 stop orders 129 storage of data 309 straight through processing (STP) 93–4, 357 INDEX stress, staff 222, 244–5 stress testing 302 strike price, options 67 structured trades 69–70 structurers 179 supervisors 204 support activities, risks 376 surfaces, market data 310–13 swaps credit default 30–1, 51–2, 65–6, 175, 209 fixings 107 foreign exchange 25, 41 interest rate 23–5, 36–7 yield curves 312–13 swaptions 66 synthetic equities (index) 45 systems see also information technology amalgamation 104–5 analytics 271–2 electronic systems 92 integrated 261 legacy IT systems 282 risks 375–6 testing 251–2, 300 tail behaviour, predicting 143, 364 team management 229–31 telephone transactions 91–2 tensions and conflicts 196–9, 360–1 testing 297–305 back testing 317 boundary testing 351 extreme values 352 fault logging 302–4 importance of 298 mathematical models 239 new products 291–2 risks 304–5, 370–1 stages 300–1 testers 188–9, 298–9 types of 301–2 unit testing 300 user acceptance testing 237, 239–40, 252, 264, 301 when to perform 299–300 theft 355 theta risk 130 time intervals (buckets) 148–9 time lag, commodities 57 389 Index time series analysis 320 timeline of a trade 79, 86–7 trade blotters 93 trade lifecycle 89–115 booking 93–4 business functions 11 changes during lifetime 105–10 confirmation 94–6 equity trades 45 example trade 113–15 execution 91–3 exercise 110–12 maturity 112–13 new products 293 overnight processes 101–5 post booking 96–7 pre execution 89–91 settlement 97–101 trade tickets 102 trade/trading 3–12 see also trade lifecycle anatomy 83–7 business functions 11 complicated trades 340 consequences of 7–8 definition 10–12 financial products 17–31 live trading 7 matching of records 94–5 policies 8 reasons for 3, 9–10 timeline 79, 86–7 transactions 5–7 types 132 tradeflow issues bonds 49 commodities 58 foreign exchange 43–4 interest rates 39–40 traders 177–8, 218–22, 223, 226–7, 258, 268 bonuses 220–1 market data usage 315 risk management 125–6, 361 trading assistants 178 trading desks 70–1, 256–7 trading floor 217–18, 235–6 trading managers 126, 193 training of staff 193 tranche correlation 131 treasury desk 71 trials for new products 290–2 trust 197, 222 UAT see user acceptance testing underlying 83 unexplained differences, P&L reports 173 unforeseen risk 16, 353 unit testing 300 unknown cashflows 345–6 unrealised P&L 122 unwinding a trade, cost of 76 user acceptance testing (UAT) 237, 239–40, 252, 264, 301 validation of models 189–90 valuation process see also calculation process calibration to market 351 mark-to-market value calculation 339–40 middle office role 181 NPV calculation 338–9, 343–8 options 67 problem debugging 242–3 risks 352, 364, 373 valuation systems 269 value at risk (VaR) 136–8, 341 vega (kappa) risk 130 vegas 175 vendors, data services 321 volatility 67, 130 volume of a trade, price effect 76 white box testing 301 workarounds 303 working in capital markets 217–24 see also case studies; people involved in trade lifecycle in 1990s 217–19 culture clashes 219 equal opportunities 219–20 office politics 220–2, 246 positive/negative aspects 222–3 yield curves 312–13 zero bonds 27, 29, 47 Index compiled by Indexing Specialists (UK) Ltd WILEY END USER LICENSE AGREEMENT Go to www.wiley.com/go/eula to access Wiley’s ebook EULA. 

Stocks for the Long Run 5/E: the Definitive Guide to Financial Market Returns & Long-Term Investment Strategies
by Jeremy Siegel
Published 7 Jan 2014

But the theory of options pricing was given a big boost in the 1970s when two academic economists, Fischer Black and Myron Scholes, developed the first mathematical formula to price options. The Black-Scholes formula was an instant success. It gave traders a benchmark for valuation where previously they used only their intuition. The formula was programmed on traders’ handheld calculators and PCs around the world. Although there are conditions when the formula must be modified, empirical research has shown that the Black-Scholes formula closely approximates the price of traded options. Myron Scholes won the Nobel Prize in Economics in 1997 for his discovery.10 Buying Index Options Options are actually more basic instruments than futures or ETFs.

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See Fund performance Becker Securities Corporation, 360 Behavioral finance avoiding behavioral traps in, 350 contrarian investing in, 352–354 Dow 10 strategy in, 354 enhancing portfolio returns in, 352–354 equity risk premiums in, 350–352 excessive trading in, 345–347 fads in, 343–344 holding on to losing trades in, 347–349 introduction to, 339–340, 342 investor sentiment in, 352–354 loss aversion in, 347–352 myopic loss aversion in, 350–352 out of favor stocks in, 354 overconfidence in, 345–347 portfolio monitoring in, 350–352 prospect theory in, 347–349 representative bias in, 345–347 rules vs., 376 social dynamics in, 343–344 stock bubbles in, 343–344 technology bubble, 1999–2001 in, 340–342 Benchmarks, 358–359 Berkshire Hathaway, 203–205, 362–363 Bernanke, Fed Chairman Ben on central banks, 33–35 on innovation, 71 on quantitative easing, 267 on TARP, 246 TARP and, 54–55 on unemployment rates, 262 on world markets, 21–22 Best Global Brands, 68 Beta, 175, 190–191 BHP Billiton, 205 Birrell, Lowell, 106 Birthrates, 58–59 Black, Fischer, 285 Black Monday. See also Stock market crash of 1987, 291–294 Black-Scholes formula, 285–286 Blackstone, 18–19 Blake, Christopher, 364 BLS (Bureau of Labor Statistics), 261–262, 266 Blue Chip Economic Indicators , 236–238 BNP Paribas, 18, 44, 46 Bogle, Jack, 365 Bogle, John, 367 Bond market 1802-present. See Bonds since 1802 flow of economic data and. See Economic data stocks vs.

Other People's Money: Masters of the Universe or Servants of the People?
by John Kay
Published 2 Sep 2015

This revolution in the technology of finance was matched by – indeed was only possible because of – the parallel revolution in information technology. When trading in financial futures began, the Chicago Mercantile Exchange still centred on ‘the pit’, in which aggressive traders shouted offers as they elbowed deals away from their colleagues. Today every trader has a screen. The Black–Scholes model, and the many techniques of quantitative finance that came out of Chicago and elsewhere, could not have been widely applied without the power of modern computers. Regulation also promoted the growth of a trading culture. The growth of the Eurodollar market demonstrated that regulatory anomalies could be used by banks to attract business.

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That consequence is critical to an understanding of how financial markets operate today. The models that have been developed in financial economics are wide-ranging, and often technically ingenious. They include the Markowitz model of portfolio allocation (to which Greenspan referred) and the Black–Scholes model (the derivative pricing model to which he alluded). The key components of academic financial theory, however, are the ‘efficient market hypothesis’ (EMH), for which Eugene Fama won the Nobel Prize in 2013, and the Capital Asset Pricing Model (CAPM), for which William Sharpe won the Nobel Prize in 1990.

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And since everything that is known is in the price, that price will represent the best available estimate of the underlying value of a security. A small further step of analogous reasoning leads to the ‘no arbitrage’ condition: each security is appropriately priced in relation to all other securities, so that it is never possible to make money by selling one and buying another. The Black–Scholes model, and the whole subsequent development of quantitative models in derivative markets, relies on that assumption. The ‘no arbitrage’ condition was what Summers had in mind when he derided financial economists as people who ask whether two quart bottles of ketchup sell for twice the price of quart bottles without taking an interest in how the price of ketchup is itself determined.

Doughnut Economics: Seven Ways to Think Like a 21st-Century Economist
by Kate Raworth
Published 22 Mar 2017

In the same year that the Exchange opened for trading, two influential economists, Fischer Black and Myron Scholes, published what came to be known as the Black–Scholes model, which used publicly available market data to calculate the expected price of options traded in the market. At first the formula’s predictions deviated widely – by 30% to 40% – from actual market prices at the CBOE. But within a few years – and with no alterations to the model – its predicted prices differed by a mere 2% on average from actual market prices. The Black–Scholes model was soon heralded as ‘the most successful theory not only in finance, but in all of economics’ and its creators were awarded Nobel-Memorial prizes.

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Page numbers in italics denote illustrations A Aalborg, Denmark, 290 Abbott, Anthony ‘Tony’, 31 ABCD group, 148 Abramovitz, Moses, 262 absolute decoupling, 260–61 Acemoglu, Daron, 86 advertising, 58, 106–7, 112, 281 Agbodjinou, Sénamé, 231 agriculture, 5, 46, 72–3, 148, 155, 178, 181, 183 Alaska, 9 Alaska Permanent Fund, 194 Alperovitz, Gar, 177 alternative enterprise designs, 190–91 altruism, 100, 104 Amazon, 192, 196, 276 Amazon rainforest, 105–6, 253 American Economic Association, 3 American Enterprise Institute, 67 American Tobacco Corporation, 107 Andes, 54 animal spirits, 110 Anthropocene epoch, 48, 253 anthropocentrism, 115 Apertuso, 230 Apple, 85, 192 Archer Daniels Midland (ADM), 148 Arendt, Hannah, 115–16 Argentina, 55, 274 Aristotle, 32, 272 Arrow, Kenneth, 134 Articles of Association and Memoranda, 233 Arusha, Tanzania, 202 Asia Wage Floor Alliance, 177 Asian financial crisis (1997), 90 Asknature.org, 232 Athens, 57 austerity, 163 Australia, 31, 103, 177, 180, 211, 224–6, 255, 260 Austria, 263, 274 availability bias, 112 AXIOM, 230 Axtell, Robert, 150 Ayres, Robert, 263 B B Corp, 241 Babylon, 13 Baker, Josephine, 157 balancing feedback loops, 138–41, 155, 271 Ballmer, Steve, 231 Bangla Pesa, 185–6, 293 Bangladesh, 10, 226 Bank for International Settlements, 256 Bank of America, 149 Bank of England, 145, 147, 256 banking, see under finance Barnes, Peter, 201 Barroso, José Manuel, 41 Bartlett, Albert Allen ‘Al’, 247 basic income, 177, 194, 199–201 basic personal values, 107–9 Basle, Switzerland, 80 Bauwens, Michel, 197 Beckerman, Wilfred, 258 Beckham, David, 171 Beech-Nut Packing Company, 107 behavioural economics, 11, 111–14 behavioural psychology, 103, 128 Beinhocker, Eric, 158 Belgium, 236, 252 Bentham, Jeremy, 98 Benyus, Janine, 116, 218, 223–4, 227, 232, 237, 241 Berger, John, 12, 281 Berlin Wall, 141 Bermuda, 277 Bernanke, Ben, 146 Bernays, Edward, 107, 112, 281–3 Bhopal gas disaster (1984), 9 Bible, 19, 114, 151 Big Bang (1986), 87 billionaires, 171, 200, 289 biodiversity, 10, 46, 48–9, 52, 85, 115, 155, 208, 210, 242, 299 as common pool resource, 201 and land conversion, 49 and inequality, 172 and reforesting, 50 biomass, 73, 118, 210, 212, 221 biomimicry, 116, 218, 227, 229 bioplastic, 224, 293 Birmingham, West Midlands, 10 Black, Fischer, 100–101 Blair, Anthony ‘Tony’, 171 Blockchain, 187, 192 blood donation, 104, 118 Body Shop, The, 232–4 Bogotá, Colombia, 119 Bolivia, 54 Boston, Massachusetts, 3 Bowen, Alex, 261 Bowles, Sam, 104 Box, George, 22 Boyce, James, 209 Brasselberg, Jacob, 187 Brazil, 124, 226, 281, 290 bread riots, 89 Brisbane, Australia, 31 Brown, Gordon, 146 Brynjolfsson, Erik, 193, 194, 258 Buddhism, 54 buen vivir, 54 Bullitt Center, Seattle, 217 Bunge, 148 Burkina Faso, 89 Burmark, Lynell, 13 business, 36, 43, 68, 88–9 automation, 191–5, 237, 258, 278 boom and bust, 246 and circular economy, 212, 215–19, 220, 224, 227–30, 232–4, 292 and complementary currencies, 184–5, 292 and core economy, 80 and creative destruction, 142 and feedback loops, 148 and finance, 183, 184 and green growth, 261, 265, 269 and households, 63, 68 living metrics, 241 and market, 68, 88 micro-businesses, 9 and neoliberalism, 67, 87 ownership, 190–91 and political funding, 91–2, 171–2 and taxation, 23, 276–7 workers’ rights, 88, 91, 269 butterfly economy, 220–42 C C–ROADS (Climate Rapid Overview and Decision Support), 153 C40 network, 280 calculating man, 98 California, United States, 213, 224, 293 Cambodia, 254 Cameron, David, 41 Canada, 196, 255, 260, 281, 282 cancer, 124, 159, 196 Capital Institute, 236 carbon emissions, 49–50, 59, 75 and decoupling, 260, 266 and forests, 50, 52 and inequality, 58 reduction of, 184, 201, 213, 216–18, 223–7, 239–41, 260, 266 stock–flow dynamics, 152–4 taxation, 201, 213 Cargill, 148 Carney, Mark, 256 Caterpillar, 228 Catholic Church, 15, 19 Cato Institute, 67 Celts, 54 central banks, 6, 87, 145, 146, 147, 183, 184, 256 Chang, Ha-Joon, 82, 86, 90 Chaplin, Charlie, 157 Chiapas, Mexico, 121–2 Chicago Board Options Exchange (CBOE), 100–101 Chicago School, 34, 99 Chile, 7, 42 China, 1, 7, 48, 154, 289–90 automation, 193 billionaires, 200, 289 greenhouse gas emissions, 153 inequality, 164 Lake Erhai doughnut analysis, 56 open-source design, 196 poverty reduction, 151, 198 renewable energy, 239 tiered pricing, 213 Chinese Development Bank, 239 chrematistics, 32, 273 Christianity, 15, 19, 114, 151 cigarettes, 107, 124 circular economy, 220–42, 257 Circular Flow diagram, 19–20, 28, 62–7, 64, 70, 78, 87, 91, 92, 93, 262 Citigroup, 149 Citizen Reaction Study, 102 civil rights movement, 77 Cleveland, Ohio, 190 climate change, 1, 3, 5, 29, 41, 45–53, 63, 74, 75–6, 91, 141, 144, 201 circular economy, 239, 241–2 dynamics of, 152–5 and G20, 31 and GDP growth, 255, 256, 260, 280 and heuristics, 114 and human rights, 10 and values, 126 climate positive cities, 239 closed systems, 74 coffee, 221 cognitive bias, 112–14 Colander, David, 137 Colombia, 119 common-pool resources, 82–3, 181, 201–2 commons, 69, 82–4, 287 collaborative, 78, 83, 191, 195, 196, 264, 292 cultural, 83 digital, 82, 83, 192, 197, 281 and distribution, 164, 180, 181–2, 205, 267 Embedded Economy, 71, 73, 77–8, 82–4, 85, 92 knowledge, 197, 201–2, 204, 229, 231, 292 commons and money creation, see complementary currencies natural, 82, 83, 180, 181–2, 201, 265 and regeneration, 229, 242, 267, 292 and state, 85, 93, 197, 237 and systems, 160 tragedy of, 28, 62, 69, 82, 181 triumph of, 83 and values, 106, 108 Commons Trusts, 201 complementary currencies, 158, 182–8, 236, 292 complex systems, 28, 129–62 complexity science, 136–7 Consumer Reaction Study, 102 consumerism, 58, 102, 121, 280–84 cooking, 45, 80, 186 Coote, Anna, 278 Copenhagen, Denmark, 124 Copernicus, Nicolaus, 14–15 copyright, 195, 197, 204 core economy, 79–80 Corporate To Do List, 215–19 Costa Rica, 172 Council of Economic Advisers, US, 6, 37 Cox, Jo, 117 cradle to cradle, 224 creative destruction, 142 Cree, 282 Crompton, Tom, 125–6 cross-border flows, 89–90 crowdsourcing, 204 cuckoos, 32, 35, 36, 38, 40, 54, 60, 159, 244, 256, 271 currencies, 182–8, 236, 274, 292 D da Vinci, Leonardo, 13, 94–5 Dallas, Texas, 120 Daly, Herman, 74, 143, 271 Danish Nudging Network, 124 Darwin, Charles, 14 Debreu, Gerard, 134 debt, 37, 146–7, 172–3, 182–5, 247, 255, 269 decoupling, 193, 210, 258–62, 273 defeat device software, 216 deforestation, 49–50, 74, 208, 210 degenerative linear economy, 211–19, 222–3, 237 degrowth, 244 DeMartino, George, 161 democracy, 77, 171–2, 258 demurrage, 274 Denmark, 180, 275, 290 deregulation, 82, 87, 269 derivatives, 100–101, 149 Devas, Charles Stanton, 97 Dey, Suchitra, 178 Diamond, Jared, 154 diarrhoea, 5 differential calculus, 131, 132 digital revolution, 191–2, 264 diversify–select–amplify, 158 double spiral, 54 Doughnut model, 10–11, 11, 23–5, 44, 51 and aspiration, 58–9, 280–84 big picture, 28, 42, 61–93 distribution, 29, 52, 57, 58, 76, 93, 158, 163–205 ecological ceiling, 10, 11, 44, 45, 46, 49, 51, 218, 254, 295, 298 goal, 25–8, 31–60 and governance, 57, 59 growth agnosticism, 29–30, 243–85 human nature, 28–9, 94–128 and population, 57–8 regeneration, 29, 158, 206–42 social foundation, 10, 11, 44, 45, 49, 51, 58, 77, 174, 200, 254, 295–6 systems, 28, 129–62 and technology, 57, 59 Douglas, Margaret, 78–9 Dreyfus, Louis, 148 ‘Dumb and Dumber in Macroeconomics’ (Solow), 135 Durban, South Africa, 214 E Earning by Learning, 120 Earth-system science, 44–53, 115, 216, 288, 298 Easter Island, 154 Easterlin, Richard, 265–6 eBay, 105, 192 eco-literacy, 115 ecological ceiling, 10, 11, 44, 45, 46, 49, 51, 218, 254, 295, 298 Ecological Performance Standards, 241 Econ 101 course, 8, 77 Economics (Lewis), 114 Economics (Samuelson), 19–20, 63–7, 70, 74, 78, 86, 91, 92, 93, 262 Economy for the Common Good, 241 ecosystem services, 7, 116, 269 Ecuador, 54 education, 9, 43, 45, 50–52, 85, 169–70, 176, 200, 249, 279 economic, 8, 11, 18, 22, 24, 36, 287–93 environmental, 115, 239–40 girls’, 57, 124, 178, 198 online, 83, 197, 264, 290 pricing, 118–19 efficient market hypothesis, 28, 62, 68, 87 Egypt, 48, 89 Eisenstein, Charles, 116 electricity, 9, 45, 236, 240 and Bangla Pesa, 186 cars, 231 Ethereum, 187–8 and MONIAC, 75, 262 pricing, 118, 213 see also renewable energy Elizabeth II, Queen of the United Kingdom, 145 Ellen MacArthur Foundation, 220 Embedded Economy, 71–93, 263 business, 88–9 commons, 82–4 Earth, 72–6 economy, 77–8 finance, 86–8 household, 78–81 market, 81–2 power, 91–92 society, 76–7 state, 84–6 trade, 89–90 employment, 36, 37, 51, 142, 176 automation, 191–5, 237, 258, 278 labour ownership, 188–91 workers’ rights, 88, 90, 269 Empty World, 74 Engels, Friedrich, 88 environment and circular economy, 220–42, 257 conservation, 121–2 and degenerative linear economy, 211–19, 222–3 degradation, 5, 9, 10, 29, 44–53, 74, 154, 172, 196, 206–42 education on, 115, 239–40 externalities, 152 fair share, 216–17 and finance, 234–7 generosity, 218–19, 223–7 green growth, 41, 210, 243–85 nudging, 123–5 taxation and quotas, 213–14, 215 zero impact, 217–18, 238, 241 Environmental Dashboard, 240–41 environmental economics, 7, 11, 114–16 Environmental Kuznets Curve, 207–11, 241 environmental space, 54 Epstein, Joshua, 150 equilibrium theory, 134–62 Ethereum, 187–8 ethics, 160–62 Ethiopia, 9, 226, 254 Etsy, 105 Euclid, 13, 15 European Central Bank, 145, 275 European Commission, 41 European Union (EU), 92, 153, 210, 222, 255, 258 Evergreen Cooperatives, 190 Evergreen Direct Investing (EDI), 273 exogenous shocks, 141 exponential growth, 39, 246–85 externalities, 143, 152, 213 Exxon Valdez oil spill (1989), 9 F Facebook, 192 fair share, 216–17 Fama, Eugene, 68, 87 fascism, 234, 277 Federal Reserve, US, 87, 145, 146, 271, 282 feedback loops, 138–41, 143, 148, 155, 250, 271 feminist economics, 11, 78–81, 160 Ferguson, Thomas, 91–2 finance animal spirits, 110 bank runs, 139 Black–Scholes model, 100–101 boom and bust, 28–9, 110, 144–7 and Circular Flow, 63–4, 87 and complex systems, 134, 138, 139, 140, 141, 145–7 cross-border flows, 89 deregulation, 87 derivatives, 100–101, 149 and distribution, 169, 170, 173, 182–4, 198–9, 201 and efficient market hypothesis, 63, 68 and Embedded Economy, 71, 86–8 and financial-instability hypothesis, 87, 146 and GDP growth, 38 and media, 7–8 mobile banking, 199–200 and money creation, 87, 182–5 and regeneration, 227, 229, 234–7 in service to life, 159, 234–7 stakeholder finance, 190 and sustainability, 216, 235–6, 239 financial crisis (2008), 1–4, 5, 40, 63, 86, 141, 144, 278, 290 and efficient market hypothesis, 87 and equilibrium theory, 134, 145 and financial-instability hypothesis, 87 and inequality, 90, 170, 172, 175 and money creation, 182 and worker’s rights, 278 financial flows, 89 Financial Times, 183, 266, 289 financial-instability hypothesis, 87, 146 First Green Bank, 236 First World War (1914–18), 166, 170 Fisher, Irving, 183 fluid values, 102, 106–9 food, 3, 43, 45, 50, 54, 58, 59, 89, 198 food banks, 165 food price crisis (2007–8), 89, 90, 180 Ford, 277–8 foreign direct investment, 89 forest conservation, 121–2 fossil fuels, 59, 73, 75, 92, 212, 260, 263 Foundations of Economic Analysis (Samuelson), 17–18 Foxconn, 193 framing, 22–3 France, 43, 165, 196, 238, 254, 256, 281, 290 Frank, Robert, 100 free market, 33, 37, 67, 68, 70, 81–2, 86, 90 free open-source hardware (FOSH), 196–7 free open-source software (FOSS), 196 free trade, 70, 90 Freeman, Ralph, 18–19 freshwater cycle, 48–9 Freud, Sigmund, 107, 281 Friedman, Benjamin, 258 Friedman, Milton, 34, 62, 66–9, 84–5, 88, 99, 183, 232 Friends of the Earth, 54 Full World, 75 Fuller, Buckminster, 4 Fullerton, John, 234–6, 273 G G20, 31, 56, 276, 279–80 G77, 55 Gal, Orit, 141 Gandhi, Mohandas, 42, 293 Gangnam Style, 145 Gardens of Democracy, The (Liu & Hanauer), 158 gender equality, 45, 51–2, 57, 78–9, 85, 88, 118–19, 124, 171, 198 generosity, 218–19, 223–9 geometry, 13, 15 George, Henry, 149, 179 Georgescu-Roegen, Nicholas, 252 geothermal energy, 221 Gerhardt, Sue, 283 Germany, 2, 41, 100, 118, 165, 189, 211, 213, 254, 256, 260, 274 Gessel, Silvio, 274 Ghent, Belgium, 236 Gift Relationship, The (Titmuss), 118–19 Gigerenzer, Gerd, 112–14 Gintis, Herb, 104 GiveDirectly, 200 Glass–Steagall Act (1933), 87 Glennon, Roger, 214 Global Alliance for Tax Justice, 277 global material footprints, 210–11 Global Village Construction Set, 196 globalisation, 89 Goerner, Sally, 175–6 Goffmann, Erving, 22 Going for Growth, 255 golden rule, 91 Goldman Sachs, 149, 170 Gómez-Baggethun, Erik, 122 Goodall, Chris, 211 Goodwin, Neva, 79 Goody, Jade, 124 Google, 192 Gore, Albert ‘Al’, 172 Gorgons, 244, 256, 257, 266 graffiti, 15, 25, 287 Great Acceleration, 46, 253–4 Great Depression (1929–39), 37, 70, 170, 173, 183, 275, 277, 278 Great Moderation, 146 Greece, Ancient, 4, 13, 32, 48, 54, 56–7, 160, 244 green growth, 41, 210, 243–85 Greenham, Tony, 185 greenhouse gas emissions, 31, 46, 50, 75–6, 141, 152–4 and decoupling, 260, 266 and Environmental Kuznets Curve, 208, 210 and forests, 50, 52 and G20, 31 and inequality, 58 reduction of, 184, 201–2, 213, 216–18, 223–7, 239–41, 256, 259–60, 266, 298 stock–flow dynamics, 152–4 and taxation, 201, 213 Greenland, 141, 154 Greenpeace, 9 Greenspan, Alan, 87 Greenwich, London, 290 Grenoble, France, 281 Griffiths, Brian, 170 gross domestic product (GDP), 25, 31–2, 35–43, 57, 60, 84, 164 as cuckoo, 32, 35, 36, 38, 40, 54, 60, 159, 244, 256, 271 and Environmental Kuznets Curve, 207–11 and exponential growth, 39, 53, 246–85 and growth agnosticism, 29–30, 240, 243–85 and inequality, 173 and Kuznets Curve, 167, 173, 188–9 gross national product (GNP), 36–40 Gross World Product, 248 Grossman, Gene, 207–8, 210 ‘grow now, clean up later’, 207 Guatemala, 196 H Haifa, Israel, 120 Haldane, Andrew, 146 Han Dynasty, 154 Hanauer, Nick, 158 Hansen, Pelle, 124 Happy Planet Index, 280 Hardin, Garrett, 69, 83, 181 Harvard University, 2, 271, 290 von Hayek, Friedrich, 7–8, 62, 66, 67, 143, 156, 158 healthcare, 43, 50, 57, 85, 123, 125, 170, 176, 200, 269, 279 Heilbroner, Robert, 53 Henry VIII, King of England and Ireland, 180 Hepburn, Cameron, 261 Herbert Simon, 111 heuristics, 113–14, 118, 123 high-income countries growth, 30, 244–5, 254–72, 282 inequality, 165, 168, 169, 171 labour, 177, 188–9, 278 overseas development assistance (ODA), 198–9 resource intensive lifestyles, 46, 210–11 trade, 90 Hippocrates, 160 History of Economic Analysis (Schumpeter), 21 HIV/AIDS, 123 Holocene epoch, 46–8, 75, 115, 253 Homo economicus, 94–103, 109, 127–8 Homo sapiens, 38, 104, 130 Hong Kong, 180 household, 78 housing, 45, 59, 176, 182–3, 269 Howe, Geoffrey, 67 Hudson, Michael, 183 Human Development Index, 9, 279 human nature, 28 human rights, 10, 25, 45, 49, 50, 95, 214, 233 humanistic economics, 42 hydropower, 118, 260, 263 I Illinois, United States, 179–80 Imago Mundi, 13 immigration, 82, 199, 236, 266 In Defense of Economic Growth (Beckerman), 258 Inclusive Wealth Index, 280 income, 51, 79–80, 82, 88, 176–8, 188–91, 194, 199–201 India, 2, 9, 10, 42, 124, 164, 178, 196, 206–7, 242, 290 Indonesia, 90, 105–6, 164, 168, 200 Indus Valley civilisation, 48 inequality, 1, 5, 25, 41, 63, 81, 88, 91, 148–52, 209 and consumerism, 111 and democracy, 171 and digital revolution, 191–5 and distribution, 163–205 and environmental degradation, 172 and GDP growth, 173 and greenhouse gas emissions, 58 and intellectual property, 195–8 and Kuznets Curve, 29, 166–70, 173–4 and labour ownership, 188–91 and land ownership, 178–82 and money creation, 182–8 and social welfare, 171 Success to the Successful, 148, 149, 151, 166 inflation, 36, 248, 256, 275 insect pollination services, 7 Institute of Economic Affairs, 67 institutional economics, 11 intellectual property rights, 195–8, 204 interest, 36, 177, 182, 184, 275–6 Intergovernmental Panel on Climate Change, 25 International Monetary Fund (IMF), 170, 172, 173, 183, 255, 258, 271 Internet, 83–4, 89, 105, 192, 202, 264 Ireland, 277 Iroquois Onondaga Nation, 116 Israel, 100, 103, 120 Italy, 165, 196, 254 J Jackson, Tim, 58 Jakubowski, Marcin, 196 Jalisco, Mexico, 217 Japan, 168, 180, 211, 222, 254, 256, 263, 275 Jevons, William Stanley, 16, 97–8, 131, 132, 137, 142 John Lewis Partnership, 190 Johnson, Lyndon Baines, 37 Johnson, Mark, 38 Johnson, Todd, 191 JPMorgan Chase, 149, 234 K Kahneman, Daniel, 111 Kamkwamba, William, 202, 204 Kasser, Tim, 125–6 Keen, Steve, 146, 147 Kelly, Marjorie, 190–91, 233 Kennedy, John Fitzgerald, 37, 250 Kennedy, Paul, 279 Kenya, 118, 123, 180, 185–6, 199–200, 226, 292 Keynes, John Maynard, 7–8, 22, 66, 69, 134, 184, 251, 277–8, 284, 288 Kick It Over movement, 3, 289 Kingston, London, 290 Knight, Frank, 66, 99 knowledge commons, 202–4, 229, 292 Kokstad, South Africa, 56 Kondratieff waves, 246 Korzybski, Alfred, 22 Krueger, Alan, 207–8, 210 Kuhn, Thomas, 22 Kumhof, Michael, 172 Kuwait, 255 Kuznets, Simon, 29, 36, 39–40, 166–70, 173, 174, 175, 204, 207 KwaZulu Natal, South Africa, 56 L labour ownership, 188–91 Lake Erhai, Yunnan, 56 Lakoff, George, 23, 38, 276 Lamelara, Indonesia, 105–6 land conversion, 49, 52, 299 land ownership, 178–82 land-value tax, 73, 149, 180 Landesa, 178 Landlord’s Game, The, 149 law of demand, 16 laws of motion, 13, 16–17, 34, 129, 131 Lehman Brothers, 141 Leopold, Aldo, 115 Lesotho, 118, 199 leverage points, 159 Lewis, Fay, 178 Lewis, Justin, 102 Lewis, William Arthur, 114, 167 Lietaer, Bernard, 175, 236 Limits to Growth, 40, 154, 258 Linux, 231 Liu, Eric, 158 living metrics, 240–42 living purpose, 233–4 Lomé, Togo, 231 London School of Economics (LSE), 2, 34, 65, 290 London Underground, 12 loss aversion, 112 low-income countries, 90, 164–5, 168, 173, 180, 199, 201, 209, 226, 254, 259 Lucas, Robert, 171 Lula da Silva, Luiz Inácio, 124 Luxembourg, 277 Lyle, John Tillman, 214 Lyons, Oren, 116 M M–PESA, 199–200 MacDonald, Tim, 273 Machiguenga, 105–6 MacKenzie, Donald, 101 macroeconomics, 36, 62–6, 76, 80, 134–5, 145, 147, 150, 244, 280 Magie, Elizabeth, 149, 153 Malala effect, 124 malaria, 5 Malawi, 118, 202, 204 Malaysia, 168 Mali, Taylor, 243 Malthus, Thomas, 252 Mamsera Rural Cooperative, 190 Manhattan, New York, 9, 41 Mani, Muthukumara, 206 Manitoba, 282 Mankiw, Gregory, 2, 34 Mannheim, Karl, 22 Maoris, 54 market, 81–2 and business, 88 circular flow, 64 and commons, 83, 93, 181, 200–201 efficiency of, 28, 62, 68, 87, 148, 181 and equilibrium theory, 131–5, 137, 143–7, 155, 156 free market, 33, 37, 67–70, 90, 208 and households, 63, 69, 78, 79 and maxi-max rule, 161 and pricing, 117–23, 131, 160 and rational economic man, 96, 100–101, 103, 104 and reciprocity, 105, 106 reflexivity of, 144–7 and society, 69–70 and state, 84–6, 200, 281 Marshall, Alfred, 17, 98, 133, 165, 253, 282 Marx, Karl, 88, 142, 165, 272 Massachusetts Institute of Technology (MIT), 17–20, 152–5 massive open online courses (MOOCs), 290 Matthew Effect, 151 Max-Neef, Manfred, 42 maxi-max rule, 161 maximum wage, 177 Maya civilisation, 48, 154 Mazzucato, Mariana, 85, 195, 238 McAfee, Andrew, 194, 258 McDonough, William, 217 Meadows, Donella, 40, 141, 159, 271, 292 Medusa, 244, 257, 266 Merkel, Angela, 41 Messerli, Elspeth, 187 Metaphors We Live By (Lakoff & Johnson), 38 Mexico, 121–2, 217 Michaels, Flora S., 6 micro-businesses, 9, 173, 178 microeconomics, 132–4 microgrids, 187–8 Micronesia, 153 Microsoft, 231 middle class, 6, 46, 58 middle-income countries, 90, 164, 168, 173, 180, 226, 254 migration, 82, 89–90, 166, 195, 199, 236, 266, 286 Milanovic, Branko, 171 Mill, John Stuart, 33–4, 73, 97, 250, 251, 283, 284, 288 Millo, Yuval, 101 minimum wage, 82, 88, 176 Minsky, Hyman, 87, 146 Mises, Ludwig von, 66 mission zero, 217 mobile banking, 199–200 mobile phones, 222 Model T revolution, 277–8 Moldova, 199 Mombasa, Kenya, 185–6 Mona Lisa (da Vinci), 94 money creation, 87, 164, 177, 182–8, 205 MONIAC (Monetary National Income Analogue Computer), 64–5, 75, 142, 262 Monoculture (Michaels), 6 Monopoly, 149 Mont Pelerin Society, 67, 93 Moral Consequences of Economic Growth, The (Friedman), 258 moral vacancy, 41 Morgan, Mary, 99 Morogoro, Tanzania, 121 Moyo, Dambisa, 258 Muirhead, Sam, 230, 231 MultiCapital Scorecard, 241 Murphy, David, 264 Murphy, Richard, 185 musical tastes, 110 Myriad Genetics, 196 N national basic income, 177 Native Americans, 115, 116, 282 natural capital, 7, 116, 269 Natural Economic Order, The (Gessel), 274 Nedbank, 216 negative externalities, 213 negative interest rates, 275–6 neoclassical economics, 134, 135 neoliberalism, 7, 62–3, 67–70, 81, 83, 84, 88, 93, 143, 170, 176 Nepal, 181, 199 Nestlé, 217 Netherlands, 211, 235, 224, 226, 238, 277 networks, 110–11, 117, 118, 123, 124–6, 174–6 neuroscience, 12–13 New Deal, 37 New Economics Foundation, 278, 283 New Year’s Day, 124 New York, United States, 9, 41, 55 Newlight Technologies, 224, 226, 293 Newton, Isaac, 13, 15–17, 32–3, 95, 97, 129, 131, 135–7, 142, 145, 162 Nicaragua, 196 Nigeria, 164 nitrogen, 49, 52, 212–13, 216, 218, 221, 226, 298 ‘no pain, no gain’, 163, 167, 173, 204, 209 Nobel Prize, 6–7, 43, 83, 101, 167 Norway, 281 nudging, 112, 113, 114, 123–6 O Obama, Barack, 41, 92 Oberlin, Ohio, 239, 240–41 Occupy movement, 40, 91 ocean acidification, 45, 46, 52, 155, 242, 298 Ohio, United States, 190, 239 Okun, Arthur, 37 onwards and upwards, 53 Open Building Institute, 196 Open Source Circular Economy (OSCE), 229–32 open systems, 74 open-source design, 158, 196–8, 265 open-source licensing, 204 Organisation for Economic Co-operation and Development (OECD), 38, 210, 255–6, 258 Origin of Species, The (Darwin), 14 Ormerod, Paul, 110, 111 Orr, David, 239 Ostrom, Elinor, 83, 84, 158, 160, 181–2 Ostry, Jonathan, 173 OSVehicle, 231 overseas development assistance (ODA), 198–200 ownership of wealth, 177–82 Oxfam, 9, 44 Oxford University, 1, 36 ozone layer, 9, 50, 115 P Pachamama, 54, 55 Pakistan, 124 Pareto, Vilfredo, 165–6, 175 Paris, France, 290 Park 20|20, Netherlands, 224, 226 Parker Brothers, 149 Patagonia, 56 patents, 195–6, 197, 204 patient capital, 235 Paypal, 192 Pearce, Joshua, 197, 203–4 peer-to-peer networks, 187, 192, 198, 203, 292 People’s QE, 184–5 Perseus, 244 Persia, 13 Peru, 2, 105–6 Phillips, Adam, 283 Phillips, William ‘Bill’, 64–6, 75, 142, 262 phosphorus, 49, 52, 212–13, 218, 298 Physiocrats, 73 Pickett, Kate, 171 pictures, 12–25 Piketty, Thomas, 169 Playfair, William, 16 Poincaré, Henri, 109, 127–8 Polanyi, Karl, 82, 272 political economy, 33–4, 42 political funding, 91–2, 171–2 political voice, 43, 45, 51–2, 77, 117 pollution, 29, 45, 52, 85, 143, 155, 206–17, 226, 238, 242, 254, 298 population, 5, 46, 57, 155, 199, 250, 252, 254 Portugal, 211 post-growth society, 250 poverty, 5, 9, 37, 41, 50, 88, 118, 148, 151 emotional, 283 and inequality, 164–5, 168–9, 178 and overseas development assistance (ODA), 198–200 and taxation, 277 power, 91–92 pre-analytic vision, 21–2 prescription medicines, 123 price-takers, 132 prices, 81, 118–23, 131, 160 Principles of Economics (Mankiw), 34 Principles of Economics (Marshall), 17, 98 Principles of Political Economy (Mill), 288 ProComposto, 226 Propaganda (Bernays), 107 public relations, 107, 281 public spending v. investment, 276 public–private patents, 195 Putnam, Robert, 76–7 Q quantitative easing (QE), 184–5 Quebec, 281 Quesnay, François, 16, 73 R Rabot, Ghent, 236 Rancière, Romain, 172 rating and review systems, 105 rational economic man, 94–103, 109, 111, 112, 126, 282 Reagan, Ronald, 67 reciprocity, 103–6, 117, 118, 123 reflexivity of markets, 144 reinforcing feedback loops, 138–41, 148, 250, 271 relative decoupling, 259 renewable energy biomass energy, 118, 221 and circular economy, 221, 224, 226, 235, 238–9, 274 and commons, 83, 85, 185, 187–8, 192, 203, 264 geothermal energy, 221 and green growth, 257, 260, 263, 264, 267 hydropower, 118, 260, 263 pricing, 118 solar energy, see solar energy wave energy, 221 wind energy, 75, 118, 196, 202–3, 221, 233, 239, 260, 263 rentier sector, 180, 183, 184 reregulation, 82, 87, 269 resource flows, 175 resource-intensive lifestyles, 46 Rethinking Economics, 289 Reynebeau, Guy, 237 Ricardo, David, 67, 68, 73, 89, 250 Richardson, Katherine, 53 Rifkin, Jeremy, 83, 264–5 Rise and Fall of the Great Powers, The (Kennedy), 279 risk, 112, 113–14 Robbins, Lionel, 34 Robinson, James, 86 Robinson, Joan, 142 robots, 191–5, 237, 258, 278 Rockefeller Foundation, 135 Rockford, Illinois, 179–80 Rockström, Johan, 48, 55 Roddick, Anita, 232–4 Rogoff, Kenneth, 271, 280 Roman Catholic Church, 15, 19 Rombo, Tanzania, 190 Rome, Ancient, 13, 48, 154 Romney, Mitt, 92 Roosevelt, Franklin Delano, 37 rooted membership, 190 Rostow, Walt, 248–50, 254, 257, 267–70, 284 Ruddick, Will, 185 rule of thumb, 113–14 Ruskin, John, 42, 223 Russia, 200 rust belt, 90, 239 S S curve, 251–6 Sainsbury’s, 56 Samuelson, Paul, 17–21, 24–5, 38, 62–7, 70, 74, 84, 91, 92, 93, 262, 290–91 Sandel, Michael, 41, 120–21 Sanergy, 226 sanitation, 5, 51, 59 Santa Fe, California, 213 Santinagar, West Bengal, 178 São Paolo, Brazil, 281 Sarkozy, Nicolas, 43 Saumweder, Philipp, 226 Scharmer, Otto, 115 Scholes, Myron, 100–101 Schumacher, Ernst Friedrich, 42, 142 Schumpeter, Joseph, 21 Schwartz, Shalom, 107–9 Schwarzenegger, Arnold, 163, 167, 204 ‘Science and Complexity’ (Weaver), 136 Scotland, 57 Seaman, David, 187 Seattle, Washington, 217 second machine age, 258 Second World War (1939–45), 18, 37, 70, 170 secular stagnation, 256 self-interest, 28, 68, 96–7, 99–100, 102–3 Selfish Society, The (Gerhardt), 283 Sen, Amartya, 43 Shakespeare, William, 61–3, 67, 93 shale gas, 264, 269 Shang Dynasty, 48 shareholders, 82, 88, 189, 191, 227, 234, 273, 292 sharing economy, 264 Sheraton Hotel, Boston, 3 Siegen, Germany, 290 Silicon Valley, 231 Simon, Julian, 70 Sinclair, Upton, 255 Sismondi, Jean, 42 slavery, 33, 77, 161 Slovenia, 177 Small Is Beautiful (Schumacher), 42 smart phones, 85 Smith, Adam, 33, 57, 67, 68, 73, 78–9, 81, 96–7, 103–4, 128, 133, 160, 181, 250 social capital, 76–7, 122, 125, 172 social contract, 120, 125 social foundation, 10, 11, 44, 45, 49, 51, 58, 77, 174, 200, 254, 295–6 social media, 83, 281 Social Progress Index, 280 social pyramid, 166 society, 76–7 solar energy, 59, 75, 111, 118, 187–8, 190 circular economy, 221, 222, 223, 224, 226–7, 239 commons, 203 zero-energy buildings, 217 zero-marginal-cost revolution, 84 Solow, Robert, 135, 150, 262–3 Soros, George, 144 South Africa, 56, 177, 214, 216 South Korea, 90, 168 South Sea Bubble (1720), 145 Soviet Union (1922–91), 37, 67, 161, 279 Spain, 211, 238, 256 Spirit Level, The (Wilkinson & Pickett), 171 Sraffa, Piero, 148 St Gallen, Switzerland, 186 Stages of Economic Growth, The (Rostow), 248–50, 254 stakeholder finance, 190 Standish, Russell, 147 state, 28, 33, 69–70, 78, 82, 160, 176, 180, 182–4, 188 and commons, 85, 93, 197, 237 and market, 84–6, 200, 281 partner state, 197, 237–9 and robots, 195 stationary state, 250 Steffen, Will, 46, 48 Sterman, John, 66, 143, 152–4 Steuart, James, 33 Stiglitz, Joseph, 43, 111, 196 stocks and flows, 138–41, 143, 144, 152 sub-prime mortgages, 141 Success to the Successful, 148, 149, 151, 166 Sugarscape, 150–51 Summers, Larry, 256 Sumner, Andy, 165 Sundrop Farms, 224–6 Sunstein, Cass, 112 supply and demand, 28, 132–6, 143, 253 supply chains, 10 Sweden, 6, 255, 275, 281 swishing, 264 Switzerland, 42, 66, 80, 131, 186–7, 275 T Tableau économique (Quesnay), 16 tabula rasa, 20, 25, 63, 291 takarangi, 54 Tanzania, 121, 190, 202 tar sands, 264, 269 taxation, 78, 111, 165, 170, 176, 177, 237–8, 276–9 annual wealth tax, 200 environment, 213–14, 215 global carbon tax, 201 global financial transactions tax, 201, 235 land-value tax, 73, 149, 180 non-renewable resources, 193, 237–8, 278–9 People’s QE, 185 tax relief v. tax justice, 23, 276–7 TED (Technology, Entertainment, Design), 202, 258 Tempest, The (Shakespeare), 61, 63, 93 Texas, United States, 120 Thailand, 90, 200 Thaler, Richard, 112 Thatcher, Margaret, 67, 69, 76 Theory of Moral Sentiments (Smith), 96 Thompson, Edward Palmer, 180 3D printing, 83–4, 192, 198, 231, 264 thriving-in-balance, 54–7, 62 tiered pricing, 213–14 Tigray, Ethiopia, 226 time banking, 186 Titmuss, Richard, 118–19 Toffler, Alvin, 12, 80 Togo, 231, 292 Torekes, 236–7 Torras, Mariano, 209 Torvalds, Linus, 231 trade, 62, 68–9, 70, 89–90 trade unions, 82, 176, 189 trademarks, 195, 204 Transatlantic Trade and Investment Partnership (TTIP), 92 transport, 59 trickle-down economics, 111, 170 Triodos, 235 Turkey, 200 Tversky, Amos, 111 Twain, Mark, 178–9 U Uganda, 118, 125 Ulanowicz, Robert, 175 Ultimatum Game, 105, 117 unemployment, 36, 37, 276, 277–9 United Kingdom Big Bang (1986), 87 blood donation, 118 carbon dioxide emissions, 260 free trade, 90 global material footprints, 211 money creation, 182 MONIAC (Monetary National Income Analogue Computer), 64–5, 75, 142, 262 New Economics Foundation, 278, 283 poverty, 165, 166 prescription medicines, 123 wages, 188 United Nations, 55, 198, 204, 255, 258, 279 G77 bloc, 55 Human Development Index, 9, 279 Sustainable Development Goals, 24, 45 United States American Economic Association meeting (2015), 3 blood donation, 118 carbon dioxide emissions, 260 Congress, 36 Council of Economic Advisers, 6, 37 Earning by Learning, 120 Econ 101 course, 8, 77 Exxon Valdez oil spill (1989), 9 Federal Reserve, 87, 145, 146, 271, 282 free trade, 90 Glass–Steagall Act (1933), 87 greenhouse gas emissions, 153 global material footprint, 211 gross national product (GNP), 36–40 inequality, 170, 171 land-value tax, 73, 149, 180 political funding, 91–2, 171 poverty, 165, 166 productivity and employment, 193 rust belt, 90, 239 Transatlantic Trade and Investment Partnership (TTIP), 92 wages, 188 universal basic income, 200 University of Berkeley, 116 University of Denver, 160 urbanisation, 58–9 utility, 35, 98, 133 V values, 6, 23, 34, 35, 42, 117, 118, 121, 123–6 altruism, 100, 104 anthropocentric, 115 extrinsic, 115 fluid, 28, 102, 106–9 and networks, 110–11, 117, 118, 123, 124–6 and nudging, 112, 113, 114, 123–6 and pricing, 81, 120–23 Veblen, Thorstein, 82, 109, 111, 142 Venice, 195 verbal framing, 23 Verhulst, Pierre, 252 Victor, Peter, 270 Viner, Jacob, 34 virtuous cycles, 138, 148 visual framing, 23 Vitruvian Man, 13–14 Volkswagen, 215–16 W Wacharia, John, 186 Wall Street, 149, 234, 273 Wallich, Henry, 282 Walras, Léon, 131, 132, 133–4, 137 Ward, Barbara, 53 Warr, Benjamin, 263 water, 5, 9, 45, 46, 51, 54, 59, 79, 213–14 wave energy, 221 Ways of Seeing (Berger), 12, 281 Wealth of Nations, The (Smith), 74, 78, 96, 104 wealth ownership, 177–82 Weaver, Warren, 135–6 weightless economy, 261–2 WEIRD (Western, educated, industrialised, rich, democratic), 103–5, 110, 112, 115, 117, 282 West Bengal, India, 124, 178 West, Darrell, 171–2 wetlands, 7 whale hunting, 106 Wiedmann, Tommy, 210 Wikipedia, 82, 223 Wilkinson, Richard, 171 win–win trade, 62, 68, 89 wind energy, 75, 118, 196, 202–3, 221, 233, 239, 260, 263 Wizard of Oz, The, 241 Woelab, 231, 293 Wolf, Martin, 183, 266 women’s rights, 33, 57, 107, 160, 201 and core economy, 69, 79–81 education, 57, 124, 178, 198 and land ownership, 178 see also gender equality workers’ rights, 88, 91, 269 World 3 model, 154–5 World Bank, 6, 41, 119, 164, 168, 171, 206, 255, 258 World No Tobacco Day, 124 World Trade Organization, 6, 89 worldview, 22, 54, 115 X xenophobia, 266, 277, 286 Xenophon, 4, 32, 56–7, 160 Y Yandle, Bruce, 208 Yang, Yuan, 1–3, 289–90 yin yang, 54 Yousafzai, Malala, 124 YouTube, 192 Yunnan, China, 56 Z Zambia, 10 Zanzibar, 9 Zara, 276 Zeitvorsoge, 186–7 zero environmental impact, 217–18, 238, 241 zero-hour contracts, 88 zero-humans-required production, 192 zero-interest loans, 183 zero-marginal-cost revolution, 84, 191, 264 zero-waste manufacturing, 227 Zinn, Howard, 77 PICTURE ACKNOWLEDGEMENTS Illustrations are reproduced by kind permission of: archive.org

Toward Rational Exuberance: The Evolution of the Modern Stock Market
by B. Mark Smith
Published 1 Jan 2001

It was a ticking time bomb destined to explode disastrously in the future. In the short run, however, all was well. By coincidence, the Chicago Board of Trade inaugurated trading in stock options the same year that Black and Scholes published their new “model” for pricing options. Option traders routinely made use of the Black-Scholes model to price their transactions. An entire new market had been created in response to the work of a few academics. As university scholars pressed the investment community from one side, the federal government weighed in on the other. In 1974, Congress passed landmark legislation establishing regulations under which pension and retirement plans would operate.

…

As he pondered his brother’s remarks, Hayne wondered if it might be possible to devise a means by which worried investment managers could protect themselves against bear markets, without having to liquidate their entire portfolios. He was well aware of the landmark work done by Fischer Black and Myron Scholes, creator of the Black-Scholes model for valuing options. What was needed, Leland reasoned as he lay in bed, was a “put option” on the market as a whole that a portfolio manager could purchase to “insure” his holdings against a bear market. (A “put” option is the opposite of a “call” option; the holder of the “put” is entitled to sell a specified security at a specified price during a specified period of time.)

…

If the value of the stock index moved higher after the futures transaction was made, the seller would have to make up the difference to the buyer, and vice versa if the stock index went down. The messy necessity of delivering exact numbers of shares in the many different stocks that made up the index was avoided. To “insure” a stock portfolio, the portfolio manager would sell an amount of futures dictated by the Black-Scholes model. The nature of the replicating (hedging) process was such that it was necessary to sell more futures contracts as stock prices declined, and to buy back those futures contracts as prices rose. Obviously there was a potential cost involved in this process; if the market was very volatile (meaning that prices moved back and forth frequently), the portfolio insurer might be required to repeatedly sell futures at lower prices, then buy them back at higher prices, thus incurring a loss.

Against the Gods: The Remarkable Story of Risk
by Peter L. Bernstein
Published 23 Aug 1996

If AT&T stock goes to 45, or 40, or even to 20 during the life of the option, the owner of the option still stands to lose no more than $2.50. Between 50 1/4 and 52 3/4, the owner will gain less than $2.50. Above 52 3/4, the potential profit is infinite-at least in theory. With all the variables cranked in, the Black-Scholes model indicates that the AT&T option was worth about $2.50 in June 1995 because investors expected AT&T stock to vary within a range of about 10%, or five points, in each direction during the four months the option would be in existence. Volatility is always the key determinant. By way of contrast to AT&T, consider the stock of software leader Microsoft.

…

The price of this option was 80% above the price of the AT&T option, although Microsoft stock was selling at only about 60% above AT&T. The price of Microsoft stock was nearly seven points away from the strike price, compared with the mere quarter of a point difference in the case of AT&T. The market clearly expected Microsoft to be more volatile than AT&T. According to the Black-Scholes model, the market expected Microsoft to be exactly twice as volatile as AT&T over the following four months. Microsoft stock is a lot riskier than AT&T stock. In 1995, AT&T had revenues of nearly $90 billion, 2.3 million shareholders, a customer in just about every household and every business in the nation, a weakened but still powerful monopolistic position in its industry, and a long history of uninterrupted dividend payments.

…

It consists of a spacious trading floor, a basement with an acre and a half of computers, enough wiring to reach twice around the Equator, and a telephone system that could service a city of 50,000. There was a second coincidence. At the very time the BlackScholes article appeared in The Journal of Political Economy and the CBOE started trading, the hand-held electronic calculator appeared on the scene. Within six months of the publication of the Black-Scholes model, Texas Instruments placed a half-page ad in The Wall Street Journal that proclaimed, "Now you can find the Black-Scholes value using our ... calculator." Before long, options traders were using technical expressions right out of the Black-Scholes article, such as hedge ratios, deltas, and stochastic differential equations.

Traders, Guns & Money: Knowns and Unknowns in the Dazzling World of Derivatives
by Satyajit Das
Published 15 Nov 2006

N(– d1) Where Ppe = price of European put option Despite the formidable appearance of the equation, you need only high school maths to derive the option values. The papers would have remained obscure had it not been for the confluence of events. In 1973, the Chicago Board Options Exchange started trading options on leading stocks and the Black–Scholes formula quickly became the market standard for pricing and trading options. HewlettPackard calculators with preprogrammed Black–Scholes option pricing model became available – the age of the super model had arrived. In 1997, Scholes and Merton received the Nobel Prize for economics in recognition of their work.

…

However, the text is different. 6 ‘What Worries Warren’ (3 March 2003) Fortune. 13_INDEX.QXD 17/2/06 4:44 pm Page 325 Index accounting rules 139, 221, 228, 257 Accounting Standards Board 33 accrual accounting 139 active fund management 111 actuaries 107–10, 205, 289 Advance Corporation Tax 242 agency business 123–4, 129 agency theory 117 airline profits 140–1 Alaska 319 Allen, Woody 20 Allied Irish Bank 143 Allied Lyons 98 alternative investment strategies 112, 308 American Express 291 analysts, role of 62–4 anchor effect 136 Anderson, Rolf 92–4 annuities 204–5 ANZ Bank 277 Aquinas, Thomas 137 arbitrage 33, 38–40, 99, 114, 137–8, 171–2, 245–8, 253–5, 290, 293–6 arbitration 307 Argentina 45 arithmophobia 177 ‘armpit theory’ 303 Armstrong World Industries 274 arrears assets 225 Ashanti Goldfields 97–8, 114 Asian financial crisis (1997) 4, 9, 44–5, 115, 144, 166, 172, 207, 235, 245, 252, 310, 319 asset consultants 115–17, 281 ‘asset growth’ strategy 255 asset swaps 230–2 assets under management (AUM) 113–4, 117 assignment of loans 267–8 AT&T 275 attribution of earnings 148 auditors 144 Australia 222–4, 254–5, 261–2 back office functions 65–6 back-to-back loans 35, 40 backwardation 96 Banca Popolare di Intra 298 Bank of America 298, 303 Bank of International Settlements 50–1, 281 Bank of Japan 220 Bankers’ Trust (BT) 59, 72, 101–2, 149, 217–18, 232, 268–71, 298, 301, 319 banking regulations 155, 159, 162, 164, 281, 286, 288 banking services 34; see also commercial banks; investment banks bankruptcy 276–7 Banque Paribas 37–8, 232 Barclays Bank 121–2, 297–8 13_INDEX.QXD 17/2/06 326 4:44 pm Page 326 Index Baring, Peter 151 Baring Brothers 51, 143, 151–2, 155 ‘Basel 2’ proposal 159 basis risk 28, 42, 274 Bear Stearns 173 bearer eurodollar collateralized securities (BECS) 231–3 ‘behavioural finance’ 136 Berkshire Hathaway 19 Bermudan options 205, 227 Bernstein, Peter 167 binomial option pricing model 196 Bismarck, Otto von 108 Black, Fischer 22, 42, 160, 185, 189–90, 193, 195, 197, 209, 215 Black–Scholes formula for option pricing 22, 185, 194–5 Black–Scholes–Merton model 160, 189–93, 196–7 ‘black swan’ hypothesis 130 Blair, Tony 223 Bogle, John 116 Bohr, Niels 122 Bond, Sir John 148 ‘bond floor’ concept 251–4 bonding 75–6, 168, 181 bonuses 146–51, 244, 262, 284–5 Brady Commission 203 brand awareness and brand equity 124, 236 Brazil 302 Bretton Woods system 33 bribery 80, 303 British Sky Broadcasting (BSB) 247–8 Brittain, Alfred 72 broad index secured trust offerings (BISTROs) 284–5 brokers 69, 309 Brown, Robert 161 bubbles 210, 310, 319 Buconero 299 Buffet, Warren 12, 19–20, 50, 110–11, 136, 173, 246, 316 business process reorganization 72 business risk 159 Business Week 130 buy-backs 249 ‘call’ options 25, 90, 99, 101, 131, 190, 196 callable bonds 227–9, 256 capital asset pricing model (CAPM) 111 capital flow 30 capital guarantees 257–8 capital structure arbitrage 296 Capote, Truman 87 carbon trading 320 ‘carry cost’ model 188 ‘carry’ trades 131–3, 171 cash accounting 139 catastrophe bonds 212, 320 caveat emptor principle 27, 272 Cayman Islands 233–4 Cazenove (company) 152 CDO2 292 Cemex 249–50 chaos theory 209, 312 Chase Manhattan Bank 143, 299 Chicago Board Options Exchange 195 Chicago Board of Trade (CBOT) 25–6, 34 chief risk officers 177 China 23–5, 276, 302–4 China Club, Hong Kong 318 Chinese walls 249, 261, 280 chrematophobia 177 Citibank and Citigroup 37–8, 43, 71, 79, 94, 134–5, 149, 174, 238–9 Citron, Robert 124–5, 212–17 client relationships 58–9 Clinton, Bill 223 Coats, Craig 168–9 collateral requirements 215–16 collateralized bond obligations (CBOs) 282 collateralized debt obligations (CDOs) 45, 282–99 13_INDEX.QXD 17/2/06 4:44 pm Page 327 Index collateralized fund obligations (CFOs) 292 collateralized loan obligations (CLOs) 283–5, 288 commercial banks 265–7 commoditization 236 commodity collateralized obligations (CCOs) 292 commodity prices 304 Commonwealth Bank of Australia 255 compliance officers 65 computer systems 54, 155, 197–8 concentration risk 271, 287 conferences with clients 59 confidence levels 164 confidentiality 226 Conseco 279–80 contagion crises 291 contango 96 contingent conversion convertibles (co-cos) 257 contingent payment convertibles (co-pays) 257 Continental Illinois 34 ‘convergence’ trading 170 convertible bonds 250–60 correlations 163–6, 294–5; see also default correlations corruption 303 CORVUS 297 Cox, John 196–7 credit cycle 291 credit default swaps (CDSs) 271–84, 293, 299 credit derivatives 129, 150, 265–72, 282, 295, 299–300 Credit Derivatives Market Practices Committee 273, 275, 280–1 credit models 294, 296 credit ratings 256–7, 270, 287–8, 297–8, 304 credit reserves 140 credit risk 158, 265–74, 281–95, 299 327 credit spreads 114, 172–5, 296 Credit Suisse 70, 106, 167 credit trading 293–5 CRH Capital 309 critical events 164–6 Croesus 137 cross-ruffing 142 cubic splines 189 currency options 98, 218, 319 custom repackaged asset vehicles (CRAVEs) 233 daily earning at risk (DEAR) concept 160 Daiwa Bank 142 Daiwa Europe 277 Danish Oil and Natural Gas 296 data scrubbing 142 dealers, work of 87–8, 124–8, 133, 167, 206, 229–37, 262, 295–6; see also traders ‘death swap’ strategy 110 decentralization 72 decision-making, scientific 182 default correlations 270–1 defaults 277–9, 287, 291, 293, 296, 299 DEFCON scale 156–7 ‘Delta 1’ options 243 delta hedging 42, 200 Deming, W.E. 98, 101 Denmark 38 deregulation, financial 34 derivatives trading 5–6, 12–14, 18–72, 79, 88–9, 99–115, 123–31, 139–41, 150, 153, 155, 175, 184–9, 206–8, 211–14, 217–19, 230, 233, 257, 262–3, 307, 316, 319–20; see also equity derivatives Derman, Emmanuel 185, 198–9 Deutsche Bank 70, 104, 150, 247–8, 274, 277 devaluations 80–1, 89, 203–4, 319 13_INDEX.QXD 17/2/06 4:44 pm Page 328 328 Index dilution of share capital 241 DINKs 313 Disney Corporation 91–8 diversification 72, 110–11, 166, 299 dividend yield 243 ‘Dr Evil’ trade 135 dollar premium 35 downsizing 73 Drexel Burnham Lambert (DBL) 282 dual currency bonds 220–3; see also reverse dual currency bonds earthquakes, bonds linked to 212 efficient markets hypothesis 22, 31, 111, 203 electronic trading 126–30, 134 ‘embeddos’ 218 emerging markets 3–4, 44, 115, 132–3, 142, 212, 226, 297 Enron 54, 142, 250, 298 enterprise risk management (ERM) 176 equity capital management 249 equity collateralized obligations (ECOs) 292 equity derivatives 241–2, 246–9, 257–62 equity index 137–8 equity investment, retail market in 258–9 equity investors’ risk 286–8 equity options 253–4 equity swaps 247–8 euro currency 171, 206, 237 European Bank for Reconstruction and Development 297 European currency units 93 European Union 247–8 Exchange Rate Mechanism, European 204 exchangeable bonds 260 expatriate postings 81–2 expert witnesses 310–12 extrapolation 189, 205 extreme value theory 166 fads of management science 72–4 ‘fairway bonds’ 225 Fama, Eugene 22, 111, 194 ‘fat tail’ events 163–4 Federal Accounting Standards Board 266 Federal Home Loans Bank 213 Federal National Mortgage Association 213 Federal Reserve Bank 20, 173 Federal Reserve Board 132 ‘Ferraris’ 232 financial engineering 228, 230, 233, 249–50, 262, 269 Financial Services Authority (FSA), Japan 106, 238 Financial Services Authority (FSA), UK 15, 135 firewalls 235–6 firing of staff 84–5 First Interstate Ltd 34–5 ‘flat’ organizations 72 ‘flat’ positions 159 floaters 231–2; see also inverse floaters ‘flow’ trading 60–1, 129 Ford Motors 282, 296 forecasting 135–6, 190 forward contracts 24–33, 90, 97, 124, 131, 188 fugu fish 239 fund management 109–17, 286, 300 futures see forward contracts Galbraith, John Kenneth 121 gamma risk 200–2, 294 Gauss, Carl Friedrich 160–2 General Motors 279, 296 General Reinsurance 20 geometric Brownian motion (GBM) 161 Ghana 98 Gibson Greeting Cards 44 Glass-Steagall Act 34 gold borrowings 132 13_INDEX.QXD 17/2/06 4:44 pm Page 329 Index gold sales 97, 137 Goldman Sachs 34, 71, 93, 150, 173, 185 ‘golfing holiday bonds’ 224 Greenspan, Alan 6, 9, 19–21, 29, 43, 47, 50, 53, 62, 132, 159, 170, 215, 223, 308 Greenwich NatWest 298 Gross, Bill 19 Guangdong International Trust and Investment Corporation (GITIC) 276–7 guaranteed annuity option (GAO) contracts 204–5 Gutenfreund, John 168–9 gyosei shido 106 Haghani, Victor 168 Hamanaka, Yasuo 142 Hamburgische Landesbank 297 Hammersmith and Fulham, London Borough of 66–7 ‘hara-kiri’ swaps 39 Hartley, L.P. 163 Hawkins, Greg 168 ‘heaven and hell’ bonds 218 hedge funds 44, 88–9, 113–14, 167, 170–5, 200–2, 206, 253–4, 262–3, 282, 292, 296, 300, 308–9 hedge ratio 264 hedging 24–8, 31, 38–42, 60, 87–100, 184, 195–200, 205–7, 214, 221, 229, 252, 269, 281, 293–4, 310 Heisenberg, Werner 122 ‘hell bonds’ 218 Herman, Clement (‘Crem’) 45–9, 77, 84, 309 Herodotus 137, 178 high net worth individuals (HNWIs) 237–8, 286 Hilibrand, Lawrence 168 Hill Samuel 231–2 329 The Hitchhiker’s Guide to the Galaxy 189 Homer, Sidney 184 Hong Kong 9, 303–4 ‘hot tubbing’ 311–12 HSBC Bank 148 HSH Nordbank 297–8 Hudson, Kevin 102 Hufschmid, Hans 77–8 IBM 36, 218, 260 ICI 34 Iguchi, Toshihude 142 incubators 309 independent valuation 142 indexed currency option notes (ICONs) 218 India 302 Indonesia 5, 9, 19, 26, 55, 80–2, 105, 146, 219–20, 252, 305 initial public offerings 33, 64, 261 inside information and insider trading 133, 241, 248–9 insurance companies 107–10, 117, 119, 150, 192–3, 204–5, 221, 223, 282, 286, 300; see also reinsurance companies insurance law 272 Intel 260 intellectual property in financial products 226 Intercontinental Hotels Group (IHG) 285–6 International Accounting Standards 33 International Securities Market Association 106 International Swap Dealers Association (ISDA) 273, 275, 279, 281 Internet stock and the Internet boom 64, 112, 259, 261, 310, 319 interpolation of interest rates 141–2, 189 inverse floaters 46–51, 213–16, 225, 232–3 13_INDEX.QXD 17/2/06 4:44 pm Page 330 330 Index investment banks 34–8, 62, 64, 67, 71, 127–8, 172, 198, 206, 216–17, 234, 265–7, 298, 309 investment managers 43–4 investment styles 111–14 irrational decisions 136 Italy 106–7 Ito’s Lemma 194 Japan 39, 43, 82–3, 92, 94, 98–9, 101, 106, 132, 142, 145–6, 157, 212, 217–25, 228, 269–70 Jensen, Michael 117 Jett, Joseph 143 JP Morgan (company) 72, 150, 152, 160, 162, 249–50, 268–9, 284–5, 299; see also Morgan Guaranty junk bonds 231, 279, 282, 291, 296–7 JWM Associates 175 Kahneman, Daniel 136 Kaplanis, Costas 174 Kassouf, Sheen 253 Kaufman, Henry 62 Kerkorian, Kirk 296 Keynes, J.M. 167, 175, 198 Keynesianism 5 Kidder Peabody 143 Kleinwort Benson 40 Korea 9, 226, 278 Kozeny, Viktor 121 Krasker, William 168 Kreiger, Andy 319 Kyoto Protocol 320 Lavin, Jack 102 law of large numbers 192 Leeson, Nick 51, 131, 143, 151 legal opinions 47, 219–20, 235, 273–4 Leibowitz, Martin 184 Leland, Hayne 42, 202 Lend Lease Corporation 261–2 leptokurtic conditions 163 leverage 31–2, 48–50, 54, 99, 102–3, 114, 131–2, 171–5, 213–14, 247, 270–3, 291, 295, 305, 308 Lewis, Kenneth 303 Lewis, Michael 77–8 life insurance 204–5 Lintner, John 111 liquidity options 175 liquidity risk 158, 173 litigation 297–8 Ljunggren, Bernt 38–40 London Inter-Bank Offered Rate (LIBOR) 6, 37 ‘long first coupon’ strategy 39 Long Term Capital Management (LTCM) 44, 51, 62, 77–8, 84, 114, 166–75, 187, 206, 210, 215–18, 263–4, 309–10 Long Term Credit Bank of Japan 94 LOR (company) 202 Louisiana Purchase 319 low exercise price options (LEPOs) 261 Maastricht Treaty and criteria 106–7 McLuhan, Marshall 134 McNamara, Robert 182 macro-economic indicators, derivatives linked to 319 Mahathir Mohammed 31 Malaysia 9 management consultants 72–3 Manchester United 152 mandatory convertibles 255 Marakanond, Rerngchai 302 margin calls 97–8, 175 ‘market neutral’ investment strategy 114 market risk 158, 173, 265 marketable eurodollar collateralized securities (MECS) 232 Markowitz, Harry 110 mark-to-market accounting 10, 100, 139–41, 145, 150, 174, 215–16, 228, 244, 266, 292, 295, 298 Marx, Groucho 24, 57, 67, 117, 308 13_INDEX.QXD 17/2/06 4:44 pm Page 331 Index mathematics applied to financial instruments 209–10; see also ‘quants’ matrix structures 72 Meckling, Herbert 117 Melamed, Leo 34, 211 merchant banks 38 Meriwether, John 167–9, 172–5 Merrill Lynch 124, 150, 217, 232 Merton, Robert 22, 42, 168–70, 175, 185, 189–90, 193–7, 210 Messier, Marie 247 Metallgesellschaft 95–7 Mexico 44 mezzanine finance 285–8, 291–7 MG Refining and Marketing 95–8, 114 Microsoft 53 Mill, Stuart 130 Miller, Merton 22, 101, 194 Milliken, Michael 282 Ministry of Finance, Japan 222 misogyny 75–7 mis-selling 238, 297–8 Mitchell, Edison 70 Mitchell & Butler 275–6 models financial 42–3, 141–2, 163–4, 173–5, 181–4, 189, 198–9, 205–10 of business processes 73–5 see also credit models Modest, David 168 momentum investment 111 monetization 260–1 monopolies in financial trading 124 moral hazard 151, 280, 291 Morgan Guaranty 37–8, 221, 232 Morgan Stanley 76, 150 mortgage-backed securities (MBSs) 282–3 Moscow, City of 277 moves of staff between firms 150, 244 Mozer, Paul 169 Mullins, David 168–70 multi-skilling 73 331 Mumbai 3 Murdoch, Rupert 247 Nabisco 220 Napoleon 113 NASDAQ index 64, 112 Nash, Ogden 306 National Australia Bank 144, 178 National Rifle Association 29 NatWest Bank 144–5, 198 Niederhoffer, Victor 130 ‘Nero’ 7, 31, 45–9, 60, 77, 82–3, 88–9, 110, 118–19, 125, 128, 292 NERVA 297 New Zealand 319 Newman, Frank 104 news, financial 133–4 News Corporation 247 Newton, Isaac 162, 210 Nippon Credit Bank 106, 271 Nixon, Richard 33 Nomura Securities 218 normal distribution 160–3, 193, 199 Northern Electric 248 O’Brien, John 202 Occam, William 188 off-balance sheet transactions 32–3, 99, 234, 273, 282 ‘offsites’ 74–5 oil prices 30, 33, 89–90, 95–7 ‘omitted variable’ bias 209–10 operational risk 158, 176 opinion shopping 47 options 9, 21–2, 25–6, 32, 42, 90, 98, 124, 197, 229 pricing 185, 189–98, 202 Orange County 16, 44, 50, 124–57, 212–17, 232–3 orphan subsidiaries 234 over-the-counter (OTC) market 26, 34, 53, 95, 124, 126 overvaluation 64 13_INDEX.QXD 17/2/06 4:44 pm Page 332 332 Index ‘overwhelming force’ strategy 134–5 Owen, Martin 145 ownership, ‘legal’ and ‘economic’ 247 parallel loans 35 pari-mutuel auction system 319 Parkinson’s Law 136 Parmalat 250, 298–9 Partnoy, Frank 87 pension funds 43, 108–10, 115, 204–5, 255 People’s Bank of China (PBOC) 276–7 Peters’ Principle 71 petrodollars 71 Pétrus (restaurant) 121 Philippines, the 9 phobophobia 177 Piga, Gustavo 106 PIMCO 19 Plaza Accord 38, 94, 99, 220 plutophobia 177 pollution quotas 320 ‘portable alpha’ strategy 115 portfolio insurance 112, 202–3, 294 power reverse dual currency (PRDC) bonds 226–30 PowerPoint 75 preferred exchangeable resettable listed shares (PERLS) 255 presentations of business models 75 to clients 57, 185 prime brokerage 309 Prince, Charles 238 privatization 205 privity of contract 273 Proctor & Gamble (P&G) 44, 101–4, 155, 298, 301 product disclosure statements (PDSs) 48–9 profit smoothing 140 ‘programme’ issuers 234–5 proprietary (‘prop’) trading 60, 62, 64, 130, 174, 254 publicly available information (PAI) 277 ‘puff’ effect 148 purchasing power parity theory 92 ‘put’ options 90, 131, 256 ‘quants’ 183–9, 198, 208, 294 Raabe, Matthew 217 Ramsay, Gordon 121 range notes 225 real estate 91, 219 regulatory arbitrage 33 reinsurance companies 288–9 ‘relative value’ trading 131, 170–1, 310 Reliance Insurance 91–2 repackaging (‘repack’) business 230–6, 282, 290 replication in option pricing 195–9, 202 dynamic 200 research provided to clients 58, 62–4, 184 reserves, use of 140 reset preference shares 254–7 restructuring of loans 279–81 retail equity products 258–9 reverse convertibles 258–9 reverse dual currency bonds 223–30 ‘revolver’ loans 284–5 risk, financial, types of 158 risk adjusted return on capital (RAROC) 268, 290 risk conservation principle 229–30 risk management 65, 153–79, 184, 187, 201, 267 risk models 163–4, 173–5 riskless portfolios 196–7 RJ Reynolds (company) 220–1 rogue traders 176, 313–16 Rosenfield, Eric 168 Ross, Stephen 196–7, 202 Roth, Don 38 Rothschild, Mayer Amshel 267 Royal Bank of Scotland 298 Rubinstein, Mark 42, 196–7 13_INDEX.QXD 17/2/06 4:44 pm Page 333 Index Rumsfeld, Donald 12, 134, 306 Rusnak, John 143 Russia 45, 80, 166, 172–3, 274, 302 sales staff 55–60, 64–5, 125, 129, 217 Salomon Brothers 20, 36, 54, 62, 167–9, 174, 184 Sandor, Richard 34 Sanford, Charles 72, 269 Sanford, Eugene 269 Schieffelin, Allison 76 Scholes, Myron 22, 42, 168–71, 175, 185, 189–90, 193–7, 263–4 Seagram Group 247 Securities and Exchange Commission, US 64, 304 Securities and Futures Authority, UK 249 securitization 282–90 ‘security design’ 254–7 self-regulation 155 sex discrimination 76 share options 250–1 Sharpe, William 111 short selling 30–1, 114 Singapore 9 single-tranche CDOs 293–4, 299 ‘Sisters of Perpetual Ecstasy’ 234 SITCOMs 313 Six Continents (6C) 275–6 ‘smile’ effect 145 ‘snake’ currency system 203 ‘softing’ arrangements 117 Solon 137 Soros, George 44, 130, 253, 318–19 South Sea Bubble 210 special purpose asset repackaging companies (SPARCs) 233 special purpose vehicles (SPVs) 231–4, 282–6, 290, 293 speculation 29–31, 42, 67, 87, 108, 130 ‘spinning’ 64 333 Spitzer, Eliot 64 spread 41, 103; see also credit spreads stack hedges 96 Stamenson, Michael 124–5 standard deviation 161, 193, 195, 199 Steinberg, Sol 91 stock market booms 258, 260 stock market crashes 42–3, 168, 203, 257, 259, 319 straddles or strangles 131 strategy in banking 70 stress testing 164–6 stripping of convertible bonds 253–4 structured investment products 44, 112, 115, 118, 128, 211–39, 298 structured note asset packages (SNAPs) 233 Stuart SC 18, 307, 316–18 Styblo Bleder, Tanya 153 Suharto, Thojib 81–2 Sumitomo Corporation 100, 142 Sun Tzu 61 Svensk Exportkredit (SEK) 38–9 swaps 5–10, 26, 35–40, 107, 188, 211; see also equity swaps ‘swaptions’ 205–6 Swiss Bank Corporation (SBC) 248–9 Swiss banks 108, 305 ‘Swiss cheese theory’ 176 synthetic securitization 284–5, 288–90 systemic risk 151 Takeover Panel 248–9 Taleb, Nassim 130, 136, 167 target redemption notes 225–6 tax and tax credits 171, 242–7, 260–3 Taylor, Frederick 98, 101 team-building exercises 76 team moves 149 technical analysis 60–1, 135 television programmes about money 53, 62–3 Thailand 9, 80, 302–5 13_INDEX.QXD 17/2/06 4:44 pm Page 334 334 Index Thatcher, Margaret 205 Thorp, Edward 253 tobashi trades 105–7 Tokyo Disneyland 92, 212 top managers 72–3 total return swaps 246–8, 269 tracking error 138 traders in financial products 59–65, 129–31, 135–6, 140, 148, 151, 168, 185–6, 198; see also dealers trading limits 42, 157, 201 trading rooms 53–4, 64, 68, 75–7, 184–7, 208 Trafalgar House 248 tranching 286–9, 292, 296 transparency 26, 117, 126, 129–30, 310 Treynor, Jack 111 trust investment enhanced return securities (TIERS) 216, 233 trust obligation participating securities (TOPS) 232 TXU Europe 279 UBS Global Asset Management 110, 150, 263–4, 274 uncertainty principle 122–3 unique selling propositions 118 unit trusts 109 university education 187 unspecified fund obligations (UFOs) 292 ‘upfronting’ of income 139, 151 Valéry, Paul 163 valuation 64, 142–6 value at risk (VAR) concept 160–7, 173 value investing 111 Vanguard 116 vanity bonds 230 variance 161 Vietnam War 182, 195 Virgin Islands 233–4 Vivendi 247–8 volatility of bond prices 197 of interest rates 144–5 of share prices 161–8, 172–5, 192–3, 199 Volcker, Paul 20, 33 ‘warehouses’ 40–2, 139 warrants arbitrage 99–101 weather, bonds linked to 212, 320 Weatherstone, Dennis 72, 268 Weil, Gotscal & Manges 298 Weill, Sandy 174 Westdeutsche Genosenschafts Zentralbank 143 Westminster Group 34–5 Westpac 261–2 Wheat, Allen 70, 72, 106, 167 Wojniflower, Albert 62 World Bank 4, 36, 38 World Food Programme 320 Worldcom 250, 298 Wriston, Walter 71 WTI (West Texas Intermediate) contracts 28–30 yield curves 103, 188–9, 213, 215 yield enhancement 112, 213, 269 ‘yield hogs’ 43 zaiteku 98–101, 104–5 zero coupon bonds 221–2, 257–8 

How Markets Fail: The Logic of Economic Calamities
by John Cassidy
Published 10 Nov 2009

Finally, in the early 1970s, Black, a man of few words, and Scholes, a voluble Canadian, derived a simple formula that related the price of an option to the volatility of the underlying stock. By coincidence, the paper that contained the Black-Scholes option pricing formula was published in May 1973, a month after the opening of the Chicago Board Options Exchange. To compute the value of an option using the Black-Scholes formula all you needed, in addition to the strike price, the current price, and the duration of the option, was the interest rate on government bonds, the standard deviation of the stock, and a table of the normal distribution. By the end of 1973, you didn’t even need a pen and paper to do the calculation: Texas Instruments had introduced a calculator that did it for you.

…

Mutual funds were able to insure themselves against the risk of corporations defaulting on their bonds, banks could insure themselves against some of their lenders defaulting, and insurance companies could insure against the chances of a freak hurricane leaving them with enormous claims from their policyholders. In each of these areas, the key was the development of mathematical methods to price risk. Almost all of these methods relied, to some extent, on the Black-Scholes formula and the bell curve. Simply by invoking the ghost of Louis Bachelier, it was possible to take much of the danger out of finance. Or was it? As far back as the 1960s and ’70s, some academics and Wall Street practitioners didn’t buy into the coin-tossing view of finance. Many old-school bankers and traders were put off by the mathematical demands it came with, but numbered among the skeptics were also some technically adept economists, including Sanford Grossman, of Wharton, and Joseph Stiglitz, who is now at Columbia.

Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined
by Lasse Heje Pedersen
Published 12 Apr 2015

From afar, it looks pretty calm; up close, it looks chaotic. I felt that the experience of the chaotic world, married to my theoretical abilities, would allow me to gain unique perspectives. For that reason, I gravitated to work for a while at Salomon Brothers. LHP: When most people think about the Black–Scholes formula, they think first about equity options, but you focused on fixed income arbitrage—why? MS: Right. The fascination with fixed-income arbitrage came about after many years of thinking about the idea that there are natural segmented clienteles. Insurance companies and pension funds tend to be at the longer end of the interest rate curve.

…

Based on the market prices in that book, there appeared to be some bonds that were mispriced. I made it my mission to educate myself on these instruments and to understand the pricing and trading of convertibles. LHP: Was the insight just based on some back of the envelope calculations, or did you need to already appreciate something like the Black–Scholes Formula or the binomial option pricing model at that time? KG: Back of the envelope, some common sense, and a bit of naïveté as to the dynamics around why these mispricings might exist. Many mispricings were driven by the inability to borrow the underlying common stock and therefore the convertible bond traded close to conversion value because the arbitrage was difficult.

13 Bankers: The Wall Street Takeover and the Next Financial Meltdown
by Simon Johnson and James Kwak
Published 29 Mar 2010

New methods for calculating the relative value of financial assets made possible arbitrage trading, where traders sought out small pricing discrepancies that, in theory, should not exist; by betting that the market would make these discrepancies disappear, they could make almost certain money. The Black-Scholes Model (developed by Black, Scholes, and Merton) provided a handy formula for calculating the price of a financial derivative, and in the process gave rise to the derivatives revolution. Thus academic finance produced important tools that would create new markets and vast new sources of revenues for Wall Street.

…

While commodity futures contracts (in which, for example, a farmer commits to sell wheat in the future for a pre-specified price) had been around for centuries,* the market for financial derivatives remained small until the early 1980s, largely because traders—or, more accurately, the managers responsible for keeping those traders in line—had no good way of calculating what they were worth. But in the 1970s, the Black-Scholes Model gave banks a new way to calculate the value of complicated derivatives and the hedges they used to protect themselves.† Wall Street embraced these quantitative models because they made it easier to price and trade derivatives in bulk. Nassim Taleb and Pablo Triana have argued that quantitative models are worse at pricing derivatives than the heuristics used by traders from the pre-quantitative era.72 Nonetheless, the formulas gave banks the confidence to sell growing volumes of increasingly complicated trades to clients, since the models enabled them to keep track of how much money they were making on each one.

How the City Really Works: The Definitive Guide to Money and Investing in London's Square Mile
by Alexander Davidson
Published 1 Apr 2008

The more time an option has until it expires, the higher this figure is likely to be, as the price of the underlying stock has more chance of changing in the option buyer’s favour. The premium consists of both intrinsic and time value, both of which can change constantly. These are factors used in the Black–Scholes model, which was developed in 1973 and is widely used in financial markets for valuing options. Other factors used in the model are volatility, the underlying stock price, and the risk-free rate of return. But Black–Scholes makes key assumptions that are not always tenable, including a constant risk-free interest rate, continuous trading and no transaction costs.

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Index 419 fraud 204 9/11 terrorist attacks 31, 218, 242, 243, 254, 257 Abbey National 22 ABN AMRO 103 accounting and governance 232–38 scandals 232 Accounting Standards Board (ASB) 236 administration 17 Allianz 207 Alternative Investment Market (AIM) 44–45, 131, 183, 238 Amaranth Advisors 170 analysts 172–78 fundamental 172–74 others 177–78 Spitzer impact 174–75 technical 175–77 anti-fraud agencies Assets Recovery Agency 211–13 City of London Police 209 Financial Services Authority 208 Financial Crime and Intelligence Division 208 Insurance Fraud Bureau 209 Insurance Fraud Investigators Group 209 International Association of Insurance Fraud Agencies 207, 210, 218 National Criminal Intelligence Service 210 Serious Fraud Office 213–15 Serious Organised Crime Agency 210–11 asset finance 24–25 Association of Investment Companies 167 backwardation 101 bad debt, collection of 26–28 Banco Santander Central Hispano 22 Bank for International Settlements (BIS) 17, 27, 85, 98, 114 bank guarantee 23 Bank of Credit and Commerce International (BCCI) 10, 214 Bank of England 6, 10–17 Court of the 11 credit risk warning 98 framework for sterling money markets 81 Governor 11, 13, 14 history 10, 15–16 Inflation Report 14 inflation targeting 12–13 interest rates and 12 international liaison 17 lender of last resort 15–17 Market Abuse Directive (MAD) 16 monetary policy and 12–15 Monetary Policy Committee (MPC) 13–14 Open-market operations 15, 82 repo rate 12, 15 role 11–12 RTGS (Real Time Gross Settlement) 143 statutory immunity 11 supervisory role 11 Bank of England Act 1988 11, 12 Bank of England Quarterly Model (BEQM) 14 Banking Act 1933 see Glass-Steagall Act banks commercial 5 investment 5 Barclays Bank 20 Barings 11, 15, 68, 186, 299 Barlow Clowes case 214 Barron’s 99 base rate see repo rate Basel Committee for Banking Supervision (BCBS) 27–28 ____________________________________________________ INDEX 303 Basel I 27 Basel II 27–28, 56 Bear Stearns 95, 97 BearingPoint 97 bill of exchange 26 Bingham, Lord Justice 10–11 Blue Arrow trial 214 BNP Paribas 145, 150 bond issues see credit products book runners 51, 92 Borsa Italiana 8, 139 bps 90 British Bankers’ Association 20, 96, 97 building societies 22–23 demutualisation 22 Building Societies Association 22 Capital Asset Pricing Model (CAPM) see discounted cash flow analysis capital gains tax 73, 75, 163, 168 capital raising markets 42–46 mergers and acquisitions (M&A) 56–58 see also flotation, bond issues Capital Requirements Directive 28, 94 central securities depository (CSD) 145 international (ICSD) 145 Central Warrants Trading Service 73 Chancellor of the Exchequer 12, 13, 229 Chicago Mercantile Exchange 65 Citigroup 136, 145, 150 City of London 4–9 Big Bang 7 definition 4 employment in 8–9 financial markets 5 geography 4–5 history 6–7 services offered 4 world leader 5–6 clearing 140, 141–42 Clearing House Automated Payment System (CHAPS) 143 Clearstream Banking Luxembourg 92, 145 commercial banking 5, 18–28 bad loans and capital adequacy 26–28 banking cards 21 building societies 22–23 credit collection 25–26 finance raising 23–25 history 18–19 overdrafts 23 role today 19–21 commodities market 99–109 exchange-traded commodities 101  fluctuations 100 futures 100 hard commodities energy 102 non-ferrous metals 102–04 precious metal 104–06 soft commodities cocoa 107 coffee 106 sugar 107 Companies Act 2006 204, 223, 236 conflict of interests 7 consolidation 138–39 Consumer Price Index (CPI) 13 contango 101 Continuous Linked Settlement (CLS) 119 corporate governance 223–38 best practice 231 Cadbury Code 224 Combined Code 43, 225 compliance 230 definition 223 Directors’ Remuneration Report Regulations 226 EU developments 230 European auditing rules 234–35 Greenbury Committee 224–25 Higgs and Smith reports 227 International Financial Reporting Standards (IFRS) 237–38 Listing Rules 228–29 Model Code 229 Myners Report 229 OECD Principles 226 operating and financial review (OFR) 235– 36 revised Combined Code 227–28 Sarbanes–Oxley Act 233–34 Turnbull Report 225 credit cards 21 zero-per-cent cards 21 credit collection 25–26 factoring and invoice discounting 26 trade finance 25–26 credit derivatives 96–97 back office issues 97 credit default swap (CDS) 96–97 credit products asset-backed securities 94 bonds 90–91 collateralised debt obligations 94–95 collateralised loan obligation 95 covered bonds 93 equity convertibles 93 international debt securities 92–93  304 INDEX ____________________________________________________ junk bonds 91 zero-coupon bonds 93 credit rating agencies 91 Credit Suisse 5, 136, 193 CREST system 141, 142–44 dark liquidity pools 138 Debt Management Office 82, 86 Department of Trade and Industry (DTI) 235, 251, 282 derivatives 60–77 asset classes 60 bilateral settlement 66 cash and 60–61 central counterparty clearing 65–66 contracts for difference 76–77, 129 covered warrants 72–73 futures 71–72 hedging and speculation 67 on-exchange vs OTC derivatives 63–65 options 69–71 Black-Scholes model 70 call option 70 equity option 70–71 index options 71 put option 70 problems and fraud 67–68 retail investors and 69–77 spread betting 73–75 transactions forward (future) 61–62 option 62 spot 61 swap 62–63 useful websites 75 Deutsche Bank 136 Deutsche Börse 64, 138 discounted cash flow analysis (DCF) 39 dividend 29 domestic financial services complaint and compensation 279–80 financial advisors 277–78 Insurance Mediation Directive 278–79 investments with life insurance 275–76 life insurance term 275 whole-of-life 274–75 NEWICOB 279 property and mortgages 273–74 protection products 275 savings products 276–77 Dow theory 175 easyJet 67 EDX London 66 Egg 20, 21 Elliott Wave Theory 176 Enron 67, 114, 186, 232, 233 enterprise investment schemes 167–68 Equiduct 133–34, 137 Equitable Life 282 equities 29–35 market indices 32–33 market influencers 40–41 nominee accounts 31 shares 29–32 stockbrokers 33–34 valuation 35–41 equity transparency 64 Eurex 64, 65 Euro Overnight Index Average (EURONIA) 85 euro, the 17, 115 Eurobond 6, 92 Euroclear Bank 92, 146, 148–49 Euronext.liffe 5, 60, 65, 71 European Central Bank (ECB) 16, 17, 84, 148 European Central Counterparty (EuroCCP) 136 European Code of Conduct 146–47, 150 European Exchange Rate Mechanism 114 European Harmonised Index of Consumer Prices 13 European Union Capital Requirements Directive 199 Market Abuse Directive (MAD) 16, 196 Market in Financial Instruments Directive (MiFID) 64, 197–99 Money Laundering Directive 219 Prospectus Directive 196–97 Transparency Directive 197 exchange controls 6 expectation theory 172 Exxon Valdez 250 factoring see credit collection Factors and Discounters Association 26 Fair & Clear Group 145–46 Federal Deposit Insurance Corporation 17 Federation of European Securities Exchanges 137 Fighting Fraud Together 200–01 finance, raising 23–25 asset 24–25 committed 23 project finance 24 recourse loan 24 syndicated loan 23–24 uncommitted 23 Financial Action Task Force on Money Laundering (FATF) 217–18 financial communications 179–89 ____________________________________________________ INDEX 305 advertising 189 corporate information flow 185 primary information providers (PIPs) 185 investor relations 183–84 journalists 185–89 public relations 179–183 black PR’ 182–83 tipsters 187–89 City Slickers case 188–89 Financial Ombudsman Service (FOS) 165, 279–80 financial ratios 36–39 dividend cover 37 earnings per share (EPS) 36 EBITDA 38 enterprise multiple 38 gearing 38 net asset value (NAV) 38 price/earnings (P/E) 37 price-to-sales ratio 37 return on capital employed (ROCE) 38 see also discounted cash flow analysis Financial Reporting Council (FRC) 224, 228, 234, 236 Financial Services Act 1986 191–92 Financial Services Action Plan 8, 195 Financial Services and Markets Act 2001 192 Financial Services and Markets Tribunal 94 Financial Services Authority (FSA) 5, 8, 31, 44, 67, 94, 97, 103, 171, 189, 192–99 competition review 132 insurance industry 240 money laundering and 219 objectives 192 regulatory role 192–95 powers 193 principles-based 194–95 Financial Services Compensation Scheme (FSCS) 17, 165, 280 Financial Services Modernisation Act 19 financial services regulation 190–99 see also Financial Services Authority Financial Times 9, 298 First Direct 20 flipping 53 flotation beauty parade 51 book build 52 early secondary market trading 53 grey market 52, 74 initial public offering (IPO) 47–53 pre-marketing 51–52 pricing 52–53 specialist types of share issue accelerated book build 54  bought deal 54 deeply discounted rights issue 55 introduction 55 placing 55 placing and open offer 55 rights issues 54–55 underwriting 52 foreign exchange 109–120 brokers 113 dealers 113 default risk 119 electronic trading 117 exchange rate 115 ICAP Knowledge Centre 120 investors 113–14 transaction types derivatives 116–17 spot market 115–16 Foreign Exchange Joint Standing Committee 112 forward rate agreement 85 fraud 200–15 advanced fee frauds 204–05 boiler rooms 201–04 Regulation S 202 future regulation 215 identity theft 205–06 insurance fraud 206–08 see also anti-fraud agencies Fraud Act 2006 200 FTSE 100 32, 36, 58, 122, 189, 227, 233 FTSE 250 32, 122 FTSE All-Share Index 32, 122 FTSE Group 131 FTSE SmallCap Index 32 FTSE Sterling Corporate Bond Index 33 Futures and Options Association 131 Generally Accepted Accounting Principles (GAAP) 237, 257 gilts 33, 86–88 Giovanni Group 146 Glass-Steagall Act 7, 19 Global Bond Market Forum 64 Goldman Sachs 136 government bonds see gilts Guinness case 214 Halifax Bank 20 hedge funds 8, 77, 97, 156–57 derivatives-based arbitrage 156 fixed-income arbitrage 157 Hemscott 35 HM Revenue and Customs 55, 211 HSBC 20, 103 Hurricane Hugo 250  306 INDEX ____________________________________________________ Hurricane Katrina 2, 67, 242 ICE Futures 5, 66, 102 Individual Capital Adequacy Standards (ICAS) 244 inflation 12–14 cost-push 12 definition 12 demand-pull 12 quarterly Inflation Report 14 initial public offering (IPO) 47–53 institutional investors 155–58 fund managers 155–56 hedge fund managers 156–57 insurance companies 157 pension funds 158 insurance industry London and 240 market 239–40 protection and indemnity associations 241 reform 245 regulation 243 contingent commissions 243 contract certainty 243 ICAS and Solvency II 244–45 types 240–41 underwriting process 241–42 see also Lloyd’s of London, reinsurance Intercontinental Exchange 5 interest equalisation tax 6 interest rate products debt securities 82–83, 92–93 bill of exchange 83 certificate of deposit 83 debt instrument 83 euro bill 82 floating rate note 83 local authority bill 83 T-bills 82 derivatives 85 forward rate agreements (FRAs) 85–86 government bonds (gilts) 86–89 money markets 81–82 repos 84 International Financial Reporting Standards (IFRS) 58, 86, 173, 237–38 International Financial Services London (IFSL) 5, 64, 86, 92, 112 International Monetary Fund 17 International Securities Exchange 138 International Swap Dealers Association 63 International Swaps and Derivatives Association 63 International Underwriting Association (IUA) 240 investment banking 5, 47–59 mergers and acquisitions (M&A) 56–58 see also capital raising investment companies 164–69 real estate 169 split capital 166–67 venture capital 167–68 investment funds 159–64 charges 163 investment strategy 164 fund of funds scheme 164 manager-of-managers scheme 164 open-ended investment companies (OEICs) 159 selection criteria 163 total expense ratio (TER) 164 unit trusts 159 Investment Management Association 156 Investment Management Regulatory Organisation 11 Johnson Matthey Bankers Limited 15–16 Joint Money Laundering Steering Group 221 KAS Bank 145 LCH.Clearnet Limited 66, 140 letter of credit (LOC) 23, 25–26 liability-driven investment 158 Listing Rules 43, 167, 173, 225, 228–29 Lloyd’s of London 8, 246–59 capital backing 249 chain of security 252–255 Central Fund 253 Corporation of Lloyd’s 248–49, 253 Equitas Reinsurance Ltd 251, 252, 255–56 Franchise Performance Directorate 256 future 258–59 Hardship Committee 251 history 246–47, 250–52 international licenses 258 Lioncover 252, 256 Member’s Agent Pooling Arrangement (MAPA) 249, 251 Names 248, one-year accounting 257 regulation 257 solvency ratio 255 syndicate capacity 249–50 syndicates 27 loans 23–24 recourse loan 24 syndicated loan 23–24 London Interbank Offered Rate (LIBOR) 74, 76 ____________________________________________________ INDEX 307 London Stock Exchange (LSE) 7, 8, 22, 29, 32, 64 Alternative Investment Market (AIM) 32 Main Market 42–43, 55 statistics 41 trading facilities 122–27 market makers 125–27 SETSmm 122, 123, 124 SETSqx 124 Stock Exchange Electronic Trading Service (SETS) 122–25 TradElect 124–25 users 127–29 Louvre Accord 114 Markets in Financial Instruments Directive (MiFID) 64, 121, 124, 125, 130, 144, 197–99, 277 best execution policy 130–31 Maxwell, Robert 186, 214, 282 mergers and acquisitions 56–58 current speculation 57–58 disclosure and regulation 58–59 Panel on Takeovers and Mergers 57 ‘white knight’ 57 ‘white squire’ 57 Merrill Lynch 136, 174, 186, 254 money laundering 216–22 Egmont Group 218 hawala system 217 know your client (KYC) 217, 218 size of the problem 222 three stages of laundering 216 Morgan Stanley 5, 136 multilateral trading facilities Chi-X 134–35, 141 Project Turquoise 136, 141 Munich Re 207 Nasdaq 124, 138 National Strategy for Financial Capability 269 National Westminster Bank 20 Nationwide Building Society 221 net operating cash flow (NOCF) see discounted cash flow analysis New York Federal Reserve Bank (Fed) 16 Nomads 45 normal market share (NMS) 132–33 Northern Rock 16 Nymex Europe 102 NYSE Euronext 124, 138, 145 options see derivatives Oxera 52  Parmalat 67, 232 pensions alternatively secured pension 290 annuities 288–89 occupational pension final salary scheme 285–86 money purchase scheme 286 personal account 287 personal pension self-invested personal pension 288 stakeholder pension 288 state pension 283 unsecured pension 289–90 Pensions Act 2007 283 phishing 200 Piper Alpha oil disaster 250 PLUS Markets Group 32, 45–46 as alternative to LSE 45–46, 131–33 deal with OMX 132 relationship to Ofex 46 pooled investments exchange-traded funds (ETF) 169 hedge funds 169–71 see also investment companies, investment funds post-trade services 140–50 clearing 140, 141–42 safekeeping and custody 143–44 registrar services 144 settlement 140, 142–43 real-time process 142 Proceeds of Crime Act 2003 (POCA) 211, 219, 220–21 Professional Securities Market 43–44 Prudential 20 purchasing power parity 118–19 reinsurance 260–68 cat bonds 264–65 dispute resolution 268 doctrines 263 financial reinsurance 263–64 incurred but not reported (IBNR) claims insurance securitisation 265 non-proportional 261 offshore requirements 267 proportional 261 Reinsurance Directive 266–67 retrocession 262 types of contract facultative 262 treaty 262 retail banking 20 retail investors 151–155 Retail Prices Index (RPI) 13, 87 264  308 INDEX ____________________________________________________ Retail Service Provider (RSP) network Reuters 35 Royal Bank of Scotland 20, 79, 221 73 Sarbanes–Oxley Act 233–34 securities 5, 29 Securities and Futures Authority 11 self-regulatory organisations (SROs) 192 Serious Crime Bill 213 settlement 11, 31, 140, 142–43 shareholder, rights of 29 shares investment in 29–32 nominee accounts 31 valuation 35–39 ratios 36–39 see also flotation short selling 31–32, 73, 100, 157 Society for Worldwide Interbank Financial Telecommunications (SWIFT) 119 Solvency II 244–245 Soros, George 114, 115 Specialist Fund Market 44 ‘square mile’ 4 stamp duty 72, 75, 166 Sterling Overnight Index Average (SONIA) 85 Stock Exchange Automated Quotation System (SEAQ) 7, 121, 126 Stock Exchange Electronic Trading Service (SETS) see Lloyd’s of London stock market 29–33 stockbrokers 33–34 advisory 33 discretionary 33–34 execution-only 34 stocks see shares sub-prime mortgage crisis 16, 89, 94, 274 superequivalence 43 suspicious activity reports (SARs) 212, 219–22 swaps market 7 interest rates 56 swaptions 68 systematic internalisers (SI) 137–38 Target2-Securities 147–48, 150 The Times 35, 53, 291 share price tables 36–37, 40 tip sheets 33 trading platforms, electronic 80, 97, 113, 117 tranche trading 123 Treasury Select Committee 14 trend theory 175–76 UBS Warburg 103, 136 UK Listing Authority 44 Undertakings for Collective Investments in Transferable Securities (UCITS) 156 United Capital Asset Management 95 value at risk (VAR) virtual banks 20 virt-x 140 67–68 weighted-average cost of capital (WACC) see discounted cash flow analysis wholesale banking 20 wholesale markets 78–80 banks 78–79 interdealer brokers 79–80 investors 79 Woolwich Bank 20 WorldCom 67, 232 Index of Advertisers Aberdeen Asset Management PLC xiii–xv Birkbeck University of London xl–xlii BPP xliv–xlvi Brewin Dolphin Investment Banking 48–50 Cass Business School xxi–xxiv Cater Allen Private Bank 180–81 CB Richard Ellis Ltd 270–71 CDP xlviii–l Charles Schwab UK Ltd lvi–lviii City Jet Ltd x–xii The City of London inside front cover EBS Dealing Resource International 110–11 Edelman xx ESCP-EAP European School of Management vi ICAS (The Inst. of Chartered Accountants of Scotland) xxx JP Morgan Asset Management 160–62 London Business School xvi–xviii London City Airport vii–viii Morgan Lewis xxix Securities & Investments Institute ii The Share Centre 30, 152–54 Smithfield Bar and Grill lii–liv TD Waterhouse xxxii–xxxiv University of East London xxxvi–xxxviii 

The Lights in the Tunnel
by Martin Ford
Published 28 May 2011

In the years that followed, and especially during the 1980s, a large number of people originally trained as physicists or mathematicians began to take much higher paying jobs on Wall Street. These guys (they were virtually all men) were referred to as “quants.” The quants started working with the Black-Scholes formula and expanded it in new ways. They turned their formulas into computer programs and gradually began to create new types of derivatives based on stocks, bonds, indexes and many other securities or combinations of securities.14 As their computers got faster and faster, the quants were able to do more and more.

Sabotage: The Financial System's Nasty Business
by Anastasia Nesvetailova and Ronen Palan
Published 28 Jan 2020

The Russian default amplified panic in the world financial markets. One of its most significant casualties would be the Long Term Capital Management (LTCM) fund, a boutique hedge fund run by two Nobel Prize winners in economics.4 The Nobel Prizes were awarded for the partners’ work on the Black–Scholes formula, used until today for calculating the prices of financial derivatives. But Russia’s default unleashed volatility on a scale far beyond what the model was designed for. Having previously been hit by the Asian crisis, LTCM suffered losses of $553m in one day. This was equivalent to 15 per cent of its capital.

All the Devils Are Here
by Bethany McLean
Published 19 Oct 2010

Guldimann says. “All I could do is ask around. Is he a good guy? Does he know what he’s doing? It was ridiculous.” There was never any question about how Guldimann and his team would approach this task. They would use statistics and probability theories that had long been popular on Wall Street. (The Black-Scholes formula, for example, developed in the early 1970s for pricing options, had become one of the linchpins of modern Wall Street.) The quants swarming Wall Street were all steeped in those theories—this was the essential building block of virtually everything they did. They knew no other way to approach the subject.

…

See Federal bailouts Bair, Sheila Baker, Richard Bankers Trust, swap deal lawsuit Bank of America Countrywide acquired by Merrill Lynch acquired by subprime branches, closing Barnes, Roy Bartiromo, Maria Basel Committee on Banking Supervision, capital reserves rule Basis Yield Alpha Fund Bear Stearns ABS index Bank of America lawsuit CDOs foreclosures, plan to prevent hedge funds, collapse of High-Grade Structured Credit Fund High-Grade Structured Credit Strategies Enhanced Leverage Limited Partnership J.P. Morgan acquisition of Beattie, Richard Behavioral economics Beneficial Bensinger, Steve Bernanke, Ben Berson, David Birnbaum, Josh BlackRock Black-Scholes formula Black swans Blankfein, Lloyd during collapse compensation from Goldman Goldman Sachs under Blue sky laws, MBSs exemption from Blum, Michael Blumenthal Stephen BNC Mortgage BNP Paribas Bolten, Joshua Bomchill, Mark Bond, Kit Bond ratings CDOs and credit enhancements failures, examples of public trust in ratings shopping system of for tranches Value at Risk (VaR) applied to See also Moody’s; Standard & Poor’s Bonuses, post-TARP Born, Brooksley biographical information derivatives, regulatory efforts style/personality of Bothwell, James Bowsher, Charles Bradbury, Darcy Brandt, Amy Breit, John Brennan, Mary Elizabeth Brickell, Mark Brightpoint fraud Broad Index Secured Trust Offering (BISTRO) AIG FP credit protection features of Broderick, Craig Bronfman, Edward and Peter Bruce, Kenneth Buffett, Warren Burry, Michael Bush, George W.

The Global Money Markets
by Frank J. Fabozzi , Steven V. Mann and Moorad Choudhry
Published 14 Jul 2002

In the "PRICING" box, the "Premium" represents the value of our hypothetical cap as a percentage of the notional amount. For our hypothetical cap, the premium is 0.1729% or approximately $1,729. Exhibit 12.18 presents Bloomberg’s Caplet Valuation screen that shows the value of caplet in the column labelled “Component Value.” Bloomberg uses a modified Black-Scholes model to value each caplet and users can choose whether to use the same volatility estimate for each caplet or allow the volatility for each caplet to differ. Binomial lattice models are also extensively in practice to value caps. EXHIBIT 12.17 Bloomberg’s Cap/Floor/Collar Calculator Source: Bloomberg Financial Markets Swaps and Caps/Floors EXHIBIT 12.18 273 Bloomberg Screen with the Valuation of a Hypothetical Cap Source: Bloomberg Financial Markets Floors It is possible to protect against a drop in interest rates by purchasing a floor.

…

See also Federal National Mortgage Association government bond. See Maturity security. See Maturity Bennett, Paul, 43 Bhattacharya, Anand K., 192 Bid/ask rates, 29 Bid-ask spreads, 33 Bid-offer spread, 236, 267, 283. See also Dealers Bids/offers, quotations, 212 Bid-to-cover ratio, 28 Bills of exchange, 94 BIS. See Bank for International Settlements Black-Scholes model, 272 Bloomberg, 8–15, 35, 69, 227. See also C5 screen; CCR function; Direct Issuer Program Description Issuer screen; MMR screen; Money Market Program Description screen; PX1 Governments screen calculation, 112 graph, 36 information, 59 news report, 48, 49 reports, 130 screens, 27, 32, 74, 88, 91, 93 display, 184, 192, 194 presentation, 120, 200, 202 services, 115, 139 usage, 272 Bloomberg-defined prepayment rate notation, 184 Board-level decisions, 285 Bond Market Association, master repurchase agreement, 123–124, 126, 141–150 default, events, 146–149 definitions, 141–144 intent, 149–150 margin maintenance, 144–145 purchased securities, segregation, 145–146 Bond markets, 67 Bond-equivalent yield (BEY), 16–19, 29, 32 formula, 17, 57 Bonds.

Infinite Powers: How Calculus Reveals the Secrets of the Universe
by Steven Strogatz
Published 31 Mar 2019

The Ubiquity of Partial Differential Equations The application of calculus to modern science is largely an exercise in the formulation, solution, and interpretation of partial differential equations. Maxwell’s equations for electricity and magnetism are partial differential equations. So are the laws of elasticity, acoustics, heat flow, fluid flow, and gas dynamics. The list goes on: the Black-Scholes model for pricing financial options, the Hodgkin-Huxley model for the spread of electrical impulses along nerve fibers—partial differential equations all. Even at the cutting edge of modern physics, partial differential equations still provide the mathematical infrastructure. Consider Einstein’s general theory of relativity.

…

See also Higham et al., The Princeton Companion, and Goriely, Applied Mathematics. 245 Boeing 787 Dreamliner: Norris and Wagner, Boeing 787, and http://www.boeing.com/commercial/787/by-design/#/featured. 246 aeroelastic flutter: Jason Paur, “Why ‘Flutter’ Is a 4-Letter Word for Pilots,” Wired (March 25, 2010), https://www.wired.com/2010/03/flutter-testing-aircraft/. 247 Black-Scholes model for pricing financial options: Szpiro, Pricing the Future, and Stewart, In Pursuit of the Unknown, chapter 17. 248 Hodgkin-Huxley model: Ermentrout and Terman, Mathematical Foundations, and Rinzel, “Discussion.” 248 Einstein’s general theory of relativity: Stewart, In Pursuit of the Unknown, chapter 13, and Ferreira, Perfect Theory.

A Mathematician Plays the Stock Market
by John Allen Paulos
Published 1 Jan 2003

And options on a stock whose volatility is high will cost more than options on stocks that barely move from quarter to quarter (just as a short man on a pogo stick is more likely to be able to peek over a nine-foot fence than a tall man who can’t jump). Less intuitive is the fact that the cost of a call option also rises with the interest rate, assuming all other parameters remain unchanged. Although there are any number of books and websites on the Black-Scholes formula, it and its variants are more likely to be used by professional traders than by gamblers, who rely on commonsense considerations and gut feel. Viewing options as pure bets, gamblers are generally as interested in carefully pricing them as casino-goers are in the payoff ratios of slot machines.

Culture and Prosperity: The Truth About Markets - Why Some Nations Are Rich but Most Remain Poor
by John Kay
Published 24 May 2004

The theory predicts that the prices of risks will follow a "random walk." A random walk is a process in which the next step is equally likely to be in any direction. Many physical processes have these characteristics, such as the movement of particles in liquids. This is an area where models derived from statistical mechanics seem to work, and the Black-Scholes model described below is grounded in the analysis of physical systems. And numerous statistical analyses of prices in markets for securities and commodities have confirmed that they display the characteristics of a random walk. In an early test of the theory, the statistician Maurice Kendall discovered that all but one of the series he studied fitted the random walk prediction. 5 It emerged that the one that did not was not in fact a series of actual market transactions but had been prepared as an average of estimated market prices.

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{index} • • • • • • • • • • • • • • • • • • • • • • • • • • accountability central planning, 108-16 disciplined pluralism, 117, 124,314 accounting rules/standards, 99, 158,224-25 adaptation, 213-14,240,246,250, 343 definition of, 214,347 mechanisms of, 216-17,255 and rationality, 217-21,229,231,347-48 and self-interest, 217,252,256,343 See also cooperation adverse selection, 238-42, 349 advertising, 225-27, 229, 255 Africa, 281,282-84 agriculture, 77, 81, 84 central planning, 105-6, 112-13 development of, 54, 69, 76 green revolution, 268, 279 Sweden (case study), 305 AGRprogram (U.K.), 111-12 airline industry, 123, 151-52, 194 Akerlof, George, 207, 223, 327, 330, 357 Allais, Maurice, 234-35, 357 altruism, 217, 252, 255 Amazon.com, 218, 273 American business model (ABM), 11, 17, 311-22 and contracts, 352 and corporations, 79,322, 342-44 and economic policy-making, 334-3 7 inadequacies of, 319 and income distribution, 203, 320-22 in]apan, 63-64 in New Zealand, 62 philosophy of, 343 and property rights, 318-19 reality vs. caricature of, 20-21 and regulation, 87 and self-interest, 315-18, 342, 343-44 supportfor, 104,203,313,355 ancient Greece, 55, 78, 146 antitrust laws, 76,87-88, 138,268,313,334 intellectual property, 273 AOL,83, 123 Apple, 119-20, 122,261,273 architecture, 311-12 Argentina,33,58,59-62, 139,285,288,344 Arkwright, Richard, 273 Arrow, Kenneth, 100, 127, 179, 181,318, 335,357 Arrow-Debreu model, 100, 134, 179, 181-83, 194,197,201-8,259,314 and economic rents, 295 function of, 208, 330-31 limitations of, 205,232 and property rights, 318,319 Asia economic development, 16, 62-68,279 market crisis (1997), 16, 53, 150-51,237 rich states, 31, 32,66 assets, 172, 175 assignment (resource allocation), 93-104 coordination of, 173-83 See also central planning ATMs (bank cash machines), 351 auctions, 95, 101-2, 143,227-29 Australia, 47, 51, 67, 68,285 cost ofliving, 48, 49 cuisine changes, 75-76 electricity auction, 227-28 "Austrian economics," 199 authority dangers of unchecked, 109-14 delegation of, 117, 124 Axelrod, Robert, 254 Babbage, Charles, 266-67 balance of payments, 177 bank notes, 100, 165-66 banks,55,69, 165-67,303 cash machines, 351 bargaining theory, 289-90, 294-95, 300, 353 Becker, Gary, 199-201,256,286,302,324, 328,333,335,338,358 behavioral economics, 220-21,235,324,333, 339 Bell Laboratories, 268 Berkshire Hathaway, 298 Berlin, Isaiah, 190, 191 Berlin Wall, 29, 30 Black, Fischer, 160 Black-Scholes model, 159, 160-61 Blanchard, Olivier, 338 blocking coalition, 294-95 Blodget, Henry, 218,229 blood donation, 257-58 bonds, 150, 167-69 bookkeeping, 55,175-78 brands,20, 74,89,296,319,352 Braque,Georges,85-86,89,90,293 Britain. See United Kingdom brokers, 147 Buchanan, James, 251,358 Buchholz, Todd, 189 Buffett, Warren, 12, 171,298-99,300,317 Bush, George W., 100, 156, 200, 335, 337 business-cycle theory, 200 California blackouts, 101, 127, 128 Canada,31,32,58,67 capital, 55, 79, 123, 124 intangible, 171-72 and living standards, 27-28 selling/ buying risks, 169-70,244 supply/demand for, 163-67 capitalism, 10, 21, 78 future of, 340-55 See also market economy Cardoso, Fernando, 285-86 { 412} Index Carlson, Chester, 117 Carrefour SA, 5, 8, 79 cash machines, 351 cell phones, 261-62, 351 central banks, 166-68 central planning, 105-14,200,333-34 adaptive behavior, 214-15 British electricity, 110-12, 141-42, 171, 214 coordination failures, 127, 173-74 decision-making scale, 18, 19, 106-9, 110, 112-14 development economics, 277-79,281 drawbacks/failures, 108, 110, 112-14, 127, 288,306-7 General Electric, 116-17 Hayek on, 198 incentive compatibility, 97-100, 199 market spontaneity vs., 19-21 Marxist, 17 Chain, Ernst, 267 chaos theory, 131 Chicago School, 199-201,205,207,210,217, 324,335 China, 36, 151,214,215 central planning, 105-14 economic development, 16-17,62-63,66, 67,288 Chubais, Anatoly, 288,319 Clark,Jim, 122-23 climate, 51, 55,90 Coase, Ronald, 205,358 Coca-Cola, 88-89, 137, 225-26, 298 economic rent, 292-93, 294, 296 trademark, 224, 272 Cohen, Jonathan, 218 colonization, 56-62, 67, 284, 355 commensurability, 187-93 communism, collapse of, 287, 306.

The Meritocracy Trap: How America's Foundational Myth Feeds Inequality, Dismantles the Middle Class, and Devours the Elite
by Daniel Markovits
Published 14 Sep 2019

Finance had found a new type of human capital—“skilled mathematicians, modelers, and computer programmers who prided themselves on their ability to adapt to new fields and put their knowledge into practice”—that almost perfectly suited its growing needs. This triggered innovations that had long lain dormant. The fundamental theoretical advances that ground modern, sophisticated finance (the capital asset pricing model and the Black-Scholes model that underwrite portfolio allocation and the pricing of options and other derivatives) were made in the 1950s, 1960s, and early 1970s, often a quarter century before finance transformed itself into a super-skilled sector by implementing them. (Indeed, the foundational ideas behind these models, which concern measuring, segregating, and then recombining risks, have been around since Pascal and other French mathematicians invented modern probability theory—an interest aroused by inquiries put to them when aristocratic gamblers sought to measure and manipulate the odds in their wagers.)

…

Maureen Murphy, The Glass-Steagall Act: A Legal Analysis (Washington, DC: Congressional Research Service, January 19, 2016), https://fas.org/sgp/crs/misc/R44349.pdf. to value such securities: The 1950s and 1960s witnessed fundamental theoretical advances in the construction and pricing of financial instruments—including the capital asset pricing model that grew out of Harry Markowitz’s work on portfolio allocation and the Black-Scholes model for pricing options and other derivatives. See Mark Rubenstein, A History of the Theory of Investments (Hoboken, NJ: John Wiley & Sons, 2006), 167–75; Fischer Black and Myron Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy 81, no. 3 (May–June 1973): 637–54.

…

See populism Apple Computer, 83, 141, 246 aristocracy capital dominance under, 92 class divide under, 46 consumption under, 216 economic justice arguments on, 15, 106, 109 elite education under, 6, 7, 17, 111–12, 114 elite leisure under, 3–4, 77, 79–80, 86–87, 95–96, 193–94, 207 and elite rituals, xii elite work under, 8–9, 11 families under, 207 industry/income opposition under, 3–4 and inheritance, xiv–xv, 4, 89, 94, 115, 145–46, 150–51, 261 meritocracy as positive alternative to, ix, xi, 14, 263–64 meritocracy as return to, 15, 47, 260–62, 268–69 nature of elite wealth under, 3–4, 35–36, 262 1960s rebellion against, 284–85 as virtuous, 262–64, 268 wealth as emancipatory under, 36, 37, 41, 193–94 Aristotle, 262, 263 asset management services, 236 See also finance industry assortative mating, 116–17 athletes, 43, 84 AT&T, 173 auto industry, 20–21, 22, 23 bankers’ hours, 10, 81, 82 banking. See finance industry Bell Labs, 237 Bender, Wilbur J., 112 Bentley Motors, 220 Beyoncé, 178, 221 Bezos, Jeff, 9, 82, 178 Biden, Joe, xii Bishop, Bill, 324n(47), 325nn(48–49), 356n(136), 378nn(199), 379nn(204), 384nn(224–25), 385nn(225, 227) Black-Scholes model, 237–38 Blankfein, Lloyd, 98 Boston Consulting Group (BCG), 245–46 Boutmy, Émile, 260 Brandeis, Louis, 71 Brewster, Kingman, 6, 113, 115, 148, 151, 263–64 Brooks, Arthur C., 109 Buckley, William F., 114 Buffett, Warren, 58, 95 Bunnell, Sterling, 251 burdens of meritocracy.

Trend Following: How Great Traders Make Millions in Up or Down Markets
by Michael W. Covel
Published 19 Mar 2007

When lightning struck LTCM, trend followers were assessing the same markets—playing the zero-sum game at the same time. In hindsight, the old-guard Chicago professors were clearly aware of the problem as Nobel Laureate Professor Merton Miller pondered: “Models that they were using, not just Black-Scholes models, but other kinds of models, were based on normal behavior in the markets and when the behavior got wild, no models were able to put up with it.”35 If only the principals at LTCM had remembered Albert Einstein’s quote that elegance was for tailors, part of his observation Chapter 4 • Big Events, Crashes, and Panics 155 about how beautiful formulas could pose problems in the real world.

…

We are influenced heavily by standard finance theory that revolves almost entirely around normal distribution worship. Michael Mauboussin and Kristen Bartholdson see clearly the state of affairs: “Normal distributions are the bedrock of finance, including the random walk, capital asset pricing, value-at-risk, and Black-Scholes models. Value-at-risk (VaR) models, for example, attempt to quantify how much loss a portfolio may suffer with a given probability. While there are various forms of VaR models, a basic version relies on standard deviation as a measure of risk. Given a normal distribution, it is relatively straightforward to measure standard deviation, and hence risk.

Fool's Gold: How the Bold Dream of a Small Tribe at J.P. Morgan Was Corrupted by Wall Street Greed and Unleashed a Catastrophe
by Gillian Tett
Published 11 May 2009

Morgan back in 2000, he had created a consultancy group that advised governments and companies on how to use innovative financial products, such as derivatives, to their benefit. The other founding members of the group were Roberto Mendoza, another former J.P. Morgan banker, and Robert Merton, the Nobel Prize–winning economist who had helped to create the pathbreaking Black-Scholes formula that had played a crucial role in the development of derivatives. For seven long years, Hancock had extolled the virtues of financial innovation, often in the face of client skepticism. Even as the banking world reeled in shock in late 2007, he remained committed to the cause. “A lot of the problems in structured finance have not been due to too much innovation, but a failure to innovate sufficiently,” Hancock observed.

Chaos Kings: How Wall Street Traders Make Billions in the New Age of Crisis
by Scott Patterson
Published 5 Jun 2023

Everything else is noise. The tail wags the dog, literally. “The problem, insists Mr. Taleb, is that most of the time we are in the land of the power law and don’t know it,” a reviewer observed in the Wall Street Journal. “Our strategies for managing risk, for instance—including Modern Portfolio Theory and the Black-Scholes formula for pricing options—are likely to fail at the worst possible time… because they are generally (and mistakenly) based on bell-curve assumptions.” Taleb’s book became a cultural touchstone and made the Black Swan something of a universal meme for surprising bad shit going down. In the fourteen years before the book was published, black swan appeared 16,569 times in a Factiva search (usually in reference to a piece of choreography in Tchaikovsky’s ballet Swan Lake called “the Black Swan pas de deux”).

The Unusual Billionaires
by Saurabh Mukherjea
Published 16 Aug 2016

Reason 3: Neutralizing the negatives of ‘noise’ Investing and holding for the long term is the most effective way of killing the ‘noise’ that interferes with the investment process. In his book, Investing—The Last Liberal Art (2013), Robert G. Hagstrom talks about the ‘chaotic environment, with so much rumour, miscalculation, and bad information swirling around’. Such an environment was labelled noise by Fischer Black, the inventor of the Black–Scholes formula. Hagstrom goes on to ask: ‘Is there a solution for noise in the market? Can we distinguish between noise prices and fundamental prices? The obvious answer is to know the economic fundamentals of your investment so you can rightly observe when prices have moved above or below your company’s intrinsic value.

Extreme Money: Masters of the Universe and the Cult of Risk
by Satyajit Das
Published 14 Oct 2011

See also Warren Buffet Berle, Adolf, 54 Berlin Wall, fall of, 101, 295 Bernanke, Ben, 170, 182, 203, 303, 338, 366 debt, 267 Great Moderation, 277 on 60 Minutes, 343 September, 2008, 342 Bernstein, Peter, 26, 129, 208 Besley, Tim, 278 Best, George, 88 beta (market returns), 241 Beveridge Report, 47 Beveridge, Sir William, 47 Beyond Belief, 338 Bhagavad Gita, 339 Bhide, Amar, 312 BHP Billiton, 59 bias, 243 Bieber, Matthew, 198 Bierce, Ambrose, 326 Big Short, The, 198 Biggs, Barton, 99 Bild, 358 Billboard Top 100 Chart, 124 Billings, Josh, 233 billionaire drivel, 327 bills of exchange, 32 bimetallism, 26 bio-fuels, 334 Bird, John, 91, 320 Black Swan, The, 95, 126 Black Wednesday, 240 Black, Fischer, 121, 127 black-box trading, 242 Black-Scholes models, 120-122, 277 Black-Scholes-Merton (BSM) option, 121 Blackrock, 170 Blackstone, 167, 325 Blackstone Group, The, 154, 318 Blair, Tony, 81 Blankfein, Lloyd, 239, 364 Blinder, Alan, 129 Blomkvist, Mikhael, 360 Bloomberg TV, 92 Bloomberg, Michael, 164 Bloomsbury group, 29 Blue Force, 264 Blumberg, Alex, 185 Boao Forum, 324 boards of directors, knowledge of business operations, 292-293 BOAT (Best of All Time), 228 Boesky, Ivan, 147, 244 Bogle, Jack, 123 Bohr, Niels, 101, 257 Boiler Room, 185 Bonanza, 31 Bond, James, 26 Bonderman, David, 154, 164, 318 bonds, 169 adjustable rate, 213 failure of securitization, 204-205 high opportunity, 143 insurance, 176 junk, 143, 145-146 Milken’s mobsters, 146-147 municipal, 211-214 PAC (planned amortization class), 178 ratings, 143, 282-285 securitization, 173 TAC (target amortization class), 178 TOBs (tender option bonds), 222 U.S.

…

, 301 Hasset, Kevin, 97 Havel, Václav, 359 Hawala, 22, 24 Hawkin, Greg, 248 Hawking, Stephen, 126 Hayek, Frederick, 103 HE (home equity), 181 Heathrow Airport, 161 Hederman, Abbot Mark Patrick, 361 Hedge Fund Alley, 239 hedge funds, 73, 77, 80, 260 Alfred Winslow Jones, 240 Amaranth, 250, 252 Centaurus Energy, 319 clientele, 247-248, 250 compensation, 314 fees, 245 formula for, 239 Fortress, 318 George Soros, 240 Hedgestock, 252, 261-262 Hyman Minsky, 260-262 leverage, 254 markets, 241 Porsche, 257-260 returns, 243-244, 255-257 Sharpe ratios, 246-247 strategies, 241-243 structure of CDOs, 195 Hedgestock, 261-262 hedge funds, 252 hedging, 235 aspect of Black-Scholes model, 122 derivatives, 216-217 Heine, Heinrich, 38, 64 Heisenberg, Werner, 101 Heller, Walter, 129 Hellman, Lillian, 350 HELOC (home equity line of credit), 181 Hennessy, Peter, 278 Heritage Foundation, 350 Herodotus, 74 Hertz, 155 Hewlett-Packard (HP), 122 Heyman, William, 270 Hickman, W.

The Education of a Value Investor: My Transformative Quest for Wealth, Wisdom, and Enlightenment
by Guy Spier
Published 8 Sep 2014

Is there any way, then, of tilting the balance in our favor so that we increase the odds of victory in a game that’s so heavily stacked against us? This is the question that underlies the next few chapters of this book. In retrospect, I should have been far more skeptical about the economic models I had learned at university. So you’ll be glad to hear that I’m not going to bore you with erudite discussions of the Black-Scholes model of option pricing, Keynesian macroeconomics and sticky prices, the IS/LM macroeconomic model, rational expectations, the Herfindahl industrial concentration ratio, or the Rüdiger Dornbusch exchange rate overshooting model. This is, of course, sexy stuff that might serve you well if you’re looking for love at a Mensa cocktail party or a gathering of central bankers.

Cogs and Monsters: What Economics Is, and What It Should Be
by Diane Coyle
Published 11 Oct 2021

The canonical example of performative economics is the model for pricing financial options. Robert K. Merton’s son, Robert C. Merton, was jointly awarded the Nobel Memorial Prize in Economics in 1997 for devising this model (along with Myron Scholes; Fisher Black, the other co-author of the original Black-Scholes model, had died earlier).3 The investment company Robert C. Merton co-founded to put the model into practice, Long Term Capital Management (LTCM), went bankrupt with losses of $4.6 billion in 2000, in a kind of trial run for the later financial crisis. It is hard not to see some strange echo of the Oedipal story in this, especially as his father Robert K. is rumoured to have invested in LTCM.

The Finance Book: Understand the Numbers Even if You're Not a Finance Professional
by Stuart Warner and Si Hussain
Published 20 Apr 2017

The options exercised during the year had a weighted average market value of £11.38 (2014: £5.33). The fair value of services received in return for share options granted is measured by reference to the fair value of share options granted. The estimate of the fair value of the services received is measured based on the Black–Scholes model for all Savings Related Share Option Schemes and Executive Share Option Schemes and for Performance Share Plan options granted from 2014 onwards. The Monte Carlo option pricing model was used for Performance Share Plans granted prior to 2014. The fair value per option granted and the assumptions used in these calculations are as follows: The expected volatility is based on historical volatility, adjusted for any expected changes to future volatility due to publicly available information.

The Startup Way: Making Entrepreneurship a Fundamental Discipline of Every Enterprise
by Eric Ries
Published 15 Mar 2017

With apologies to our friends in finance, who would say that this simplistic formula is not quite right: 1. We’re not taking into account the time value of money; the payoff is only $1 billion in future dollars, we need a net-present-value (NPV) calculation, and 2. This is actually more like an option, which should be valued according to the Black-Scholes formula, or something similar. Granted! But these involve complexity that few practitioners understand. Some of these advanced issues are discussed in Chapter 9. 9. This is why we call it a minimum viable product. It’s not just research or a standalone prototype. It’s an attempt to serve a real customer, even if in a limited way. 10.

Age of Greed: The Triumph of Finance and the Decline of America, 1970 to the Present
by Jeff Madrick
Published 11 Jun 2012

These men built computer models and teased out relationships within complex securities that others had not found. The computations were often based on an estimate of the value of a stock option first published by economist Myron Scholes of the University of Chicago and mathematician Fischer Black of MIT. The Black-Scholes model, based on estimated fluctuations (volatility) of securities prices, became the basis of derivatives trading and the measurement of portfolio risk. Mispricing in the markets was, with refinements, basically a deviation from the Black-Scholes price. Meriwether was able to understand these advanced models sufficiently and bridge the gap between his intellectual hirees and the more rough-and-tumble traditional traders at Salomon.

…

.; financial services of, 1.30, 1.31, 1.32, 1.33, 1.34, 2.9, 6.27, 6.28, 6.29, 16.16, 16.17, 16.18, 17.18; foreign loans by, 6.30, 8.3, 11.11, 11.12, 11.13, 14.8, 14.9, 16.19, 16.20, 19.27, 19.28; fraud in, 1.35, 1.36, 4.5, 5.5, 12.1, 13.5, 14.10, 15.16, 17.19, 19.29, 19.30, 19.31; government bailouts of, 1.37, 3.3, 6.31, 6.32, 11.14, 12.2, 14.11, 15.17, 19.32, 19.33, 19.34, 19.35; greed in, itr.1, 1.38, 1.39, 4.6, 5.6, 6.33, 6.34, 13.6, 14.12, 15.18, 15.19, 15.20, 16.21, 19.36, 19.37, 19.38, 19.39; holding companies in, 1.40, 6.35, 6.36; interest rates for, 1.41, 1.42, 1.43, 1.44, 1.45, 3.4, 3.5, 6.37, 6.38, 6.39, 6.40, 6.41, 6.42, 9.2, 9.3, 11.15, 11.16, 13.7, 14.13, 17.20, 17.21, 19.40; international, 1.46, 1.47, 1.48, 6.43, 6.44, 11.17, 14.14, 14.15, 14.16, 15.21, 16.22, 16.23, 19.41, 19.42, 19.43; investment, 1.49, 1.50, 1.51, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 5.7, 5.8, 12.3, 12.4, 13.8, 14.17, 14.18, 15.22, 16.24, 17.22, 17.23 17.24, 19.44, 19.45, 19.46; see also brokerage firms; loans by, 1.52, 1.53, 1.54, 2.10, 2.11, 3.6, 3.7, 6.45, 6.46, 15.23, 16.25, 16.26, 17.25, 17.26, 19.47, 19.48, 19.49; profits vs. losses in, 1.55, 1.56, 1.57, 6.47, 6.48, 6.49, 6.50, 6.51; reserves of, 2.12, 3.8, 6.52, 11.18, 19.50; risk assumed by, 1.58, 1.59, 1.60, 2.13, 5.9, 6.53, 6.54, 15.24, 15.25, 15.26, 15.27, 15.28, 15.29, 16.27, 17.27, 17.28, 18.8, 18.9, 18.10, 19.51, 19.52, 19.53, 19.54, 19.55, 19.56, 19.57; saving deposits in, x, 1.61, 1.62, 1.63, 1.64, 1.65, 1.66, 1.67, 1.68, 2.14, 6.55, 14.19, 14.20, 18.11, 18.12, 19.58, 19.59; thrifts (savings and loans) in, 6.56, 6.57, 11.19, 11.20, 12.5, 13.9, 13.10, 13.11, 14.21, 14.22, 17.29, 18.13, 18.14, 18.15, 18.16, 19.60, 19.61, 19.62, 19.63, 19.64; see also specific banks and financial institutions Bank of America, 16.1, 16.2, 18.1, 18.2, 19.1, 19.2 bankruptcies, 1.1, 3.1, 6.1, 8.1, 11.1, 13.1, 13.2, 13.3, 14.1, 17.1, 17.2, 19.1, 19.2, 19.3, 19.4 Baruch, Bernard Basel Agreements (1975), 15.1, 19.1 bear markets, 4.1, 5.1, 12.1, 16.1, 16.2, 16.3, 16.4 Bear Stearns, 5.1, 13.1, 14.1, 16.1, 18.1, 18.2, 18.3, 19.1, 19.2, 19.3, 19.4, 19.5, 19.6, 19.7, 19.8, 19.9, 19.10, 19.11, 19.12 Beatrice Foods, 13.1, 13.2, 13.3 Beatty, Warren Ben Franklin chain, 8.1, 8.2 Bent, Bruce Bentsen, Lloyd Bergerac, Michel Berkowitz, Howard Berkshire Hathaway, 8.1, 15.1 Berlind, Roger, 16.1, 16.2 Bernanke, Ben, 2.1, 14.1, 19.1, 19.2, 19.3, 19.4, 19.5, 19.6 Beverly Hills Hotel Biggs, Barton Birmingham, Stephen Black, Fischer, 15.1, 15.2 Black-Scholes model Blackstone Group, 4.1, 18.1 Blanchard, Olivier Blankfein, Lloyd, 19.1, 19.2 Bliley, Thomas Blinder, Alan, 2.1, 3.1, 9.1, 11.1, 11.2, 14.1, 14.2, 14.3, 14.4, 19.1, 19.2 Blodget, Henry Bloomberg, Mike Bluhdorn, Charles, 8.1, 8.2 Blumenthal, Michael, 9.1, 9.2, 9.3, 9.4, 9.5 Boesky, Ivan, 5.1, 5.2, 12.1, 13.1, 13.2, 13.3, 14.1, 17.1, 17.2 Boesky, Seema Silberstein, 5.1, 5.2, 5.3 Boesky, William Bogle, John bonds, 1.1, 1.2, 1.3, 4.1, 5.1, 5.2, 6.1, 6.2, 6.3, 9.1, 9.2, 11.1, 11.2, 12.1, 14.1, 14.2, 15.1, 15.2, 15.3, 15.4, 15.5, 15.6, 15.7, 18.1, 18.2, 18.3, 19.1, 19.2; see also Treasury bills Bork, Robert Born, Brooksley Boston Consulting Group (BCG), 4.1, 12.1 Bosworth, Barry, 9.1, 9.2 Bozell, L.

The Inequality Puzzle: European and US Leaders Discuss Rising Income Inequality
by Roland Berger , David Grusky , Tobias Raffel , Geoffrey Samuels and Chris Wimer
Published 29 Oct 2010

Again, going back to the comments I just made, if you list the top one hundred or five hundred CEOs’ compensation in the last five to ten years, I would be very surprised if a disproportionate number of the ones who have received the eye popping packages are not in the financial sector. Second, the Black-Scholes model for the value of stock options makes compensation reports often misleading. For the first time since double-entry bookkeeping, you have an expense that is dragged through the profit-and-loss statement, and if the value of the options goes south, you never reverse the entry. That’s never been done.

More Than You Know: Finding Financial Wisdom in Unconventional Places (Updated and Expanded)
by Michael J. Mauboussin
Published 1 Jan 2006

The good news is that these assumptions are reasonable for the most part. The bad news, as physicist Phil Anderson notes above, is that the tails of the distribution often control the world. Tell Tail Normal distributions are the bedrock of finance, including the random walk, capital asset pricing, value-at-risk (VaR), and Black-Scholes models. Value-at-risk models, for example, attempt to quantify how much loss a portfolio may suffer with a given probability. While there are various forms of VaR models, a basic version relies on standard deviation as a measure of risk. Given a normal distribution, it is relatively straightforward to measure standard deviation, and hence risk.

Is God a Mathematician?
by Mario Livio
Published 6 Jan 2009

Even the brief description I have presented so far already provides overwhelming evidence of a universe that is either governed by mathematics or, at the very least, susceptible to analysis through mathematics. As this book will show, much, and perhaps all, of the human enterprise also seems to emerge from an underlying mathematical facility, even where least expected. Examine, for instance, an example from the world of finance—the Black-Scholes option pricing formula (1973). The Black-Scholes model won its originators (Myron Scholes and Robert Carhart Merton; Fischer Black passed away before the prize was awarded) the Nobel Memorial Prize in economics. The key equation in the model enables the understanding of stock option pricing (options are financial instruments that allow bidders to buy or sell stocks at a future point in time, at agreed-upon prices).

Python for Finance
by Yuxing Yan
Published 24 Apr 2014

A beginner could download the program to try small functions contained in the program. Summary In this chapter, we deliberately avoided any mathematical formula related to the option theory. Thus, within a short period of time, such as less than two hours, a reader who has no clue about the option theory could price a European call option based on the famous Black-Scholes model. [ 76 ] Chapter 4 In Chapter 5, Introduction to Modules, we will introduce modules formally, and it is the first chapter of a three-chapter block that focuses on modules. A module is a package or a set of programs written by one or a group of experts for a specific purpose. For example, in Chapter 6, Introduction to NumPy and SciPy, we will show that five lines, instead of 13 lines, could be used to price a call option since we could use the cumulative standard normal distribution function contained in the SciPy module.

The Big Short: Inside the Doomsday Machine
by Michael Lewis
Published 1 Nov 2009

They hired a PhD student from the statistics department at the University of California at Berkeley to help them, but he quit after they asked him to study the market for pork belly futures. "It turned out that he was a vegetarian," said Jamie. "He had a problem with capitalism in general, but the pork bellies pushed him over the edge." They were left to grapple on their own with a lot of complicated financial theory. "We spent a lot of time building Black-Scholes models ourselves, and seeing what happened when you changed various assumptions in them," said Jamie. What struck them powerfully was how cheaply the models allowed a person to speculate on situations that were likely to end in one of two dramatic ways. If, in the next year, a stock was going to be worth nothing or $100 a share, it was silly for anyone to sell a year-long option to buy the stock at $50 a share for $3.

I Love Capitalism!: An American Story
by Ken Langone
Published 14 May 2018

As you’ll remember, the early years of the twenty-first century—and here we circle back around to the Enron and WorldCom scandals breaking then and the fight I was starting to have with Spitzer over Grasso’s pay—were the silly season for CEO compensation stories. Executive pay was the hot-button item, and Nardelli became a poster boy: the business journals were reporting that Bob’s options were worth over $200 million. But they didn’t have that monetary value at that point—nothing like it. By applying a commonly used financial formula called the Black-Scholes model, you could place a theoretical value of about $40 million on Nardelli’s options. But Home Depot’s stock would have to rise significantly for that value to become real, and there was no guarantee (especially with Lowe’s beating us like a drum) when—or if—Home Depot’s stock would go that high.

Alex's Adventures in Numberland
by Alex Bellos
Published 3 Apr 2011

Beat the Dealer is not just a gambling classic. It also reverberated through the worlds of economics and finance. A generation of mathematicians inspired by Thorp’s book began to create models of the financial markets and apply betting strategies to them. Two of them, Fischer Black and Myron Scholes, created the Black-Scholes formula indicating how to price financial derivatives – Wall Street’s most famous (and infamous) equation. Thorp ushered in an era when the quantitative analyst, the ‘quant’ – the name given to the mathematicians relied on by banks to find clever ways of investing – was king. ‘Beat the Dealer was kind of the first quant book out there and it led fairly directly to quite a revolution,’ said Thorp, who can claim – with some justification – to being the first-ever quant.

Misbehaving: The Making of Behavioral Economics
by Richard H. Thaler
Published 10 May 2015

Where should this leave us regarding the validity of the Becker conjecture—that the 10% of people who can do probabilities will end up in the jobs where such skills matter? At some level we might expect this conjecture to be true. All NFL players are really good at football; all copyeditors are good at spelling and grammar; all option traders can at least find the button on their calculators that can compute the Black–Scholes formula, and so forth. A competitive labor market does do a pretty good job of channeling people into jobs that suit them. But ironically, this logic may become less compelling as we move up the managerial ladder. All economists are at least pretty good at economics, but many who are chosen to be department chair fail miserably at that job.

The Road to Ruin: The Global Elites' Secret Plan for the Next Financial Crisis
by James Rickards
Published 15 Nov 2016

Monetarism has been intellectually dominant for about sixty years since it emerged from the University of Chicago under Milton Friedman in the 1960s. Eugene Fama’s efficient markets hypothesis percolated in academic studies in the 1960s, yet only started to exert market influence in the 1970s with the options pricing model of Fischer Black, Myron Scholes, and Robert Merton. The Black-Scholes model enabled derivatives and leverage. David Ricardo’s theory of comparative advantage is two hundred years old, yet was first implemented in a widespread rules-based way after 1947 in the General Agreement on Tariffs and Trade. The link between money and gold was abandoned in stages from 1971 to 1973, concurrent with the rise of floating exchange rate regimes.

Trillions: How a Band of Wall Street Renegades Invented the Index Fund and Changed Finance Forever
by Robin Wigglesworth
Published 11 Oct 2021

Rowe Price, 127 at Wellington Management, 97–99, 101, 102 Riley, Ivers, xii, 172, 180 Rimmer, Andrew, 211 risk premia, 155, 159 Roll, Richard, 147 Roosevelt, Theodore “Teddy,” 97 Root, Charles, 98n, 100 Rosenberg, Barr, 153–54 Ross, Jim, 176, 183 Ross, Stephen, 153–54 Rotemberg, Julio, 294–95 Royal Mail, 238 Rubinstein, Mark, 178 Rubio, Marco, 259 Russell Investments, 142 Russell 2000, 142, 200 Saint Louis University, 63 Salomon Brothers, 78n, 207, 208 Samsonite, 75–77, 78 Samuelson, Paul, 21, 49 on Bachelier, 21, 36, 48 “Challenge to Judgment,” 106–7, 109 Economics: An Introductory Analysis, 90 on Markowitz, 38–39 on pension funds, 85 on Vanguard 500, 112, 123 S&P Dow Jones Indices, 111n, 251–52, 254–56, 277, 282n S&P High Yield Dividend Aristocrats Index, 263 S&P 500, 10, 109, 124, 180n, 246, 251 history of, 29–30, 96 SPDRs, 176–77, 179–83, 195, 196–97, 240 S&P 500 index effect, 254–57 S&P 500 index funds, 3, 7–8, 64–65, 67, 68, 73, 77–80, 124, 232 American National Bank, 64–65, 78–79 Vanguard First Index Investment Trust (FIIT), 107–17, 121–22 Vanguard 500 Index Fund, 15, 122–25, 133–34, 181 Sauter, George, 123–24 Savage, Leonard “Jimmie,” 21–22, 23–24, 36, 48 S.C. Johnson & Son, 128 Schioldager, Amy, 196–97, 233 Schlosstein, Ralph, xiii, 208–9 at BlackRock, 213–19 BGI acquisition, 223 founding, 209–12 IPO, 214–15 Schmalz, Martin, 295 Scholes, Myron, 70–71, 74–75, 147 Black-Scholes model, 71, 147, 152–53 Schroders, 145, 160, 234 Schwarzenegger, Arnold, 138, 160 Schwarzman, Steve, 210, 213–14 Schwed, Fred, 3, 26 Securities and Exchange Commission (SEC), 30, 101, 108, 245, 262, 295 ETFs and, 171, 173, 177, 179–80 Seides, Ted, ix on investor career, 16 wager with Buffett, 1–2, 3–4, 6, 9–11, 15–17, 267n semi-transparent ETFs, 245 Shareholder Equity Alliance, 293 Sharpe, William, x, 37, 41–45, 70 “The Arithmetic of Active Management,” 276–77 background of, 42–43 capital asset pricing model, 44–45, 74, 152, 153 Markowitz and, 41–42, 43–45 at Stanford, 68, 185, 187 Shearson Lehman Hutton, 208–9 Sherrerd, Jay, 93–94 Shiller, Robert, 29 Shopkorn, Stanley, 78n “short,” 74 Shteyngart, Gary, 283 Shwayder, Keith, 75–77 “Silent Road to Serfdom, The” (Fraser-Jenkins), 279 Simplify Asset Management, 266 Sinclair, Upton, 82 Singer, Paul, 18–19, 287–88, 290 Sinquefield, Jeanne, xii, 63, 147–48, 150 Sinquefield, Rex, x, 53, 62–65 at American National Bank, 53, 63–65, 78–81, 110, 144 S&P 500 index fund, 64–65, 78 background of, 62–63 at Chicago, 35, 63, 64, 140 CRSP data, 35, 53 at DFA, 146–48, 150, 159–60, 162–63 Klotz’s departure, 156–59 size begets size, 267, 269–70 skunk works, 58, 61 small-cap funds, 142–44, 154, 156, 159–60 smart beta, 151, 155 154, 159–60 Smith, Richard, 101 Smith Barney, 53, 55, 58 Smuckers, 148 socially responsible investing, 237 Société Générale, 253n Sony Pictures Entertainment, 241 Sorbonne (University of Paris), 22–23 Soros, George, 2, 219 South Korea, 42–43, 258 SPDRs (Standard & Poor’s Depositary Receipts), 176–77, 179–83, 195, 196–97, 240 SPDR S&P Dividend ETF, 263–64 Spear, Leeds & Kellogg, 180 Spieth, Lawrence, 150n Standard and Poor’s Index Receipts (SPIRs), 176n Standard and Poor’s 500.

file:///C:/Documents%20and%...
by vpavan

And while valuing options is not simple, it's not impossible. Accounting is often imprecise, especially when it comes to estimating the future value of a corporate jet, or the losses a bank will suffer on its loans. In both cases, companies and their accountants have figured out ways to make reliable estimates. Most companies today use the Black-Scholes model, developed by economists Fischer Black and Myron Scholes, who won a Nobel Prize in economics for his work on the model, to explain to employees what their stock options are worth. Once they run that calculation, which considers such variables as the stock price when granted, the exercise price, the options' expected life, stock price fluctuations, and interest rates over the life of the option, companies can easily figure the long-term cost of options to shareholders.

Security Analysis
by Benjamin Graham and David Dodd
Published 1 Jan 1962

Even complex derivatives not imagined in an earlier era can be scrutinized with the value investor’s eye. While traders today typically price put and call options via the Black-Scholes model, one can instead use value-investing precepts—upside potential, downside risk, and the likelihood that each of various possible scenarios will occur—to analyze these instruments. An inexpensive option may, in effect, have the favorable risk-return characteristics of a value investment—regardless of what the Black-Scholes model dictates. Institutional Investing Perhaps the most important change in the investment landscape over the past 75 years is the ascendancy of institutional investing.

Fed Up: An Insider's Take on Why the Federal Reserve Is Bad for America
by Danielle Dimartino Booth
Published 14 Feb 2017

Mabee, thanks for being a guide to so much more than fishing. Looking back a bit further, thank you Dr. Keith Brown for introducing me to the wonders and discipline of finance during in my business school days at the University of Texas. I officially forgive you for dragging me through the longhand derivation of the Black–Scholes model. You were right. It helped build my character. As for my days at Donaldson, Lufkin & Jenrette, you know I’m eternally grateful to you, Raymur Plant Walton Rachels, my sweet friend from the South and fellow MBA trainee of the class of 1996; thank you for your unwavering support of my vision and friendship for all these years.

What Happened to Goldman Sachs: An Insider's Story of Organizational Drift and Its Unintended Consequences
by Steven G. Mandis
Published 9 Sep 2013

Goldman opens its first international office in London. 1971: Merrill Lynch goes public. 1972: Goldman starts a private wealth division and a fixed income division. Goldman pioneers a “white knight” strategy, defending Electric Storage Battery against a hostile take-over bid from International Nickel and Goldman rival Morgan Stanley. 1973: Fischer Black and Myron Scholes first describe their Black-Scholes model to price options. 1975: May 1 marks the end of fixed trading commissions in the stock market, forcing investment banks to compete in negotiations over transaction fees. 1976: After Gus Levy’s death, John L. Weinberg (Sidney’s son) and John Whitehead take over as senior partners and continue to build Goldman’s investment banking business.

Asset and Risk Management: Risk Oriented Finance
by Louis Esch , Robert Kieffer and Thierry Lopez
Published 28 Nov 2005

In this case, there is a need to construct specific models that take account of this additional ingredient. We no longer have a stationary random model, such as Sharpe’s example, but a model that combines the random and temporal elements; this is known as a stochastic process. An example of this type of model is the Black–Scholes model for equity options (see Section 5.3.2), where the price p is a function of various variables (price of underlying asset, realisation price, maturity, volatility of underlying asset, risk-free interest rate). In this model, the price of the underlying asset is itself modelled by a stochastic process (standard Brownian motion). 3 Equities 3.1 THE BASICS An equity is a financial asset that corresponds to part of the ownership of a company, its value being indicative of the health of the company in question.

The Invisible Hands: Top Hedge Fund Traders on Bubbles, Crashes, and Real Money
by Steven Drobny
Published 18 Mar 2010

Stochastic Volatility Stochastic volatility models are used to evaluate various derivative securities, whereby—as their name implies—they treat the volatility of the underlying securities as a random process. Stochastic volatility models attempt to capture the changing nature of volatility over the life of a derivative contract, something that the traditional Black-Scholes model and other constant volatility models fail to address. In summary, the damage in 2008 was caused by asset allocations being overexposed to equities, active management being overexposed to illiquidity, and risk systems that were unable to keep up with the rapidly changing short-term risks of all of these investments.

Vultures' Picnic: In Pursuit of Petroleum Pigs, Power Pirates, and High-Finance Carnivores
by Greg Palast
Published 14 Nov 2011

While panicked regulators watched the explosion with fear, Clinton’s Treasury Secretary, Robert Rubin, who’d come from Goldman Sachs, saw only one new world, a post-industrial America. The USA would “manufacture” and sell financial “products,” while we would leave the dull manufacturing of objects to China. In 1997, with the world’s stock markets climbing through the clouds, Myron Scholes received the Nobel Prize for the Black-Scholes Model. The committee could not honor Black, my guide to the Brave New Numerology, who had died of throat cancer years earlier. Then the rains came. How could my master Black have gotten it so horrifically wrong? He had slipped on the banana peel dropped by Milton Friedman. Friedman had sold Black and the world the idea that markets are perfectly “efficient,” from its pricing of French fries to derivatives and money itself, all set in a perfectly rational and fair way.

Data Science for Business: What You Need to Know About Data Mining and Data-Analytic Thinking
by Foster Provost and Tom Fawcett
Published 30 Jun 2013

It preserves, and sometimes further simplifies, the relevant information. For example, a road map keeps and highlights the roads, their basic topology, their relationships to places one would want to travel, and other relevant information. Various professions have well-known model types: an architectural blueprint, an engineering prototype, the Black-Scholes model of option pricing, and so on. Each of these abstracts away details that are not relevant to their main purpose and keeps those that are. In data science, a predictive model is a formula for estimating the unknown value of interest: the target. The formula could be mathematical, or it could be a logical statement such as a rule.

Investment: A History
by Norton Reamer and Jesse Downing
Published 19 Feb 2016

The second contribution Black-Scholes made was to one of the models that immediately preceded it: that of James Boness, whose work has since been largely forgotten by practitioners. Boness’s model had a few vital errors that made the difference between his relative obscurity and a chance for enduring acclaim. The first error was the discount rate used.20 The discount rate in the Black-Scholes model is the risk-free rate, again because of the no-arbitrage condition. Boness, though, used the expected return of the stock as the discount rate, but this is not logical in light of the dynamic hedging strategy. Also, Boness tried to incorporate risk preferences into his work, but Black-Scholes imposed the assumption of risk neutrality and did not distinguish between the risk characteristics of various parties.21 As for the equation itself, it is a partial differential equation—with partial derivatives that are now known as the Greeks: delta, gamma, vega, theta, and rho—that bears some semblance to thermodynamic equations.

New York 2140
by Kim Stanley Robinson
Published 14 Mar 2017

—Ken Thompson, “Reflections on Trusting Trust” A bird in the hand is worth what it will bring. noted Ambrose Bierce c) Franklin Numbers often fill my head. While waiting for my building’s morose super to free my Jesus bug from the boathouse rafters where it had spent the night, I was looking at the little waves lapping in the big doors and wondering if the Black-Scholes formula could frame their volatility. The canals were like a perpetual physics class’s wave-tank demonstration—backwash interference, the curve of a wave around a right angle, the spread of a wave through a gap, and so on—it was very suggestive as to how liquidity worked in finance as well. Too much time to give to this question, the super being so sullen and slow.

Why Stock Markets Crash: Critical Events in Complex Financial Systems
by Didier Sornette
Published 18 Nov 2002

Stocks for the Long Run, 2nd ed. (McGraw Hill, New York). 379. Simon, H. (1982). Models of Bounded Rationality, Vols. 1 and 2 (MIT Press, Cambridge, MA). 380. Simon, J. L. (1996). The Ultimate Resource 2? (Princeton University Press, Princeton, NJ). 381. Sircar, K. R. and Papanicolaou, G. (1998). General Black-Scholes models accounting for increased market volatility from hedging strategies, Applied Mathematical Finance 5, 45–82. 382. Slater, M. D. and Rouner, D. (1992). Confidence in beliefs about social groups as an outcome of message exposure and its role in belief change persistence, Communication Research 19, 597–617. 383.

Never Let a Serious Crisis Go to Waste: How Neoliberalism Survived the Financial Meltdown
by Philip Mirowski
Published 24 Jun 2013

Once one recognizes this distinct trend, then the appearance of the EMH in 1965 in Samuelson and Fama, and its rapid exfoliation throughout finance theory and macroeconomics, becomes something more than just a fluke. Indeed, the EMH served as the first bedrock theoretical tenet of the nascent field of “financial economics” in the late 1960s. Almost every trademark model, from CAPM to the Black-Scholes model of option pricing, has it built in. Most academic financial engineers treat it as an inviolate premise. The notion that all relevant information is adequately embodied in price data was one incarnation of what was fast becoming one of the core commitments of the neoclassical approach to markets, not to mention the First Commandment of models of financial assets.

Valuation: Measuring and Managing the Value of Companies
by Tim Koller , McKinsey , Company Inc. , Marc Goedhart , David Wessels , Barbara Schwimmer and Franziska Manoury
Published 16 Aug 2015

If the probability of each scenario is 50 percent, the weighted average value of equity is $150 million. The scenario valuation approach treats equity like a call option on enterprise value. A more comprehensive model would estimate the entire distribution of potential enterprise values and use an option-pricing model, such as the Black-Scholes model, to value equity.13 Using an option-pricing model rather than scenario analysis to value equity, however, has serious practical drawbacks. First, to model the distribution of enterprise values, you must forecast the expected change and volatility for each source of uncertainty, such as revenue growth and gross margin.