Emanuel Derman Concepts

The Volatility Smile

by Emanuel Derman,Michael B.Miller · 6 Sep 2016

is globally committed to developing and marketing print and electronic products and services for our customers’ professional and personal knowledge and understanding. The Volatility Smile EMANUEL DERMAN MICHAEL B. MILLER with contributions by David Park Cover image: Under the Wave off Kanagawa by Hokusai © Fine Art Premium / Corbis Images Cover design: Wiley

…

Copyright © 2016 by Emanuel Derman and Michael B. Miller. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication

…

www.wiley.com. Library of Congress Cataloging-in-Publication Data: Names: Derman, Emanuel, author. | Miller, Michael B. (Michael Bernard), 1973- author. Title: The volatility smile / Emanuel Derman, Michael B. Miller. Description: Hoboken, New Jersey : Wiley, 2016. | Series: The Wiley finance series | Includes index. Identifiers: LCCN 2016012191 (print) | LCCN 2016019398 (ebook) | ISBN 9781118959169

…

∗ 1 + P (K, T) dK − T ∗ ∫ S K2 0 (4.36) ∞ + 2 1 C(K, T) dK ∫S∗ K2 This section follows closely Kresimir Demeterfi, Emanuel Derman, Michael Kamal, and Joseph Zou, “A Guide to Volatility and Variance Swaps,” Journal of Derivatives 4 (1999): 9–32. 76 THE VOLATILITY SMILE Here P

…

, we divide future stock price scenarios into two general classes, as displayed in Figure 12.5: Either the stock hits 2 This section closely follows Emanuel Derman, Deniz Ergener, and Iraj Kani, “Static Options Replication,” Journal of Derivatives (Summer 1995): 78–95. All option prices in this example assume BSM dynamics. 215

…

described by dS = (r − b)dt + 𝜎(S, t)dZ S 1 (14.2) This section and much of the chapter are based in part on Emanuel Derman and Iraj Kani, “The Volatility Smile and Its Implied Tree,” Risk 7, no. 2 (February 1994): 32–39. 251 Local Volatility Models Su q F

…

rule of two.3 Later we’ll prove it more rigorously. We restrict ourselves to the simple case 3 This proof follows the appendix of Emanuel Derman, Iraj Kani, and Joseph Z. Zou, “The Local Volatility Surface,” Financial Analysts Journal (July–August 1996): 25–36. 262 THE VOLATILITY SMILE in which the

…

a Meltdown: The Risk Neutral Density for the S&P 500 in the Fall of 2008.” Journal of Financial Markets 15, no. 2. Black, Fischer, Emanuel Derman, and William Toy. 1990. “A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options.” Financial Analysts Journal 46, no. 1 (January

…

.” Journal of Financial Economics 7: 229–263. 497 498 REFERENCES Crepey, Stephane. 2004. “Delta-Hedging Vega Risk?” Quantitative Finance 4 (October): 559–579. Demeterfi, Kresimir, Emanuel Derman, Michael Kamal, and Joseph Zou. 1999. “A Guide to Volatility and Variance Swaps.” Journal of Derivatives 4:9–32. Derman, Emanuel, Deniz Ergener, and Iraj

Models. Behaving. Badly.: Why Confusing Illusion With Reality Can Lead to Disaster, on Wall Street and in Life

by Emanuel Derman · 13 Oct 2011 · 240pp · 60,660 words

MARKETS AND MORALS TAT TV AM ASI Appendix Acknowledgments Notes Index About the Author ALSO BY EMANUEL DERMAN My Life as a Quant: Reflections on Physics and Finance This edition first published in 2011 Copyright © 2011 by Emanuel Derman Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ

…

about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of Emanuel Derman to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. First published in

…

symbol indicates an infinitesimally small change in the quantity represented by the second symbol. Thus At is an arbitrarily small increment in time. 9. See Emanuel Derman, “The Perception of Time, Risk and Return During Periods of Speculation,” Quantitative Finance 2, no. 4 (2002): 282–96. 10. “Exclusive” in describing an apartment

…

mysteries of World War II. See Second World War/ World War II worth: definition of Yahweh, Z-bosons Zionism Zippy model airplane About The Author Emanuel Derman is head of risk at Prisma Capital Partners and a professor at Columbia University, where he directs the program in financial engineering. He is the

My Life as a Quant: Reflections on Physics and Finance

by Emanuel Derman · 1 Jan 2004 · 313pp · 101,403 words

armchair sociologists interested in the machinations of both academia and industry." -Peter Carr, Head of Quantitative Research, Bloomberg, and Director, Masters in Math Finance, NYU Emanuel Derman To the Memory of My Parents Ambition is a state of permanent dissatisfaction with the present. PROLOGUE THE TWO CULTURES 1 Physics and finance ■ What

The Physics of Wall Street: A Brief History of Predicting the Unpredictable

by James Owen Weatherall · 2 Jan 2013 · 338pp · 106,936 words

). Meanwhile, college enrollment began to drop, largely because the Baby Boom years were over. Once the “Boomers” had graduated, universities stopped hiring new faculty members. Emanuel Derman was a South African physicist who experienced this funding roller coaster firsthand. He entered graduate school, at Columbia University, in 1966, at the high point

…

certain graphs. The smile appeared suddenly and presented a major mystery for financial engineers in the early 1990s, when its prevalence was first recognized. Notably, Emanuel Derman came up with a way of modifying the Black-Scholes model to account for the volatility smile, though he never came up with a principled

…

and heterodox group of people to discuss how to move the field forward after the recent crisis. In addition to the organizers, Doyne Farmer and Emanuel Derman participated. So did some mainstream economists, such as Nouriel Roubini of New York University and Richard Freeman of Harvard, as well as Nassim Taleb. Richard

…

like a physicist is different from (merely) using mathematical models or physical theories. It’s how you understand the models that counts. In early 2009, Emanuel Derman, the former physicist who worked with Fischer Black at Goldman Sachs during the eighties and nineties, teamed up with Paul Wilmott, founder of Oxford University

…

), Merton and Scholes (1995), Lehmann (2005), Derman (2004, 2011a), Figlewski (1995), Forfar (2007), Bernstein (2010), and Bernstein (1993), as well as from an interview with Emanuel Derman, who worked and collaborated with Black at Goldman Sachs. “Within a week, Black was in jail for participating in student riots . . .”: Strangely enough, the impetus

…

pointing out the relationship between the decay of Bretton Woods and the rise of derivatives trading. “The distinction may seem inconsequential . . .”: I am grateful to Emanuel Derman for pointing out to me how consequential the differences are, from the perspective of practicing bankers. See, however, Derman and Taleb (2005) and Haug and

…

://www.aip.org/statistics/. The data on the NASA budget over time are from the Office of Management and Budget, as reported by Rogers (2010). “Emanuel Derman was a South African physicist who experienced . . .”: Material on Derman is from Derman (2004, 2011b) and from an interview I conducted with him. “Beginning with

…

volatility smile even before the crash of 1987 — that is, it didn’t appear so suddenly after all, if you knew to look for it! “. . . Emanuel Derman came up with a way of modifying the Black-Scholes model . . .”: See Derman and Kani (1994). “There’s an interesting, and rarely told, twist to

…

.” Nature 348 (November): 56–58. Derman, Emanuel. 2004. My Life as a Quant. Hoboken, NJ: John Wiley and Sons. — — — . 2011a. “Emanuel Derman on Fischer Black.” Available at https://www.quantnet.com/emanuel-derman-fischer-black/. — — — . 2011b. Models Behaving Badly. New York: Free Press. Derman, Emanuel, and Iraj Kani. 1994. “The Volatility Smile and Its

How I Became a Quant: Insights From 25 of Wall Street's Elite

by Richard R. Lindsey and Barry Schachter · 30 Jun 2007

-fashioned human hunches but on calculations designed and monitored by computer wizards using abstruse mathematical formulas . . . developed by so-called quants . . . ”2 Wizards, indeed. Even Emanuel Derman, one of the most famous of quants, feels compelled to assert that “[t]he Black-Scholes model tells us, almost miraculously, how to manufacture an

…

16:55 Neil Chriss 123 I wanted to get feedback on my paper and so I sent it around to various academics and also to Emanuel Derman, who was head of Goldman Sachs’ Quantitative Strategies Group, which was the leading group in derivatives pricing research at the time. Derman’s group was

…

, and later my former Yale classmate but now well-known professor Will Goetzmann. In 2005, I returned to teach at Columbia at the encouragement of Emanuel Derman, along with Leon Metzger. In the early 1990s Jack Marshall and Bob Schwartz asked me to become involved in a professional society they were then

…

of the leading thinkers who contributed to the development of what we now call financial engineering. Among these were Robert Merton, Myron Scholes, John Hull, Emanuel Derman, Merton Miller, Franco Modigliani, Steve Ross, Harry Markowitz, Mark Rubinstein, and many others too numerous to mention. I was introduced to several of these people

…

.cam.ac.uk/∼twk/Joshi.pdf. Accessed June 8, 2006. 2. Peter Bernstein, Against the Gods (New York: John Wiley & Sons, 1996), p. 304. 3. Emanuel Derman, My Life as a Quant (Hoboken, NJ: John Wiley & Sons, 2004), p. 7. 4. G.H. Hardy, A Mathematician’s Apology (Cambridge, UK: Cambridge University

The Quants

by Scott Patterson · 2 Feb 2010 · 374pp · 114,600 words

. “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

…

Renaissance Hotel, Wilmott boarded a plane at Heathrow Airport in London and returned to New York City. In New York, he met with über-quant Emanuel Derman. A lanky, white-haired South African, Derman headed up Columbia University’s financial engineering program. He was one of the original quants on Wall Street

…

Turbulence, by Benoit Mandelbrot and Richard L. Hudson (Basic Books, 2006). “I realized that the existence of the smile”: My Life as a Quant, by Emanuel Derman (John Wiley & Sons, 2004), 226. A squad of fifty armed federal marshals: Certain details come from Den of Thieves, by James Stewart (Simon & Schuster, 1991

…

asked not to be identified. Black believed in rationality: Many details of Black’s life derive from interviews with people who knew him, including Asness, Emanuel Derman, and others, as well as his biography, Fischer Black and the Revolutionary Idea of Finance, by Perry Mehrling (John Wiley & Sons, 2005). One day Weinstein

…

Morgan Stanley. A virtual army of traders and professors helped me better understand the world of the quants, including Mark Spitznagel, Nassim Taleb, Paul Wilmott, Emanuel Derman, Aaron Brown, Benoit Mandelbrot, and so many others. Ed Thorp devoted far too much time to help me understand the true nature of trading and

Extreme Money: Masters of the Universe and the Cult of Risk

by Satyajit Das · 14 Oct 2011 · 741pp · 179,454 words

in question. Differential equations, positive definite matrices or the desirable statistical properties of an estimator rarely determine the price of traded financial instruments. Goldman Sachs’ Emanuel Derman, a trained physicist, identified the difference: “In physics, a model is correct if it predicts the future trajectories of planets or the existence and properties

…

The Gods: The Remarkable Story of Risk, John Wiley, New York: 1. 2. Jorge Luis Borges (1999) Collected Fiction, Penguin Books, New York: 105. 3. Emanuel Derman (2004) My Life As A Quant: Reflection on Physics and Finance, John Wiley, New Jersey. 4. Berkshire Hathaway Letter to Shareholders (2002). 5. Martin Z

…

March 2009), ABC Radio, Australia. 11. Sylvain Raynes “The state of financial engineering” (3 December 2008) (www.quantnet.com/forum/showthread.php?t=3978). 12. Emanuel Derman (2004) My Life as a Quant: Reflections on Physics and Finance, John Wiley, New Jersey: 266, 267. 13. “Prophet of climate doom a scientific black

…

Financial Derivatives, FT Prentice Hall, London. Glyn Davies (2002) A History of Money: From Ancient Times to the Present Day, University of Wales Press, Cardiff. Emanuel Derman (2004) My Life as a Quant: Reflections on Physics and Finance, John Wiley, New Jersey. Kevin Dowd and Martin Hutchinson (2010) Alchemists of Loss: How

The Meritocracy Trap: How America's Foundational Myth Feeds Inequality, Dismantles the Middle Class, and Devours the Elite

by Daniel Markovits · 14 Sep 2019 · 976pp · 235,576 words

(Chicago: University of Chicago Press, in preparation). See more at http://web.mit.edu/dikaiser/www/CWB.html#CWBChapters. “science in the service of war”: Emanuel Derman, My Life as a Quant: Reflections on Physics and Finance (Hoboken, NJ: John Wiley & Sons, 2004), 4. Hereafter cited as Derman, My Life as a

Makers and Takers: The Rise of Finance and the Fall of American Business

by Rana Foroohar · 16 May 2016 · 515pp · 132,295 words

-second time intervals, reducing the average holding period of a stock from about eight years in the 1960s to just four months by 2012.55 Emanuel Derman, a quantitative mathematician and physicist who pioneered some of those trading models at Goldman and now teaches financial engineering at Columbia, believes that the focus

…

Turbeville, Thomas Hoenig, Charles Morris, Joe Nocera, Charles Ferguson, Bob Lutz, Lisa Donner, Rebecca Henderson, Margaret Heffernan, Andrew Lo, Dominic Barton, Nitin Nohria, Rakesh Khurana, Emanuel Derman, Mark Bertolini, Andrew Smithers, Lynn Stout, Sam Palmisano, Greg Smith, Joseph Blasi, David Rothkopf, Ken Miller, Marc Fasteau, Robert R. Locke, Ruchir Sharma, Gautam Mukunda

…

in ‘Shareholder Value,’ ” New York Times, June 27, 2012. Also see LPL Financial Research, “Weekly Market Commentary,” by Jeffrey Kleintop, CFA, August 6, 2012. 56. Emanuel Derman, “Apologia Pro Vita Sua,” Journal of Derivatives 20, no. 1 (2012). 57. Author interview with Nitin Nohria, dean of Harvard Business School, for this book

The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution

by Gregory Zuckerman · 5 Nov 2019 · 407pp · 104,622 words

and implementing these mathematical models. At first, they were called rocket scientists by those who assumed rocketry was the most advanced branch of science, says Emanuel Derman, who received a PhD in theoretical physics at Columbia University before joining a Wall Street firm. Over time, these specialists became known as quants, short

…

, 1976, https://www.nytimes.com/1976/04/25/archives/prince-of-the-pit-richard-dennis-knows-how-to-keep-his-head-at-the.html. 6. Emanuel Derman, My Life as a Quant: Reflections on Physics and Finance (Hoboken, NJ: John Wiley & Sons, 2004). 7. Edward O. Thorp, A Man for All Markets