Louis Bachelier

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

Baggs (1774), London; reprinted by Gregg International Publishers (1969). 6. Robert J. Leonard, “Creating a Context for Game Theory,” History of Political Economy, 24 (Supplement) (1992), 29–76, at p. 39. 7. http://en.wikipedia.org/wiki/Louis_Bachelier, date accessed January 23, 2012. 8. Alfred Cowles and H. Jones, “Some A Posteriori Probabilities in Stock Market Action,” Econometrica, 5(3) (1937), 280–94. 9. Louis Bachelier, “Theorie de la speculation,” Annales scientifiques de l’Ecole Normale Superieure, 3rd series, 17 (1900), 21–86. 10. C.M. Sprenkle, “Warrant Prices as Indications of Expectations and Preferences,” Yale Economic Essays, 1(22) (1961), 178–231. 16 Applications 1.

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The modern quants, and trillions 6 The Rise of the Quants of dollars of financial investment each year, now rely on the pricing tools provided by William Sharpe, Fischer Black and Myron Scholes, and Robert Merton, based on the earlier foundational work of Jacob Marschak and a then obscure but brilliant French PhD student at the turn of the twentieth century named Louis Bachelier. In our future, we shall inevitably rely even more on the products of these great minds. We will now turn to how the concepts came about and now affect us all so profoundly. Part I Jacob Marschak We can often discover the formative roots of one or two great insights that eventually culminated in a Nobel Prize for many of the great minds described in this series.

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The scientific analysis of securities pricing By 1950, Marschak had introduced to finance theory a method to price risk, through his mean-variance approach. Much later, however, we discovered that he was not the first to offer a measure of the cost of volatility of financial instruments. At the turn of the twentieth century, the French mathematician Louis Bachelier (1870–1946) produced a PhD thesis with the title “The Theory of Speculation.” In this revolutionary thesis, Bachelier was the first to apply the mathematical model of Brownian motion to the movement of security prices. He did so five years before Albert Einstein applied the same model to the movement of small particles.

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

Courtault, Jean-Michel, and Youri Kabanov. 2002. Louis Bachelier: Aux origines de la finance mathématique. Paris: Presses Universitaires Franc-Comtoises. Cox, John C., and Mark Rubinstein. 1985. Options Markets. Englewood Cliffs, NJ: Prentice Hall. Dash, Mike. 1999. Tulipomania: The Story of the World’s Most Coveted Flower and the Extraordinary Passions It Aroused. New York: Three Rivers Press. David, F. N. 1962. Games, Gods & Gambling: A History of Probability and Statistical Ideas. New York: Simon & Schuster. Davis, Mark, and Alison Etheridge. 2006. Louis Bachelier’s Theory of Speculation: The Origins of Modern Finance.

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For an hour each day they met beneath ornately carved reliefs and a massive skylight to trade the permanent government bonds, called rentes, that had funded France’s global ambitions for a century. Imperial and imposing, it was the center of the city at the center of the world. Or so it would have seemed to Louis Bachelier as he approached it for the first time, in 1892. He was in his early twenties, an orphan from the provinces. He had just arrived in Paris, fresh from his mandatory military service, to resume his education at the University of Paris. He was determined to be a mathematician or a physicist, whatever the odds — and yet, he had a sister and a baby brother to support back home.

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He was sitting in his office, in the economics department at MIT. The year was 1955, or thereabouts. Laid out in front of him was a half-century-old PhD dissertation, written by a Frenchman whom Samuelson was quite sure he had never heard of. Bachelor, Bacheler. Something like that. He looked at the front of the document again. Louis Bachelier. It didn’t ring any bells. Its author’s anonymity notwithstanding, the document open on Samuelson’s desk was astounding. Here, fifty-five years previously, Bachelier had laid out the mathematics of financial markets. Samuelson’s first thought was that his own work on the subject over the past several years — the work that was supposed to form one of his students’ dissertation — had lost its claim to originality.

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

Henri Poincaré, The Value of Science: Essential Writings of Henri Poincaré (New York: The Modern Library, 2001), 402. 4. Louis Bachelier, “Theory of Speculation,” in The Random Character of Stock Prices, trans. A. James Boness, ed. Paul Cootner (Cambridge, Mass.: MIT Press, 1969), 28. 5. Bachelier, “Theory of Speculation,” 17. 6. Poincaré, Value of Science, 419. 7. Bachelier, “Theory of Speculation,” 25–26. 8. This and all other biographical information on Bachelier is from Jean-Michel Courtault et al., “Louis Bachelier on the Centenary of Théorie de la Spéculation,” Mathematical Finance (July 2000): 341–53. Poincaré’s report on Bachelier’s thesis, translated by Selime Baftiri-Balazoski and Ulrich Haussman, is also included in the article. 9.

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Fisher was just the first in a line of distinguished scholars who saw reason and scientific order in the market and made fools of themselves on the basis of this conviction. Most of the others came along much later, though. Irving Fisher was ahead of his time. HE WAS NOT, HOWEVER, ALONE in his advanced thoughts about financial markets. In Paris, mathematics student Louis Bachelier studied the price fluctuations on the Paris Bourse (exchange) in a similar spirit. The result was a doctoral thesis that, when unearthed more than half a century after its completion in 1900, would help to relaunch the study of financial markets. Bachelier undertook his investigation at a time when scientists had begun to embrace the idea that while there could be no absolute certainty about anything, uncertainty itself could be a powerful tool.

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To get it to that point, he had to face head-on some knotty questions that he had ignored in his original paper. The biggest conundrum was how a person was supposed to go about being a statistical man not in a game with clearly defined rules but in a messy, uncertain world. How was one to assign numerical probabilities to uncertain future events? The answer—as Louis Bachelier had concluded back in 1900—is that there is no one way. Everyone’s assessments of the future are of necessity personal and subjective. But rules could be devised for how to adjust those assessments in the face of new evidence, and the man who set them down in the early 1950s was Jimmie Savage, Markowitz’s statistics professor.

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

Futures Commission Merchant Reports for 2003. On the Web at http://www.cftc.gov/tm/tmfcm.htm. Cootner, Paul H, ed. 1964. The Random Character of Stock Market Prices. Cambridge, MA.: MIT Press. Courtault, Jean-Michel. 2000. Louis Bachelier: On the centenary of Théorie de la Spéculation. Mathematical Finance 10 (3) July: 339-353. Courtault, Jean-Michel et al. 2000. Louis Bachelier: Fondateur de la finance mathématique. A Web site, sponsored by the Université de Franche-Comté, publishing primary manuscripts and photographs of Bachelier’s life and times, for the centenary of his doctoral thesis: http://sjepg.univfcomte.fr/La_recherche/Libre/bachelier/page01/page01.htm.

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The fundamental concept: Prices are not predictable, but their fluctuations can be described by the mathematical laws of chance. Therefore, their risk is measurable, and manageable. This is now orthodoxy to which I subscribe—up to a point. Work in this field began in 1900, when a youngish French mathematician, Louis Bachelier, had the temerity to study financial markets at a time “real” mathematicians did not touch money. In the very different world of the seventeenth century, Pascal and Fermat (he of the famous “last theorem” that took 350 years to be proved) invented probability theory to assist some gambling aristocrats.

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He had a keen sense of the beautiful in mathematics. He once said: “A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.” Before Poincaré on that day in 1900 was one of his doctoral students, Louis Bachelier.1 Jobs for Ph.D.’s were scarce; and so the award of a doctorate in France was a formal, trying process. The young mathematician’s schooling had been mediocre, at best. Now he had to pass two final tests before Poincaré and the doctoral “jury.” The lesser one was an oral examination on a standard topic, chosen and approved beforehand.

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

While no one goes so far as to say that it is impossible to make good predictions or that all predictions are destined to be wrong, the abundant evidence and the robust character of the theories that explain the evidence confirm that the task of predicting stock prices is formidable by any measure. The exploration into whether investors can successfully forecast stock prices has roots that reach all the way back to 1900, when Louis Bachelier, a young French mathematician, completed his dissertation for the degree of Doctor of Mathematical Sciences at the Sorbonne. The title of the dissertation was “The Theory of Speculation.” This extraordinary piece of work, some seventy pages long, was the first effort ever to employ theory, including mathematical techniques, to explain why the stock market behaves as it does.

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Sharpe’s work was not all they were unaware of. An impressive body of research on the predictability of stock prices was readily available to anyone who wanted to look at it—but few people did. The researchers who carried out this research and the theorists who explained its findings built a powerful structure on the foundations that Louis Bachelier and Alfred Cowles had prepared for them. They include a famous columnist on Newsweek magazine, a college football star who majored in French and never took a course in math, a compulsive marathon-runner, and an economist at MIT whose gloomy conclusions led him to observe, “I must confess that the fun has gone out of it somehow.”

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A 1688 treatise on the workings of the Amsterdam stock exchange by Joseph de la Vega reveals that options and similar types of securities in common use today were already dominating trading activities at the time. This is significant, as Amsterdam was the most sophisticated and important financial center of the seventeenth century, even more important than London. And we have seen that Louis Bachelier, in the course of writing his thesis in Paris in 1900, was attracted to the problem of valuing options. Options are everywhere around us. The father who tells his little boy to stop watching television and go to bed “or else” is giving his son an interesting option. The boy has no obligation to turn off the TV and go to bed, but his father has given him the right to take up the option of keeping the set on and accepting his punishment.

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

Peter Bernstein, Capital Ideas: The Improbable Origins of Modern Wall Street (New York: Wiley, 1992), 23. 2. Bernstein, Capital Ideas, 23. 3. Mark Davis, “Louis Bachelier’s Theory of Speculation,” talk, Imperial College, https://f-origin.hypotheses.org/wp-content/blogs.dir/1596/files/2014/12/Mark-Davis-Talk.pdf. 4. L. Carraro and P. Crépel, “Louis Bachelier,” Encyclopedia of Math, www.encyclopediaofmath.org/images/f/f1/LouisBACHELIER.pdf. 5. Carraro and Crépel, “Louis Bachelier.” 6. Colin Read, The Efficient Market Hypothesists: Bachelier, Samuelson, Fama, Ross, Tobin, and Shiller (Basingstoke, UK: Palgrave Macmillan, 2013), 48. 7.

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The cofounder of Protégé Partners, a hedge fund investment firm, who took Buffett up on his bet that an index fund could beat the finest money managers in the world over a decade. JACK BOGLE. The founder of Vanguard, one of the biggest index fund managers in the world, and often dubbed “Saint Jack” due to his exhortation for the investment industry to give more people a “fair shake” through cheap passive investment vehicles. LOUIS BACHELIER. An early-twentieth-century French mathematician who died in obscurity, but whose work on the “random walk” of stocks would make him the intellectual godfather of passive investing. ALFRED COWLES III. The wealthy tuberculosis-plagued heir of a newspaper fortune who undertook one of the first rigorous studies of how well investment professionals actually performed versus the broader stock market.

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Chapter 2 THE GODFATHER LEONARD “JIMMIE” SAVAGE, a University of Chicago statistics professor with Coke-bottle glasses and an eclectic, brilliant mind, was rummaging through the university library in 1954 when he made a discovery: a book by a little-known turn-of-the-twentieth-century French mathematician named Louis Bachelier with ideas astonishingly far ahead of their time. Savage sent postcards lauding the work to some of his friends and asked if they had “ever heard of this guy?”1 One of the recipients was Paul Samuelson, a rock-star economist who would go on to become the first American to win a Nobel Prize in the field.

The Wisdom of Finance: Discovering Humanity in the World of Risk and Return
by Mihir Desai
Published 22 May 2017

Putnam’s Magazine 2, no. 11 (November 1853): 546–57; and Bellow, Saul. Seize the Day. New York: Viking Press, 1956. For more on the role of government securities in English literature, see “Percents and Sensibility; Personal Finance in Jane Austen’s Time.” Economist, December 24, 2005. On the contributions of Louis Bachelier, see Bachelier, Louis. Louis Bachelier’s Theory of Speculation: The Origins of Modern Finance. Translated and with an introduction by Mark Davis and Alison Etheridge. Princeton, NJ: Princeton University Press, 2006; Bernstein, Jeremy. “Bachelier.” American Journal of Physics 73, no. 5 (2005): 395; Pearle, Philip, Brian Collett, Kenneth Bart, David Bilderback, Dara Newman, and Scott Samuels.

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This narrative concludes that finance lost its way by promoting precision and models over human reality by trying to describe inherently social phenomena with physics and quantum mechanics. This is a convenient narrative that suits those who are dissatisfied with the rise of finance—but it is shoddy intellectual history. In fact, the person who beat Albert Einstein to the punch by five years was Louis Bachelier, a doctoral student in Paris. Rather than studying the movement of particles, he studied the movement of stocks and derived the mathematics to describe all kinds of motion, including the motion of pollen particles observed by Robert Brown. How did he do it? He realized that he could employ and generalize the magical distribution created by the quincunx into settings where outcomes weren’t the locations of falling balls, but rather processes of motion that were the result of lots of molecules behaving as if they were going through a quincunx.

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

The force which moves them checks the inflow gradually and time elapses before it can be told with certainty whether the tide has been seen or not. Coincidentally, as Charles Dow was propounding his theory of stock price movements, a young French mathematician, starting with a similar conception of the market, reached profoundly different conclusions. Louis Bachelier completed his doctoral dissertation at the Sorbonne in Paris in 1900. Entitled “The Theory of Speculation,” it was the first work to employ mathematical techniques to explain stock market behavior. Bachelier, like Dow, believed that the stock market at all times accurately represented the collective wisdom of all participants.

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Bachelier has evidenced an original and precise mind,” but also commented, “The topic is somewhat remote from those our candidates are in the habit of treating.”13 Over fifty years were to pass before anyone took the slightest interest in his work. J. P. Morgan and his associates undoubtedly never heard of Louis Bachelier and were probably quite unfamiliar with the Dow theory. The problem they faced as they attempted to bring U.S. Steel to market was much more immediate: how to ensure that the market could absorb the heavy weight of the new securities to be issued. Fortunately, the tone of the market in 1901 was good, even exuberant.

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While this concept may seem unremarkable, it was to be at the root of a raging debate at the end of the decade between a new generation of impertinent academic researchers on one side and high-profile portfolio managers on the other. For the first time, formerly ignored voices of scholars like Louis Bachelier and Harry Markowitz would finally make themselves heard on Wall Street. An SEC investigation of the 1962 market “crash” concluded that “neither this study nor that of the New York Stock Exchange was able to isolate and identify the cause of the market events [of late May 1962].” The SEC noted that “there was some speculation at the time that these events might be the result of some conspiracy or deliberate misconduct.

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

He was short and plump, carried an enormous head set off by a thick spade beard and splendid mustache, was myopic, stooped, distraught in speech, absent-minded and wore pince-nez glasses attached to a black silk ribbon.5 Poincare was another mathematician in the long line of child prodigies that we have met along the way. He grew up to be the leading French mathematician of his time. Nevertheless, Poincare made the great mistake of underestimating the accomplishments of a student named Louis Bachelier, who earned a degree in 1900 at the Sorbonne with a dissertation titled "The Theory of Speculation."6 Poincare, in his review of the thesis, observed that "M. Bachelier has evidenced an original and precise mind [but] the subject is somewhat remote from those our other candidates are in the habit of treating."

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[I]t is meaningless and fatally misleading to speak of the probability, in an objective sense, that a judgment is correct."12 Knight, like Arrow, had no liking for clouds of vagueness. Knight's ideas are particularly relevant to financial markets, where all decisions reflect a forecast of the future and where surprise occurs regularly. Louis Bachelier long ago remarked, "Clearly the price considered most likely by the market is the true current price: if the market judged otherwise, it would quote not this price, but another price higher or lower." The consensus forecasts embedded in security prices mean that those prices will not change if the expected happens.

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Perhaps they ignored the challenge of valuing an option because the key to the puzzle is in the price of uncertainty, a concept that seems more appropriate to our own times than it may have seemed to theirs. The first effort to use mathematics rather than intuition in valuing an option was made by Louis Bachelier back in 1900. In the 1950s and 1960s, a few more people tried their hands at it, including Paul Samuelson. The puzzle was finally solved in the late 1960s by an odd threesome, none of whom was yet thirty years old when their collaboration began.' Fischer Black was a physicist-mathematician with a doctorate from Harvard who had never taken a course in economics or finance.

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

Indeed, the demand curve for a financial asset is far more complicated and subject to much greater change than it is, for example, for consumer goods, in which case it emerges out of simple human desires to consume certain quantities of the good at particular prices. What, then, is the appropriate way to think about pricing financial assets? The Father of Mathematical Finance It has been said that mathematical finance emerged largely out of Louis Bachelier’s work on the theory of derivatives pricing at the turn of the twentieth century. Bachelier’s father was a vendor of wine who also dabbled in science as a hobby. When Louis’s parents died abruptly after he achieved his bachelor’s degree, he found himself thrust into the position of steward of his family’s business.

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This was not an obvious result before its publication, and it ultimately generated a flurry of literature in the field of corporate finance on the role of capital structure and its interaction with asset pricing. Paul Samuelson and Bridging the Gap in Derivatives Theory We now come full circle within the discussion of the evolution of asset pricing theory and return to the pricing of derivatives. The man who, in a sense, connected the earlier work of Louis Bachelier to that of Black and Scholes, described later, was Paul Samuelson. Samuelson made a stunning breadth of contributions to economics until the end of his life at the age of ninety-four. Hailing from Gary, Indiana, he studied at the University of Chicago in the early 1930s, taking several classes alongside such distinguished classmates as Milton Friedman.

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.; Dan Kedmey, “2 Years and 900 Pages Later, the Volcker Rule Gets the Green Light,” TIME.com, December 11, 2013, http://business.time .com/2013/12/11/2-years-and-900-pages-later-the-volcker-rule-gets -the-green-light. Carmen M. Reinhart and Kenneth S. Rogoff, This Time Is Different: Eight Centuries of Financial Folly (Princeton, NJ: Princeton University Press, 2011), xliv–xlv and 238–239. 7. THE EMERGENCE OF INVESTMENT THEORY 1. Jean-Michel Courtault et al., “Louis Bachelier on the Centenary of Théorie de la Spéculation,” Mathematical Finance 10, no. 3 (July 2000): 342–343. 370 7. The Emergence of Investment Theory 2. Ibid., 341–344. 3. Ibid., 346–347. 4. “Fisher, Irving” in Concise Encyclopedia of Economics, ed. David R. Henderson, Library of Economics and Liberty, 2008, http://www .econlib.org/library/Enc/bios/Fisher.html. 5.

Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else
by Jordan Ellenberg
Published 14 May 2021

Taqqu, “Bachelier and His Times: A Conversation with Bernard Bru,” Finance and Stochastics 5, no. 1 (2001): 5, from which most of this account is drawn. Jean-Michel Courtault et al., in “Louis Bachelier on the Centenary of Theorie de la Speculation,” Mathematical Finance 10, no. 3 (July 2000): 341–53, says on p. 343 that Bachelier’s grades were quite good. Dreyfus was convicted: All material on Poincaré and the Dreyfus affair is from Gray, Henri Poincaré, 166–69. “[O]ne might fear”: Courtault et al., “Louis Bachelier on the Centenary of Théorie de la Spéculation,” 348. Bachelier did end up: The story of Bachelier is drawn from Taqqu, “Bachelier and His Times,” 3–32.

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It was once often called a “drunkard’s walk,” though in the kinder present era most people no longer think of a life-ruining addiction as an amusing peg to hang a mathematical concept on. A RANDOM WALK TO THE BOURSE Ross and Pearson weren’t the only people thinking about random walks as the new century rolled in. In Paris, Louis Bachelier, a young man from Normandy, was working at the Bourse, the great stock exchange at the financial center of France. He began studying mathematics at the Sorbonne in the 1890s, taking great interest in the probability courses, which were taught by Henri Poincaré. Bachelier was not a typical student; an orphan, he had to work for his living, and hadn’t received the lycée training that had molded most of his peers in the styles and mores of French mathematics.

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In 1926 he fell ill from a nasty infestation of parasitic amoebas, and he had to move back to the United States. A few years afterward, the stock market went haywire and threw the world into depression, so Elliott had a lot of free time, and a lot of motivation to restore some order to a financial world that no longer fit into neat double-entry bookkeeping. Elliott surely didn’t know about Louis Bachelier’s work on stock prices as a random walk, but if he had, he wouldn’t have given it a minute. He didn’t want to believe stock prices were randomly jittering like dust suspended in fluid. He wanted something more like the comforting physical laws that kept the planets safely in their orbits. Elliott compared himself to Edmond Halley, who figured out in the seventeenth century that the apparently random comings and goings of comets actually obeyed a rigid timetable.

The Quants
by Scott Patterson
Published 2 Feb 2010

(The mystery remained unsolved for decades, until Albert Einstein, in 1905, discovered that the strange movement, by then known as Brownian motion, was the result of millions of microscopic particles buzzing around in a frantic dance of energy.) The connection between Brownian motion and market prices was made in 1900 by a student at the University of Paris named Louis Bachelier. That year, he’d written a dissertation called “The Theory of Speculation,” an attempt to create a formula that would capture the movement of bonds on the Paris stock exchange. The first English translation of the essay, which had lapsed into obscurity until it resurfaced again in the 1950s, had been included in the book about the market’s randomness that Thorp had read in New Mexico.

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Everywhere he looked he saw the same thing: huge leaps where they didn’t belong—on the outer edges of the bell curve. After combing through the data, Mandelbrot wrote a paper detailing his findings, “The Variation of Certain Speculative Prices.” Published as an internal research report at IBM, it was a direct attack on the normal distributions used to model the market. While praising Louis Bachelier, a personal hero of Mandelbrot’s, the mathematician asserted that “the empirical distributions of price changes are usually too ‘peaked’ relative to samples” from standard distributions. The reason: “Large price changes are much more frequent than predicted.” Mandelbrot proposed an alternative method to measure the erratic behavior of prices, one that borrows a mathematical technique devised by the French mathematician Paul Lévy, whom he’d studied under in Paris.

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The future, therefore, is random, a Brownian motion coin flip, a drunkard’s walk through the Parisian night. The groundwork for the efficient-market hypothesis had begun in the 1950s with the work of Markowitz and Sharpe, who eventually won the Nobel Prize for economics (together with Merton Miller) in 1990 for their work. Another key player was Louis Bachelier, the obscure French mathematician who argued that bond prices move according to a random walk. In 1954, MIT economist Paul Samuelson—another future Nobel laureate—received a postcard from Leonard “Jimmie” Savage, a statistician at Chicago. Savage had been searching through stacks at a library and stumbled across the work of Bachelier, which had largely been forgotten in the half century since it had been written.

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

This may be why market pundits seem so much more certain than, say, sports commentators, who are comparatively frank in acknowledging the huge role of chance. Efficiency and Random Walks The Efficient Market Hypothesis formally dates from the 1964 dissertation of Eugene Fama, the work of Nobel prize-winning economist Paul Samuelson, and others in the 1960s. Its pedigree, however, goes back much earlier, to a dissertation in 1900 by Louis Bachelier, a student of the great French mathematician Henri Poincare. The hypothesis maintains that at any given time, stock prices reflect all relevant information about the stock. In Fama’s words: “In an efficient market, competition among the many intelligent participants leads to a situation where, at any point in time, actual prices of individual securities already reflect the effects of information based both on events that have already occurred and on events which, as of now, the market expects to take place in the future.”

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Although the practice and theory of insurance have a long history (Lloyd’s of London dates from the late seventeenth century), it wasn’t until 1973 that a way was found to rationally assign costs to options. In that year Fischer Black and Myron Scholes published a formula that, although much refined since, is still the basic valuation tool for options of all sorts. Their work and that of Robert Merton won the Nobel prize for economics in 1997. Louis Bachelier, whom I mentioned in chapter 4, also devised a formula for options more than one hundred years ago. Bachelier’s formula was developed in connection with his famous 1900 doctoral dissertation in which he was the first to conceive of the stock market as a chance process in which price movements up and down were normally distributed.

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

Before too long, other investors will hear about the geniuses’ methods and copy them. When this happens, the market will incorporate the new information, and the juicy returns that the geniuses were making will be arbitraged away. Prediction will no longer work, and the market will return to a state of being unfathomable. The first person to develop this type of logic was Louis Bachelier, a French mathematician who, way back in 1900, wrote a doctoral dissertation entitled “The Theory of Speculation.” Take an individual stock. At any moment in time, Bachelier observed, some optimists think it will go up; some pessimists think it will go down. If there are more of the former than the latter, their purchases will bid the price up.

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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.

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The defenders of VAR sidestepped this problem by redefining risk as volatility and assuming that the future would resemble recent history. In the simplest version of VAR, which involves a portfolio consisting of a single asset class, the risk modeler calls up some data and looks at how much the portfolio has jumped around in the past, perhaps by calculating its standard deviation. The next step involves invoking the ghost of Louis Bachelier—this is where the illusion of predictability comes in—and assuming that daily movements in financial prices follow the bell curve, or normal distribution, which places exact numbers on the likelihood of unlikely events. (For example, in any given trading session the probability of a stock rising or falling by more than three times its standard deviation is about 0.003, less than one in three hundred.)

Crisis Economics: A Crash Course in the Future of Finance
by Nouriel Roubini and Stephen Mihm
Published 10 May 2010

Samuels, Jeff E. Biddle, and John B. Davis, eds., A Companion to the History of Economic Thought (Oxford: Blackwell, 2003), 112-29; Alessandro Roncaglia, The Wealth of Ideas: A History of Economic Thought (Cambridge, U.K.: Cambridge University Press, 2005), 179-243, 278-96, 322-83. 40 Louis Bachelier: Louis Bachelier, “Théorie de la spéculation,” in Annales Scientifiques de l’École Normale Supérieure 3 (1900): 21-86; Justin Fox, The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street (New York: Harper Business, 2009), 6-8. 40 “The consensus of judgment . . .”: Lawrence quoted in John Kenneth Galbraith, The Great Crash, 1929 (Boston: Houghton Mifflin, 1954), 75. 41 postwar academic departments: Fox, Myth of the Rational Market, 89-107. 41 “random walk” theory: Burton G.

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Faith in the fundamental stability of markets gave rise to an important corollary: if markets are fundamentally self-regulating, and their collective wisdom is always right, then the prices of assets bought and sold in the market are accurate and justified. Early-twentieth-century economists tried to give this theory some mathematical validity. They relied in part on the work of French mathematician Louis Bachelier, whose Théorie de la spéculation, completed in 1900, argued that an asset’s price accurately reflects all known information about it. There is no such thing, in his view, as an undervalued or overvalued asset; the market is a perfect reflection of the underlying fundamentals. To be sure, asset prices change, often dramatically, but merely as a rational and automatic response to the arrival of new information.

The Fractalist
by Benoit Mandelbrot
Published 30 Oct 2012

Two Pictures of Price Variation How do prices vary on the organized markets called bourses, stock exchanges, or commodity exchanges? For centuries, such markets have thrived without the benefit of a systematic mathematical model. The first such model was put forward in 1900 by an outsider in French mathematics, Louis Bachelier (1870–1946). It came out astonishingly early—well ahead of its time—and was odd indeed. It became the standard financial model, and was the one Houthakker was using with cotton prices. The model was advanced financially, but not buttressed by any data whatsoever. Originally, it drew little attention, but over time two events revived it.

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While I would be elected on the basis of my work in finance, I could teach anything I chose. This mattered to few persons other than me. I realize now that I was about to be pushed out of the economic mainstream by a major step in academic economics: the 1972 revival by Black-Scholes-Merton of the formula of Louis Bachelier. Could I have both fought and outwaited them in a protected site? Unfortunately, the downside was big. From the viewpoint of the dream that ruled my life, the timing was dreadful. Fractal geometry was on a roll, and at IBM I had squirreled away sufficient resources to prepare the 1975 French book and undertake a longer English one.

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

It was rumored that Savage’s peripatetic career had something to do with his habit of informing associates of their stupidity. In 1954 Savage was looking for a book on a library shelf. He came across a slim volume by Louis Bachelier. The thesis of Bachelier’s book was that the changes in stock prices are completely random. Savage sent postcards to a number of people he thought might be interested, including Samuelson. On the cards Savage wrote, “Ever hear of this guy?” The answer was no. The world had forgotten Louis Bachelier. His 1900 thesis, “A Theory of Speculation,” argued that the day-to-day changes in stock prices are fundamentally unpredictable. When a stock’s price reflects everything known about a company and all reasonable projections, then future changes in price should be, by definition, unpredictable.

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

We meet several interesting figures; the first is the Parisian broker and financial economist Jules Regnault, who developed the theory of efficient markets. The second is Henri Lefèvre, the accountant for the Rothschild bank in Paris who designed a way to calculate complex positions of stocks and bonds simultaneously. The third is Louis Bachelier, the French academic mathematician whose fascination with pricing options trading on the Paris Bourse led to the discovery of Brownian motion—an abstract model of how a system evolves through time. Together, their insights led to virtually all the tools of modern financial engineering. The limitations of these tools ultimately exposed the potential for failure of even our most complex models.

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., two years rather than one month) should also be worth more money because of the rule Jules Regnault came up with: the expected price change (up or down) grows with time. BROWNIAN MOTION These general intuitions about what makes options more or less expensive can only get you so far. Toward the end of the nineteenth century, a French mathematician, Louis Bachelier (1870–1946), developed a mathematical technique for calculating the precise prices of options. As expected, it required as an input to the equation the riskiness of the stock—what Regnault had earlier called its “vibration.” It also required the time period for which the option is granted (the “maturity” of the option).

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Lévy’s research focused on “stochastic processes”: mathematical models that describe the behavior of some variable through time. For example, we saw in Chapter 15 that Jules Regnault proposed and tested a stochastic process that varied randomly, which resulted in a rule about risk increasing with the square root of time. Likewise, Louis Bachelier more formally developed a random-walk stochastic process. Paul Lévy formalized these prior random walk models into a very general family of stochastic processes referred to as Lévy processes. Brownian motion was just one process in the family of Lévy processes—and perhaps the best behaved of them.

Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures
by Frank J. Fabozzi
Published 25 Feb 2008

Complex derivative instruments such as options, caps, floors, and swaptions can only be valued (i.e., priced) using tools from probability and statistical theory. While the model for such pricing was first developed by Black and Scholes (1976) and known as the Black-Scholes option pricing model, it relies on models that can be traced back to the mathematician Louis Bachelier (1900). In the remainder of this introductory chapter, we do two things. First, we briefly distinguish between the study of probability and the study of statistics. Second, we provide a roadmap for the chapters to follow in this book. PROBABILITY VS. STATISTICS Thus far, we have used the terms “probability” and “statistics” collectively as if they were one subject.

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For example, in equation (D.3), we bound the integral by the P(Sτ ≤ K)-quantile K of the probability distribution of Sτ.313 Then, we saw how quantiles changed as we replace one random variable with another. This was displayed, for example, in the second equation of equation (D.6) where K was the P(Sτ ≤ K)-quantile of Sτ, which translated into the P(Sτ ≤ K)-quantile K/S0 of the new random variable Y = Sτ/S0. References Bachelier, Louis. [1900] 2006. Louis Bachelier’s Theory of Speculation: The Origins of Modern Finance. Translated by Mark Davis and Alison Etheridge. Princeton, N.J.: Princeton university Press. Barndorff-Nielsen, Ole E. 1997. “Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling.” Scandinavian Journal of Statistics 24 (1): 1-13.

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

Fund managers with high returns simply took higher risk rather than possessing supernatural skill. Demon of Chance The efficient market hypothesis (EMH) stated that the stock prices followed a random walk, a formal mathematical statement of a trajectory consisting of successive random steps. Pioneers Jules Regnault (in the nineteenth century) and Louis Bachelier (early twentieth century) had discovered that short-term price changes were random—a coin toss could predict up or down moves. Bachelier’s Sorbonne thesis established that the probability of a given change in price was consistent with the Gaussian or bell-shaped normal distribution, well-known in statistical theory.

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Insurance, with its long history, offered guidance on valuation. The insurer’s profit was the difference between statistical loss experience, based on historical knowledge of claims, and the premiums paid, plus investment income on the premiums. Applying insurance theory to options proved difficult. Louis Bachelier applied random walk models to pricing options. Paul Cootner and Paul Samuleson worked on the problem. In their 1967 book Beat the Market, mathematicians Sheen Kassouf and Edward Thorp outlined the relationship between the price of an option and the price of the underlying stock. Thorp, whose interest was gambling and beating the casino at roulette and baccarat, developed a model, anticipating the Black-Scholes equation.

Derivatives Markets
by David Goldenberg
Published 2 Mar 2016

This includes a discussion of the difference between hedging stock portfolios with forwards and hedging with futures; 11. an entry into understanding swaps, by viewing them as structured products, based on the forward concept; 12. the difference between commodity and interest rate swaps, and a detailed explanation of what it means to pay fixed and receive floating in an interest rate swap; 13. understanding Eurodollar futures strips, notation shifts, and the role of the quote mechanism; 14. discussion of swaps as a zero-sum game, and research challenges to the comparative advantage argument; 15. swaps pricing and alternative interpretations of the par swap rate; 16. a step-by-step approach to options starting in Chapter 9 with the usual emphasis on the quote mechanism, as well as incorporation of real asset options examples; 17. an American option pricing model in Chapter 9, and its extension to European options in Chapter 11; 18. the importance of identifying short, not just long, positions in an underlying asset and the hedging demand they create; 19. two chapters on option trading strategies; one basic, one advanced, including the three types of covered calls, the protective put strategy, and their interpretations; 20. a logical categorization of rational option pricing results in Chapter 11, and the inclusion of American puts and calls; 21. neither monotonicity nor convexity, which are usually assumed, are rational option results; 22. partial vs. full static replication of European options; 23. working backwards from payoffs to costs as a method for devising and interpreting derivatives strategies; 24. the introduction of generalized forward contracts paves the way for the connection between (generalized) forward contracts and options, and the discussion of American put-call parity; 25. the Binomial option pricing model, N=1, and why it works—which is not simply no-arbitrage; 26. three tools of modern mathematical finance: no-arbitrage, replicability and complete markets, and dynamic and static replication, and a rule of thumb on the number of hedging vehicles required to hedge a given number of independent sources of uncertainty; 27. static replication in the Binomial option pricing model, N=1, the hedge ratio can be 1.0 and a preliminary discussion in Chapter 13 on the meaning of risk-neutral valuation; 28. dynamic hedging as the new component of the BOPM, N>1, and a path approach to the multi-period Binomial option pricing model; 29. equivalent martingale measures (EMMs) in the representation of option and stock prices; 30. the efficient market hypothesis (EMH) as a guide to modeling prices; 31. arithmetic Brownian motion (ABM) and the Louis Bachelier model of option prices; 32. easy introduction to the tools of continuous time finance, including Itô’s lemma; 33. Black–Scholes derived from Bachelier, illustrating the important connection between these two models; 34. modeling non-constant volatility: the deterministic volatility model and stochastic volatility models; 35. why Black–Scholes is still important; 36. and a final synthesis chapter that includes a discussion of the different senses of risk-neutral valuation, their meaning and economic basis, and a complete discussion of the dynamics of the hedge portfolio in the BOPM, N=1.

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Black–Scholes derived from Bachelier, illustrating the important connection between these two models; 34. modeling non-constant volatility: the deterministic volatility model and stochastic volatility models; 35. why Black–Scholes is still important; 36. and a final synthesis chapter that includes a discussion of the different senses of risk-neutral valuation, their meaning and economic basis, and a complete discussion of the dynamics of the hedge portfolio in the BOPM, N=1. I would like to thank the giants of the derivatives field including: Louis Bachelier, Fischer Black, John Cox, Darrell Duffie, Jonathan Ingersoll, Kiyoshi Itô, Robert Merton, Paul Samuelson, Myron Scholes, Stephen Ross, Mark Rubinstein, and many others. I sincerely hope that the reader enjoys traveling along the path to understanding Derivatives Markets. David Goldenberg Independent researcher, NY, USA ACKNOWLEDGMENTS I would like to thank everyone at Routledge for their hard work on this book.

Quantitative Value: A Practitioner's Guide to Automating Intelligent Investment and Eliminating Behavioral Errors
by Wesley R. Gray and Tobias E. Carlisle
Published 29 Nov 2012

They started meeting together once a week in an effort to solve the warrant valuation conundrum. Thorp found the answer in an unlikely place. In a collection of essays called The Random Character of Stock Market Prices (1964), Thorp read the English translation of a French dissertation written in 1900 by a student at the University of Paris, Louis Bachelier. Bachelier's dissertation unlocked the secret to valuing warrants: the so-called “random walk” theory. As the name suggests, the “random walk” holds that the movements made by security prices are random. While it might seem paradoxical, the random nature of the moves makes it possible to probabilistically determine the future price of the security.

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

This idea of the random walk has permeated many scientific fields and is commonly used as the model mechanism behind a variety of unpredictable continuous-time processes. The lognormal random walk based on Brownian motion is the classical paradigm for the stock market. See Brown (1827). 1900 Bachelier Louis Bachelier was the first to quantify the concept of Brownian motion. He developed a mathematical theory for random walks, a theory rediscovered later by Einstein. He proposed a model for equity prices, a simple normal distribution, and built on it a model for pricing the almost unheard of options. His model contained many of the seeds for later work, but lay ‘dormant’ for many, many years.

The Bogleheads' Guide to Investing
by Taylor Larimore , Michael Leboeuf and Mel Lindauer
Published 1 Jan 2006

They have given us sophisticated theories that we can use to select our investments and combine them in the most efficient manner to give us maximum return with minimum volatility. THE EFFICIENT MARKET THEORY (EMT) To understand EMT, we'll go back to the year 1900 when a young French mathematician named Louis Bachelier wrote his Ph.D. thesis, which contained the seeds of the Efficient Market Theory. EMT can be described as "an investment theory that states that it is impossible to `beat the market' because existing share prices already incorporate and reflect all relevant information." Another student of the stock market was Alfred Cowles, who came to prominence about 20 years later.

Concentrated Investing
by Allen C. Benello
Published 7 Dec 2016

His research led him to fill three library shelves with books, including Adam Smith’s Wealth of Nations, John von Neumann and Oskar Morgenstern’s Theory of Games and Economic Behavior, Paul Samuelson’s Economics, and Fred Schwed’s Where Are the Customer’s Yachts? In a notebook Shannon recorded a varied list of thinkers, including French mathematician Louis Bachelier, Benjamin 74 Concentrated Investing Graham, and Benoit Mandelbrot. He took notes about margin trading; short selling; stop‐loss orders; the effects of market panics; capital gains taxes and transaction costs. The only surviving document from Shannon’s research is a mimeographed handout from one of the lectures he delivered at MIT in the spring term of 1956, in a class called Seminar of Information Theory.

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

It was a problem, he said, that went back a century to the work of a neurotic French economist in Paris. “Prices of course go up and down, that was known to everybody, and there are all kinds of nice maxims about it,” Mandelbrot said in a thick French accent. “In 1900, an incredible genius looked at the problem. His name was Louis Bachelier. Nobody noticed him. He had a very miserable life. But he wrote in 1900 a [dissertation] in mathematics, believe it or not, called ‘The Theory of Speculation.’ Speculation meant speculation on the stock market or bond market. And he introduced for the first time in loose and incomplete fashion Brownian motion,” he said, referring to the nineteenth-century observation by Scottish botanist Robert Brown that the motion of pollen in a liquid is a random process.

Capital Ideas Evolving
by Peter L. Bernstein
Published 3 May 2007

If capital goes to the wrong uses or does not f low at all, the economy will operate inefficiently, and ultimately economic growth will be low.”1 The data of financial markets reveal, for better or for worse, “the brain of the economy” and “the lifeblood of economic activity.” This extraordinary data bank was the key mechanism that revealed the fundamental character of financial markets as early as 1900 to Louis Bachelier, little-known but surely among the most powerful of finance theorists (see Capital Ideas, pp. 18–23), and later to all to the creators of Capital Ideas. Much more was to follow.* Although time had to pass before practitioners could persuade themselves to accept the implications of theory, the data bank became the stepping-stone to implementation, from the first index fund at Wells Fargo Investment Advisors in 1971 to the diverse activities of today’s practitioners described in this book.

High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems
by Irene Aldridge
Published 1 Dec 2009

The strong form deals with all kinds of public and nonpublic information; the semistrong form excludes nonpublic information from the information set. As in most contemporary academic literature on market efficiency, we restrict the tests to the weak form analysis only. Non-Parametric Runs Test Several tests of market efficiency have been developed over the years. The very first test, constructed by Louis Bachelier in 1900, measured the probability of a number of consecutively positive or consecutively negative price changes, or “runs.” As with tossing a fair coin, the probability of two successive price changes of the same sign (a positive change followed by a positive change, for example) is 1/(22 ) = 0.25.

The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution
by Gregory Zuckerman
Published 5 Nov 2019

During the 1970s, Thorp helped lead a hedge fund, Princeton/Newport Partners, recording strong gains and attracting well-known investors—including actor Paul Newman, Hollywood producer Robert Evans, and screenwriter Charles Kaufman. Thorp’s firm based its trading on computer-generated algorithms and economic models, using so much electricity that their office in Southern California was always boiling hot. Thorp’s trading formula was influenced by the doctoral thesis of French mathematician Louis Bachelier, who, in 1900, developed a theory for pricing options on the Paris stock exchange using equations similar to those later employed by Albert Einstein to describe the Brownian motion of pollen particles. Bachelier’s thesis, describing the irregular motion of stock prices, had been overlooked for decades, but Thorp and others understood its relevance to modern investing.

Licence to be Bad
by Jonathan Aldred
Published 5 Jun 2019

The eighteenth-century French mathematician Abraham de Moivre was the first to realize that repeated random events such as these generate a bell-curve distribution.fn4 The problems begin when we carry over these ideas to the wrong places. Again, Jimmie Savage played a key role. Savage had discovered the work of Louis Bachelier, an obscure French mathematician who in 1900 had published a ‘theory of speculation’ suggesting prices in financial markets move completely randomly. Savage produced the first English translation of Bachelier’s theory, and Bachelier’s ideas gained further attention with the emergence of the ‘efficient market hypothesis’ in the 1960s.

Finance and the Good Society
by Robert J. Shiller
Published 1 Jan 2012

It can be attacked empirically, but this method of research is likely to be costly.8 It may seem strange that a well-developed options trading industry existed in Schwed’s day and yet there was still no theory of options pricing—a prerequisite that would seem essential to trading in that market. Actually a serviceable options pricing theory had been published in 1900 by the French mathematician Louis Bachelier.9 But there is no evidence that anyone in the options market had even heard of his paper. That did not change until 1964, when the mathematical treatises of A. J. Boness and Case Sprenkle appeared.10 Boness remarked on the strangeness of this: “Investment analysis is largely in a pre-theoretic stage of development.

When Einstein Walked With Gödel: Excursions to the Edge of Thought
by Jim Holt
Published 14 May 2018

Why should the pattern of ups and downs in the market for cotton bear such a striking resemblance to the wildly unequal way wealth was spread through society? This was certainly not consistent with the orthodox model of financial markets, which was originally proposed in 1900 by a French mathematician named Louis Bachelier (who had copied it from the physics of a gas in equilibrium). According to the Bachelier model, price variation in a stock or commodity market is supposed to be smooth and mild; fluctuations in price, arranged by size, should line up nicely in a classic bell curve. This is the basis of what became known as the efficient market hypothesis.

The Missing Billionaires: A Guide to Better Financial Decisions
by Victor Haghani and James White
Published 27 Aug 2023

See Shiller, 2015. 4. Bogle, 2005. 5. As noted in Dichev, 2007 Chapter 1; Hsu et al., 2016; Dalbarm 2021; and Morningstar “Mind the Gap” reports. 6. While Fama is the financial economist most popularly linked to the efficient market hypothesis, his work built upon that of many predecessors from Louis Bachelier (1900) to Friedrich Hayek (1945) to Paul Samuelson (1965). 7. APT was introduced by Ross (1976), but Robert C. Merton (1973) proposed the first multi‐factor, intertemporal extension of CAPM. 8. Treynor, 1961; Sharpe, 1964; Lintner, 1965; and Mossin, 1966. 9. For example, Black, Jensen, and Scholes (1972) found that low beta assets earn more, and high beta assets earn less, than predicted from CAPM. 10.

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

Though it was not sufficiently mispriced then, the history of how warrant prices behaved indicated this could happen before it expired in 1975. When it did we bet a significant part of the partnership’s net worth. — We were guided in this trade and thousands of others by a formula that had its beginnings in 1900 in the PhD thesis of French mathematician Louis Bachelier. Bachelier used mathematics to develop a theory for pricing options on the Paris stock exchange (the Bourse). His thesis adviser, the world-famous mathematician Henri Poincaré, didn’t value Bachelier’s effort, and Bachelier spent the rest of his life as an obscure provincial professor. Meanwhile a twenty-six-year-old Swiss patent clerk named Albert Einstein would soon publish in his single “miraculous year” of 1905 a series of articles that would transform physics.

No One Would Listen: A True Financial Thriller
by Harry Markopolos
Published 1 Mar 2010

Like me, maybe even more than me, he could glance at numbers and draw meaningful conclusions from them. At Bentley College, he played a lot of poker, ran a small bookie operation, and came to believe firmly in the efficient markets hypothesis. Believing that concept was where Neil and I differed most. The efficient markets hypothesis, which was first suggested by French mathematician Louis Bachelier in 1900 and was applied to the modern financial markets by Professor Eugene Fama at the University of Chicago in 1965, claims that if all information is simultaneously and freely available to everyone in the market, no one can have an edge. In this hypothesis having an edge means that for all intents and purposes you have accurate information that your competitors don’t have.

Wall Street: How It Works And for Whom
by Doug Henwood
Published 30 Aug 1998

In more popular, more ideological versions of efficient market theory, expectations are imbued with an almost mystical importance: the collective wisdom of "the market" is treated as if it were omniscient. Notions of market efficiency have their roots in a long-standing observation that it's damn hard to beat the market, and that prices seem to move in random ways. Louis Bachelier argued in a 1900 study (that was ignored WALL STREET for 60 years) that over the long term, speculators should consistently earn no extraordinary profits; market prices, in other words, are a "fair game." Another precursor of EM theory was Alfred Cowles, who showed in two studies (Cowles 1933; 1944) that a variety of forecasts by pundits and investment professionals yielded results that were at best no better than the overall market, and often quite worse.

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

(To be fully precise, the stock price should follow a random walk after adjustment for dividends and a risk premium.) The notion of random walks can be traced back to 1827, when botanist Robert Brown used a microscope to examine dust grains floating in water and noticed their erratic behavior, later memorialized as Brownian motion. On March 29, 1900, a French postgraduate student, Louis Bachelier, successfully defended his dissertation, “The Theory of Speculation,” in which he proposed a model of Brownian motion to explain a similarly random movement but in security prices rather than dust grains—five years before Albert Einstein famously determined the cause of Brown’s observations, providing evidence that atoms and molecules existed.2 Bachelier’s research was largely forgotten for half a century until it was rediscovered by University of Chicago mathematician Leonard Jimmie Savage, who translated the work and brought it to the attention of Paul Samuelson, the first American recipient of the Nobel Prize in Economics.

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

There are very powerful scientific methods of cyclical analysis, particularly Fourier analysis, which was invented in the nineteenth century, William Eckhardt / 123 essentially to understand heat transfer. Fourier analysis has been tried again and again on market prices, starting in the late nineteenth century with the work of the French mathematician Louis Bachelier. All this scientific research has failed to uncover any systematic cyclic components in price data. This failure argues strongly against the validity of various trading systems based on cycles. And, I want to stress that the techniques for finding cycles are much stronger than the techniques for finding trends.

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

In other words, the liquidity and efficiency of markets control the degree of correlation that is compatible with a near absence of arbitrage opportunity. THE EFFICIENT MARKET HYPOTHESIS AND THE RANDOM WALK Such observations have been made for a long time. A pillar of modern finance is the 1900 Ph.D. thesis dissertation of Louis Bachelier, in Paris, and his subsequent work, especially in 1906 and 1913 [25]. To account for the apparent erratic motion of stock market prices, he proposed that price trajectories are identical to random walks. The Random Walk The concept of a random walk is simple but rich for its many applications, not only in finance but also in physics and the description of natural phenomena.

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

These are discussed in Chapter 18. 2See M. G. Kendall, “The Analysis of Economic Time Series, Part I. Prices,” Journal of the Royal Statistical Society 96 (1953), pp. 11–25. Kendall’s idea was not wholly new. It had been proposed in an almost forgotten thesis written 53 years earlier by a French doctoral student, Louis Bachelier. Bachelier’s accompanying development of the mathematical theory of random processes anticipated by five years Einstein’s famous work on the random Brownian motion of colliding gas molecules. See L. Bachelier, Théorie de la Speculation (Paris: Gauthiers-Villars, 1900). Reprinted in English (A.

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Finance, finance.yahoo.com Now look at the quotes for options maturing in April 2012 and January 2013. Notice how the option price increases as option maturity is extended. For example, at an exercise price of $400, the December 2011 call option costs $24.30, the April 2012 option costs $44.05, and the January 2013 option costs $70.00. In Chapter 13 we met Louis Bachelier, who in 1900 first suggested that security prices follow a random walk. Bachelier also devised a very convenient shorthand to illustrate the effects of investing in different options. We use this shorthand to compare a call option and a put option on Apple stock. The position diagram in Figure 20.1(a) shows the possible consequences of investing in Apple April 2012 call options with an exercise price of $400 (boldfaced in Table 20.1).

The Snowball: Warren Buffett and the Business of Life
by Alice Schroeder
Published 1 Sep 2008

Inevitably, therefore, he became the target of a group of finance professors who were at that very moment attempting to prove that someone like Buffett was a mere accident who should not be paid attention, much less worshipped. These academics had started by positing the reasonable but not necessarily obvious truth that if a whole lot of people were trying to be better than average, they would become the average. Paul Samuelson, an MIT economist, revived and circulated the 1900 work of Louis Bachelier, who observed that the market is made up of speculators who cohere into a whole that operates according to a “random walk.”38 A professor from the University of Chicago, Eugene Fama, took Bachelier’s work and tested it empirically in the modern-day market, which he described as “efficient.” The scrabbling efforts of legions of investors to beat the market made those very efforts futile, he said.