Louis Bachelier

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pages: 338 words: 106,936

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

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Albert Einstein, algorithmic trading, Antoine Gombaud: Chevalier de Méré, Asian financial crisis, bank run, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, butterfly effect, capital asset pricing model, Carmen Reinhart, Claude Shannon: information theory, collateralized debt obligation, collective bargaining, dark matter, Edward Lorenz: Chaos theory, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial innovation, George Akerlof, Gerolamo Cardano, Henri Poincaré, invisible hand, Isaac Newton, iterative process, John Nash: game theory, Kenneth Rogoff, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, martingale, new economy, Paul Lévy, prediction markets, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk-adjusted returns, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Coase, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, statistical arbitrage, statistical model, stochastic process, The Chicago School, The Myth of the Rational Market, tulip mania, V2 rocket, volatility smile

An Introduction to the Standard Model of Particle Physics. Cambridge: Cambridge University Press. 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. Princeton, NJ: Princeton University Press. Davis, Monte. 1984. “Benoît Mandelbrot.”

Inside, its cavernous main hall was large enough to fit hundreds of brokers and staff members. 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. He had recently sold the family business, which had provided sufficient money for the moment, but it wouldn’t last forever.

Paul Samuelson asked himself, for the second time in as many minutes. 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.

 

pages: 206 words: 70,924

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

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Albert Einstein, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, collateralized debt obligation, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, David Ricardo: comparative advantage, discovery of penicillin, discrete time, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, floating exchange rates, full employment, Henri Poincaré, implied volatility, index fund, Isaac Newton, John von Neumann, Joseph Schumpeter, Long Term Capital Management, Louis Bachelier, margin call, market clearing, martingale, means of production, moral hazard, naked short selling, price stability, principal–agent problem, quantitative trading / quantitative finance, RAND corporation, random walk, risk tolerance, risk/return, Ronald Reagan, shareholder value, Sharpe ratio, short selling, stochastic process, The Chicago School, the scientific method, too big to fail, transaction costs, tulip mania, Works Progress Administration, yield curve

Isaac de Pinto (1771), An Essay on Circulation of Currency and Credit in Four Parts and a Letter on the Jealousy of Commerce, translated with annotations by S. 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. Perry Mehrling, Fischer Black and the Revolutionary Idea of Finance.

The genie is out of the bottle and financial worlds will never go back to a more primitive and simplistic state. 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. Others made brilliant observations or offered up techniques in finance with which they are forever associated.

Hence, investors remain concerned about risk aversion and the mean and variance of the securities that constitute their portfolios. 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. Einstein and Bachelier both noted that, beyond a common drift element, the movement of a particle or a stock from one period to the next is uncorrelated.

 

pages: 364 words: 101,286

The Misbehavior of Markets by Benoit Mandelbrot

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Albert Einstein, asset allocation, Augustin-Louis Cauchy, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black-Scholes formula, British Empire, Brownian motion, buy low sell high, capital asset pricing model, carbon-based life, discounted cash flows, diversification, double helix, Edward Lorenz: Chaos theory, Elliott wave, equity premium, Eugene Fama: efficient market hypothesis, Fellow of the Royal Society, full employment, Georg Cantor, Henri Poincaré, implied volatility, index fund, informal economy, invisible hand, John von Neumann, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market microstructure, new economy, paper trading, passive investing, Paul Lévy, Plutocrats, plutocrats, price mechanism, quantitative trading / quantitative finance, Ralph Nelson Elliott, RAND corporation, random walk, risk tolerance, Robert Shiller, Robert Shiller, short selling, statistical arbitrage, statistical model, Steve Ballmer, stochastic volatility, transfer pricing, value at risk, volatility smile

H.E.Hurst, D.Sc., CMG (1880–1978). Journal of Hydrology 46: 1-3. Commodity Futures Trading Commission. 2003. 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. Cowles, Alfred. 1933. Can stock market forecasters forecast?

And so was born what business schools now call “modern” finance. It emerged from the mathematics of chance and statistics. 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. In 1900, Bachelier passed over fundamental analysis and charting. Instead, he set in motion the next big wave in the field of probability theory, by expanding it to cover French government bonds.

And had Henri not died prematurely in his fifties, he would probably have received the Nobel Prize in physics (there is none in math). 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. Bachelier’s was on fluid mechanics; and it tested both his knowledge and oratory—an important consideration for a man who hoped to become a professor.

 

pages: 461 words: 128,421

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

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Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, bank run, Benoit Mandelbrot, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, card file, Cass Sunstein, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, discovery of the americas, diversification, diversified portfolio, Edward Glaeser, endowment effect, Eugene Fama: efficient market hypothesis, experimental economics, financial innovation, Financial Instability Hypothesis, floating exchange rates, George Akerlof, Henri Poincaré, Hyman Minsky, implied volatility, impulse control, index arbitrage, index card, index fund, invisible hand, Isaac Newton, John Nash: game theory, John von Neumann, joint-stock company, Joseph Schumpeter, libertarian paternalism, linear programming, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market design, New Journalism, Nikolai Kondratiev, Paul Lévy, pension reform, performance metric, Ponzi scheme, prediction markets, pushing on a string, quantitative trading / quantitative finance, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk/return, road to serfdom, Robert Shiller, Robert Shiller, rolodex, Ronald Reagan, shareholder value, Sharpe ratio, short selling, side project, Silicon Valley, South Sea Bubble, statistical model, The Chicago School, The Myth of the Rational Market, The Predators' Ball, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, Thomas L Friedman, Thorstein Veblen, Tobin tax, transaction costs, tulip mania, value at risk, Vanguard fund, volatility smile, Yogi Berra

These two books are the source of all Fisher biographical information in this book, except as otherwise noted. 3. 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.

But it is nonetheless a myth, an oversimplification that, when taken too literally, can lead to all sorts of trouble. 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.

Markowitz wanted the book to be a truly practical, if densely quantitative, guide to modern investing. 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. “Jimmie would say, ‘The role of statistics is not to discover truth.

 

pages: 425 words: 122,223

Capital Ideas: The Improbable Origins of Modern Wall Street by Peter L. Bernstein

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Albert Einstein, asset allocation, backtesting, Benoit Mandelbrot, Black-Scholes formula, Bonfire of the Vanities, Brownian motion, buy low sell high, capital asset pricing model, debt deflation, diversified portfolio, Eugene Fama: efficient market hypothesis, financial innovation, financial intermediation, fixed income, full employment, implied volatility, index arbitrage, index fund, interest rate swap, invisible hand, John von Neumann, Joseph Schumpeter, law of one price, linear programming, Louis Bachelier, mandelbrot fractal, martingale, means of production, new economy, New Journalism, profit maximization, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk/return, Robert Shiller, Robert Shiller, Ronald Reagan, stochastic process, the market place, The Predators' Ball, the scientific method, The Wealth of Nations by Adam Smith, Thorstein Veblen, transaction costs, transfer pricing, zero-coupon bond

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. Bachelier supported his novel theoretical analysis with a sophisticated study of the French capital markets at the turn of the century.

But in 1969 the stars were blissfully unaware of the inevitability of this outcome or of how the logic of Sharpe’s analysis would make it inevitable. 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.” We will now let them state their case. aMilton Friedman has described how computing fifty years ago combined what now seems primitive capability with what must have seemed a miracle then.

If the olive crop had turned out to be disappointing, Thales would have let his options lapse; he would have exercised them only if the crop had turned out to be great enough to overwhelm the olive-pressing capacity of the community. 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.

 

pages: 415 words: 125,089

Against the Gods: The Remarkable Story of Risk by Peter L. Bernstein

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Albert Einstein, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, Big bang: deregulation of the City of London, Bretton Woods, buttonwood tree, capital asset pricing model, cognitive dissonance, Daniel Kahneman / Amos Tversky, diversified portfolio, double entry bookkeeping, Edmond Halley, Edward Lloyd's coffeehouse, endowment effect, experimental economics, fear of failure, Fellow of the Royal Society, Fermat's Last Theorem, financial deregulation, financial innovation, full employment, index fund, invention of movable type, Isaac Newton, John Nash: game theory, John von Neumann, linear programming, loss aversion, Louis Bachelier, mental accounting, moral hazard, Nash equilibrium, probability theory / Blaise Pascal / Pierre de Fermat, random walk, Richard Thaler, Robert Shiller, Robert Shiller, spectrum auction, statistical model, The Bell Curve by Richard Herrnstein and Charles Murray, The Wealth of Nations by Adam Smith, trade route, transaction costs, tulip mania, Vanguard fund

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." The thesis was awarded "mention honorable," rather than the highest award of "mention tres honorable," which was essential for anyone hoping to find a decent job in the academic community.

But Knight insisted that the errors in such forecasts "must be radically distinguished from probability or chance.... [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. The volatility of stock and bond prices is evidence of the frequency with which the expected fails to happen and investors turn out to be wrong.

The Dutch tulip mania, a striking example of what happens when "oldfashioned human hunches" take over, had occurred only twenty years before Pascal and Fermat first laid out the principles of probability theory; the memory of it must still have been vivid when they began their historic deliberations. 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. He soon found his scientific academic studies too abstract for his taste and went to work at the Boston-based management consulting firm of Arthur D.

 

Investment: A History by Norton Reamer, Jesse Downing

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Albert Einstein, algorithmic trading, asset allocation, backtesting, banking crisis, Berlin Wall, Bernie Madoff, Brownian motion, buttonwood tree, California gold rush, capital asset pricing model, Carmen Reinhart, carried interest, colonial rule, credit crunch, Credit Default Swap, Daniel Kahneman / Amos Tversky, debt deflation, discounted cash flows, diversified portfolio, equity premium, estate planning, Eugene Fama: efficient market hypothesis, Fall of the Berlin Wall, family office, Fellow of the Royal Society, financial innovation, fixed income, Gordon Gekko, Henri Poincaré, high net worth, index fund, interest rate swap, invention of the telegraph, James Hargreaves, James Watt: steam engine, joint-stock company, Kenneth Rogoff, labor-force participation, land tenure, London Interbank Offered Rate, Long Term Capital Management, loss aversion, Louis Bachelier, margin call, means of production, Menlo Park, merger arbitrage, moral hazard, mortgage debt, Network effects, new economy, Nick Leeson, Own Your Own Home, pension reform, Ponzi scheme, price mechanism, principal–agent problem, profit maximization, quantitative easing, RAND corporation, random walk, Renaissance Technologies, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, Sand Hill Road, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, spinning jenny, statistical arbitrage, technology bubble, The Wealth of Nations by Adam Smith, time value of money, too big to fail, transaction costs, underbanked, Vanguard fund, working poor, yield curve

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. He became quite fluent in finance as a result of this experience, and soon Bachelier found himself back in academia working under the polymath Henri Poincaré.1 He defended the first portion of his thesis, entitled “Theory of Speculation,” in March 1900.

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. After earning his bachelor’s degree at twenty, he went to Harvard for his graduate degree and wrote Foundations of Economic Analysis in 1947, a piece of scholarship that won the David Wells dissertation prize and made Samuelson the very first economist to win the nowprestigious John Bates Clark Medal, earned by economists under the age of forty who have made significant contributions to the field.15 He would soon go to MIT and work on diverse theories of consumer optimization, trade, growth, and equilibrium.

.; 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. Irving Fisher, “Out of Keynes’s Shadow,” Economist, February 14, 2009, http://www.economist.com/node/13104022; David J.

 

pages: 295 words: 66,824

A Mathematician Plays the Stock Market by John Allen Paulos

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Benoit Mandelbrot, Black-Scholes formula, Brownian motion, business climate, butterfly effect, capital asset pricing model, correlation coefficient, correlation does not imply causation, Daniel Kahneman / Amos Tversky, diversified portfolio, Donald Trump, double entry bookkeeping, Elliott wave, endowment effect, Erdős number, Eugene Fama: efficient market hypothesis, four colour theorem, George Gilder, global village, greed is good, index fund, invisible hand, Isaac Newton, John Nash: game theory, Long Term Capital Management, loss aversion, Louis Bachelier, mandelbrot fractal, margin call, mental accounting, Nash equilibrium, Network effects, passive investing, Paul Erdős, Ponzi scheme, price anchoring, Ralph Nelson Elliott, random walk, Richard Thaler, Robert Shiller, Robert Shiller, short selling, six sigma, Stephen Hawking, transaction costs, ultimatum game, Vanguard fund, Yogi Berra

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.”

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. His work, which utilized the mathematical theory of Brownian motion, was way ahead of its time and hence was largely ignored.

 

pages: 374 words: 114,600

The Quants by Scott Patterson

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Albert Einstein, asset allocation, automated trading system, Benoit Mandelbrot, Bernie Madoff, Bernie Sanders, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Brownian motion, buttonwood tree, buy low sell high, capital asset pricing model, centralized clearinghouse, Claude Shannon: information theory, cloud computing, collapse of Lehman Brothers, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Donald Trump, Doomsday Clock, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, Gordon Gekko, greed is good, Haight Ashbury, index fund, invention of the telegraph, invisible hand, Isaac Newton, job automation, John Nash: game theory, law of one price, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, merger arbitrage, NetJets, new economy, offshore financial centre, Paul Lévy, Ponzi scheme, quantitative hedge fund, quantitative trading / quantitative finance, race to the bottom, random walk, Renaissance Technologies, risk-adjusted returns, Rod Stewart played at Stephen Schwarzman birthday party, Ronald Reagan, Sergey Aleynikov, short selling, South Sea Bubble, speech recognition, statistical arbitrage, The Chicago School, The Great Moderation, The Predators' Ball, too big to fail, transaction costs, value at risk, volatility smile, yield curve, éminence grise

After testing a range of other plant specimens, even the ground dust of rocks, and observing similar herky-jerky motion, he concluded that he was observing a phenomenon that was completely and mysteriously random. (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. The key to Bachelier’s analysis was his observation that bond prices move in a way identical to the phenomenon first discovered by Brown in 1827.

He looked into wheat prices, railroad stocks, and interest rates. 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.

Since all current information is built into the stock’s price and future information is essentially unknowable, it is impossible to predict whether a stock will rise or fall. 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.

 

pages: 545 words: 137,789

How Markets Fail: The Logic of Economic Calamities by John Cassidy

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Albert Einstein, Andrei Shleifer, anti-communist, asset allocation, asset-backed security, availability heuristic, bank run, banking crisis, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Black-Scholes formula, Bretton Woods, British Empire, capital asset pricing model, centralized clearinghouse, collateralized debt obligation, Columbine, conceptual framework, Corn Laws, correlation coefficient, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, Daniel Kahneman / Amos Tversky, debt deflation, diversification, Elliott wave, Eugene Fama: efficient market hypothesis, financial deregulation, financial innovation, Financial Instability Hypothesis, financial intermediation, full employment, George Akerlof, global supply chain, Haight Ashbury, hiring and firing, Hyman Minsky, income per capita, incomplete markets, index fund, invisible hand, John Nash: game theory, John von Neumann, Joseph Schumpeter, laissez-faire capitalism, liquidity trap, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, market bubble, market clearing, mental accounting, Mikhail Gorbachev, Mont Pelerin Society, moral hazard, mortgage debt, Naomi Klein, Network effects, Nick Leeson, Northern Rock, paradox of thrift, Ponzi scheme, price discrimination, price stability, principal–agent problem, profit maximization, quantitative trading / quantitative finance, race to the bottom, Ralph Nader, RAND corporation, random walk, Renaissance Technologies, rent control, Richard Thaler, risk tolerance, risk-adjusted returns, road to serfdom, Robert Shiller, Robert Shiller, Ronald Coase, Ronald Reagan, shareholder value, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, statistical model, technology bubble, The Chicago School, The Great Moderation, The Market for Lemons, The Wealth of Nations by Adam Smith, too big to fail, transaction costs, unorthodox policies, value at risk, Vanguard fund

But the financial industry is extremely competitive, and there are no patents on smart ideas. 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. If there are more pessimists, their sales will bring the price down.

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.

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.)

 

pages: 389 words: 109,207

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

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Albert Einstein, anti-communist, asset allocation, Benoit Mandelbrot, Black-Scholes formula, Brownian motion, buy low sell high, capital asset pricing model, Claude Shannon: information theory, computer age, correlation coefficient, diversified portfolio, en.wikipedia.org, Eugene Fama: efficient market hypothesis, high net worth, index fund, interest rate swap, Isaac Newton, Johann Wolfgang von Goethe, John von Neumann, Long Term Capital Management, Louis Bachelier, margin call, market bubble, market fundamentalism, Marshall McLuhan, New Journalism, Norbert Wiener, offshore financial centre, publish or perish, quantitative trading / quantitative finance, random walk, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Shiller, Ronald Reagan, short selling, speech recognition, statistical arbitrage, The Predators' Ball, The Wealth of Nations by Adam Smith, transaction costs, traveling salesman, value at risk, zero-coupon bond

Anyone who substantially disagreed with Savage was, in his freely offered opinion, stupid. 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.

 

pages: 695 words: 194,693

Money Changes Everything: How Finance Made Civilization Possible by William N. Goetzmann

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Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, banking crisis, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, Cass Sunstein, collective bargaining, colonial exploitation, compound rate of return, conceptual framework, corporate governance, Credit Default Swap, David Ricardo: comparative advantage, debt deflation, delayed gratification, Detroit bankruptcy, disintermediation, diversified portfolio, double entry bookkeeping, Edmond Halley, en.wikipedia.org, equity premium, financial independence, financial innovation, financial intermediation, fixed income, frictionless, frictionless market, full employment, high net worth, income inequality, index fund, invention of the steam engine, invention of writing, invisible hand, James Watt: steam engine, joint-stock company, joint-stock limited liability company, laissez-faire capitalism, Louis Bachelier, mandelbrot fractal, market bubble, means of production, money: store of value / unit of account / medium of exchange, moral hazard, new economy, passive investing, Paul Lévy, Ponzi scheme, price stability, principal–agent problem, profit maximization, profit motive, quantitative trading / quantitative finance, random walk, Richard Thaler, Robert Shiller, Robert Shiller, shareholder value, short selling, South Sea Bubble, sovereign wealth fund, spice trade, stochastic process, the scientific method, The Wealth of Nations by Adam Smith, Thomas Malthus, time value of money, too big to fail, trade liberalization, trade route, transatlantic slave trade, transatlantic slave trade, tulip mania, wage slave

In this chapter, we jump ahead and follow this story into modern times. 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.

For the same reason, options that are granted for a long period of time (e.g., 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). Bachelier presented his book, Théorie de la Spéculation, as his doctoral thesis in mathematics at the Sorbonne in 1900.

Mandelbrot was a student of Paul Lévy’s—the son of the man who gave Bachelier bad marks at his examination at the École Polytechnique in 1900. 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. Other stochastic processes have such things as discontinuous jumps and unusually large shocks (which might, for example, explain the crash of 1987, when the US stock market lost 22.6% of its value in a single day).

 

pages: 263 words: 75,455

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

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Albert Einstein, Andrei Shleifer, asset allocation, Atul Gawande, backtesting, Black Swan, capital asset pricing model, Checklist Manifesto, cognitive bias, compound rate of return, corporate governance, correlation coefficient, credit crunch, Daniel Kahneman / Amos Tversky, discounted cash flows, Eugene Fama: efficient market hypothesis, forensic accounting, hindsight bias, Louis Bachelier, p-value, passive investing, performance metric, quantitative hedge fund, random walk, Richard Thaler, risk-adjusted returns, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, statistical model, systematic trading, The Myth of the Rational Market, time value of money, transaction costs

Thorp started working on the key element of what would become his quantitative investment strategy when he moved to UCI in 1964.7 There he met Sheen Kassouf, another professor at UCI, who had been working on the same problem: how to value a warrant, an unusual security that converted into stock on a certain event. 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. The implications of the random walk theory are profound, and they weren't lost on Thorp.

 

pages: 741 words: 179,454

Extreme Money: Masters of the Universe and the Cult of Risk by Satyajit Das

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affirmative action, Albert Einstein, algorithmic trading, Andy Kessler, Asian financial crisis, asset allocation, asset-backed security, bank run, banking crisis, banks create money, Basel III, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Black Swan, Bonfire of the Vanities, bonus culture, Bretton Woods, BRICs, British Empire, capital asset pricing model, Carmen Reinhart, carried interest, Celtic Tiger, clean water, cognitive dissonance, collapse of Lehman Brothers, collateralized debt obligation, corporate governance, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, debt deflation, Deng Xiaoping, deskilling, discrete time, diversification, diversified portfolio, Doomsday Clock, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, eurozone crisis, Fall of the Berlin Wall, financial independence, financial innovation, fixed income, full employment, global reserve currency, Goldman Sachs: Vampire Squid, Gordon Gekko, greed is good, happiness index / gross national happiness, haute cuisine, high net worth, Hyman Minsky, index fund, interest rate swap, invention of the wheel, invisible hand, Isaac Newton, job automation, Johann Wolfgang von Goethe, joint-stock company, Joseph Schumpeter, Kenneth Rogoff, Kevin Kelly, labour market flexibility, laissez-faire capitalism, load shedding, locking in a profit, Long Term Capital Management, Louis Bachelier, margin call, market bubble, market fundamentalism, Marshall McLuhan, Martin Wolf, merger arbitrage, Mikhail Gorbachev, Milgram experiment, Mont Pelerin Society, moral hazard, mortgage debt, mortgage tax deduction, mutually assured destruction, Naomi Klein, Network effects, new economy, Nick Leeson, Nixon shock, Northern Rock, nuclear winter, oil shock, Own Your Own Home, pets.com, Plutocrats, plutocrats, Ponzi scheme, price anchoring, price stability, profit maximization, quantitative easing, quantitative trading / quantitative finance, Ralph Nader, RAND corporation, random walk, Ray Kurzweil, regulatory arbitrage, rent control, rent-seeking, reserve currency, Richard Feynman, Richard Feynman, Richard Thaler, risk-adjusted returns, risk/return, road to serfdom, Robert Shiller, Robert Shiller, Rod Stewart played at Stephen Schwarzman birthday party, rolodex, Ronald Reagan, Ronald Reagan: Tear down this wall, savings glut, shareholder value, Sharpe ratio, short selling, Silicon Valley, six sigma, Slavoj Žižek, South Sea Bubble, special economic zone, statistical model, Stephen Hawking, Steve Jobs, The Chicago School, The Great Moderation, the market place, the medium is the message, The Myth of the Rational Market, The Nature of the Firm, The Predators' Ball, The Wealth of Nations by Adam Smith, Thorstein Veblen, too big to fail, trickle-down economics, Turing test, Upton Sinclair, value at risk, Yogi Berra, zero-coupon bond

On average, investors buying all the stocks in the market would earn higher returns with lower risk. 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. Aware of the importance of his insights, Bachelier claimed: “the present theory resolves the majority of problems in the study of speculation.”5 His examiners disagreed.

Conversely, sellers of options risk large losses (the potentially large payout they must make if the price of the asset moves by a large amount) in return for a small gain (the premium received). 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.

 

pages: 819 words: 181,185

Derivatives Markets by David Goldenberg

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Black-Scholes formula, Brownian motion, capital asset pricing model, commodity trading advisor, compound rate of return, conceptual framework, Credit Default Swap, discounted cash flows, discrete time, diversification, diversified portfolio, en.wikipedia.org, financial innovation, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, law of one price, locking in a profit, London Interbank Offered Rate, Louis Bachelier, margin call, market microstructure, martingale, Norbert Wiener, price mechanism, random walk, reserve currency, risk/return, riskless arbitrage, Sharpe ratio, short selling, stochastic process, stochastic volatility, time value of money, transaction costs, volatility smile, Wiener process, Y2K, yield curve, zero-coupon bond

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; PREFACE xxxv 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. 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.

 

pages: 335 words: 94,657

The Bogleheads' Guide to Investing by Taylor Larimore, Michael Leboeuf, Mel Lindauer

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asset allocation, buy low sell high, corporate governance, correlation coefficient, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, Donald Trump, endowment effect, estate planning, financial independence, financial innovation, high net worth, index fund, late fees, Long Term Capital Management, loss aversion, Louis Bachelier, margin call, market bubble, mental accounting, passive investing, random walk, risk tolerance, risk/return, Sharpe ratio, statistical model, transaction costs, Vanguard fund, yield curve

The academic community has spent a great deal of time and research trying to answer these two questions. 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. Mr. Cowles was an investor who carefully followed the stock market forecasts of professional "experts" and stock market gurus prior to the worst stock market crash the United States has ever experienced.

 

pages: 354 words: 26,550

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

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algorithmic trading, asset allocation, asset-backed security, automated trading system, backtesting, Black Swan, Brownian motion, business process, capital asset pricing model, centralized clearinghouse, collapse of Lehman Brothers, collateralized debt obligation, collective bargaining, diversification, equity premium, fault tolerance, financial intermediation, fixed income, high net worth, implied volatility, index arbitrage, interest rate swap, inventory management, law of one price, Long Term Capital Management, Louis Bachelier, margin call, market friction, market microstructure, martingale, New Journalism, p-value, paper trading, performance metric, profit motive, purchasing power parity, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk tolerance, risk-adjusted returns, risk/return, Sharpe ratio, short selling, Small Order Execution System, statistical arbitrage, statistical model, stochastic process, stochastic volatility, systematic trading, trade route, transaction costs, value at risk, yield curve

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 probability of three successive price changes of the same sign is 1/(23 ) = 0.125. Four successive price changes of the same sign are even less likely, having the probability of 1/(24 ) = 0.0625 or 6.25 percent.

 

pages: 345 words: 86,394

Frequently Asked Questions in Quantitative Finance by Paul Wilmott

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Albert Einstein, asset allocation, Black-Scholes formula, Brownian motion, butterfly effect, capital asset pricing model, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discrete time, diversified portfolio, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, iterative process, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, market bubble, martingale, Norbert Wiener, quantitative trading / quantitative finance, random walk, regulatory arbitrage, risk/return, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, stochastic volatility, transaction costs, urban planning, value at risk, volatility arbitrage, volatility smile, Wiener process, yield curve, zero-coupon bond

Where possible I give dates, name names and refer to the original sources.1 1827 Brown The Scottish botanist, Robert Brown, gave his name to the random motion of small particles in a liquid. 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. It is told that his thesis was not a great success and, naturally, Bachelier’s work was not appreciated in his lifetime.

 

pages: 586 words: 159,901

Wall Street: How It Works And for Whom by Doug Henwood

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accounting loophole / creative accounting, affirmative action, Andrei Shleifer, asset allocation, asset-backed security, bank run, banking crisis, barriers to entry, borderless world, Bretton Woods, British Empire, capital asset pricing model, capital controls, central bank independence, corporate governance, correlation coefficient, correlation does not imply causation, credit crunch, currency manipulation / currency intervention, David Ricardo: comparative advantage, debt deflation, declining real wages, deindustrialization, dematerialisation, diversification, diversified portfolio, Donald Trump, equity premium, Eugene Fama: efficient market hypothesis, experimental subject, facts on the ground, financial deregulation, financial innovation, Financial Instability Hypothesis, floating exchange rates, full employment, George Akerlof, George Gilder, hiring and firing, Hyman Minsky, implied volatility, index arbitrage, index fund, interest rate swap, Internet Archive, invisible hand, Isaac Newton, joint-stock company, Joseph Schumpeter, kremlinology, labor-force participation, late capitalism, law of one price, liquidationism / Banker’s doctrine / the Treasury view, London Interbank Offered Rate, Louis Bachelier, market bubble, Mexican peso crisis / tequila crisis, microcredit, minimum wage unemployment, moral hazard, mortgage debt, mortgage tax deduction, oil shock, payday loans, pension reform, Plutocrats, plutocrats, price mechanism, price stability, prisoner's dilemma, profit maximization, Ralph Nader, random walk, reserve currency, Richard Thaler, risk tolerance, Robert Gordon, Robert Shiller, Robert Shiller, shareholder value, short selling, Slavoj Žižek, South Sea Bubble, The Market for Lemons, The Nature of the Firm, The Predators' Ball, The Wealth of Nations by Adam Smith, transaction costs, transcontinental railway, women in the workforce, yield curve, zero-coupon bond

No one can see an expected return; one can only extrapolate from past experience. 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.

 

pages: 431 words: 132,416

No One Would Listen: A True Financial Thriller by Harry Markopolos

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backtesting, barriers to entry, Bernie Madoff, call centre, centralized clearinghouse, correlation coefficient, diversified portfolio, Emanuel Derman, Eugene Fama: efficient market hypothesis, family office, fixed income, forensic accounting, high net worth, index card, Long Term Capital Management, Louis Bachelier, offshore financial centre, Ponzi scheme, price mechanism, quantitative trading / quantitative finance, regulatory arbitrage, Renaissance Technologies, risk-adjusted returns, risk/return, rolodex, Sharpe ratio, statistical arbitrage, too big to fail, transaction costs

Math came naturally to Neil. 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. It basically means that you can’t beat the market, that there is no free lunch.

 

pages: 512 words: 162,977

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

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backtesting, Benoit Mandelbrot, Berlin Wall, Black-Scholes formula, butterfly effect, commodity trading advisor, Elliott wave, fixed income, full employment, implied volatility, interest rate swap, Louis Bachelier, margin call, market clearing, market fundamentalism, paper trading, pattern recognition, placebo effect, prediction markets, Ralph Nelson Elliott, random walk, risk tolerance, risk/return, Saturday Night Live, Sharpe ratio, the map is not the territory, transaction costs, War on Poverty

What about cyclical analysis, which is another technique traders use to try to pick tops and bottoms? 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. Finding cycles is a classic scientific problem. What about all the various studies that purport to find cycles in price data?

 

pages: 442 words: 39,064

Why Stock Markets Crash: Critical Events in Complex Financial Systems by Didier Sornette

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Asian financial crisis, asset allocation, Berlin Wall, Bretton Woods, Brownian motion, capital asset pricing model, capital controls, continuous double auction, currency peg, Deng Xiaoping, discrete time, diversified portfolio, Elliott wave, Erdős number, experimental economics, financial innovation, floating exchange rates, frictionless, frictionless market, full employment, global village, implied volatility, index fund, invisible hand, John von Neumann, joint-stock company, law of one price, Louis Bachelier, mandelbrot fractal, margin call, market bubble, market clearing, market design, market fundamentalism, mental accounting, moral hazard, Network effects, new economy, oil shock, open economy, pattern recognition, Paul Erdős, quantitative trading / quantitative finance, random walk, risk/return, Ronald Reagan, Schrödinger's Cat, short selling, Silicon Valley, South Sea Bubble, statistical model, stochastic process, Tacoma Narrows Bridge, technological singularity, The Coming Technological Singularity, The Wealth of Nations by Adam Smith, Tobin tax, total factor productivity, transaction costs, tulip mania, VA Linux, Y2K, yield curve

We can conclude that the residual correlations are those little enough not to be profitable by strategies such as those described above due to “imperfect” market conditions. 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. It is arguably one of the most important founding concepts in modern physics as well as in finance, as it underlies the theories of elementary particles, which are the building blocks of our universe, as well as those describing the complex organization of matter around us.

 

pages: 288 words: 16,556

Finance and the Good Society by Robert J. Shiller

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bank run, banking crisis, barriers to entry, Bernie Madoff, capital asset pricing model, capital controls, Carmen Reinhart, Cass Sunstein, cognitive dissonance, collateralized debt obligation, collective bargaining, computer age, corporate governance, Daniel Kahneman / Amos Tversky, Deng Xiaoping, diversification, diversified portfolio, Donald Trump, Edward Glaeser, eurozone crisis, experimental economics, financial innovation, full employment, fundamental attribution error, George Akerlof, income inequality, invisible hand, joint-stock company, Joseph Schumpeter, Kenneth Rogoff, land reform, loss aversion, Louis Bachelier, Mahatma Gandhi, Mark Zuckerberg, market bubble, market design, means of production, microcredit, moral hazard, mortgage debt, Occupy movement, passive investing, Ponzi scheme, prediction markets, profit maximization, quantitative easing, random walk, regulatory arbitrage, Richard Thaler, road to serfdom, Robert Shiller, Robert Shiller, Ronald Reagan, self-driving car, shareholder value, Sharpe ratio, short selling, Simon Kuznets, Skype, Steven Pinker, telemarketer, The Market for Lemons, The Wealth of Nations by Adam Smith, Thorstein Veblen, too big to fail, Vanguard fund, young professional, Zipcar

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. Security analysis, narrowly defined, consists chiefly of naïve extrapolations from ratios based on accounting data.”11 Why, if the pricing of options was of such central importance to these markets, did no one care about the mathematical theory behind it?

 

pages: 1,336 words: 415,037

The Snowball: Warren Buffett and the Business of Life by Alice Schroeder

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affirmative action, Albert Einstein, anti-communist, Ayatollah Khomeini, barriers to entry, Bonfire of the Vanities, Brownian motion, capital asset pricing model, card file, centralized clearinghouse, collateralized debt obligation, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, desegregation, Donald Trump, Eugene Fama: efficient market hypothesis, global village, Golden Gate Park, Haight Ashbury, haute cuisine, Honoré de Balzac, If something cannot go on forever, it will stop, In Cold Blood by Truman Capote, index fund, indoor plumbing, interest rate swap, invisible hand, Isaac Newton, Jeff Bezos, joint-stock company, joint-stock limited liability company, Long Term Capital Management, Louis Bachelier, margin call, market bubble, Marshall McLuhan, medical malpractice, merger arbitrage, Mikhail Gorbachev, moral hazard, NetJets, new economy, New Journalism, North Sea oil, paper trading, passive investing, pets.com, Plutocrats, plutocrats, Ponzi scheme, Ralph Nader, random walk, Ronald Reagan, Scientific racism, shareholder value, short selling, side project, Silicon Valley, Steve Ballmer, Steve Jobs, supply-chain management, telemarketer, The Predators' Ball, The Wealth of Nations by Adam Smith, Thomas Malthus, too big to fail, transcontinental railway, Upton Sinclair, War on Poverty, Works Progress Administration, Y2K, zero-coupon bond

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.