Pricing the Future: Finance, Physics, and the 300-year Journey to the Black-Scholes Equation by George G Szpiro (PDF)

Description

Options have been traded for hundreds of years, but investment decisions were based on gut feelings until the Nobel Prize — winning discovery of the Black-Scholes options pricing model in 1973 ushered in the era of the “quants.” Wall Street would never be the same. In Pricing the Future, financial economist George G. Szpiro tells the fascinating stories of the pioneers of mathematical finance who conducted the search for the elusive options pricing formula. From the broker’s assistant who published the first mathematical explanation of financial markets to Albert Einstein and other scientists who looked for a way to explain the movement of atoms and molecules, Pricing the Future retraces the historical and intellectual developments that ultimately led to the widespread use of mathematical models to drive investment strategies on Wall Street.

User’s Reviews

Editorial Reviews: Review Robert P. Inman, Richard K. Mellon Professor of Finance and Economics, The Wharton School of the University of Pennsylvania “One of the major intellectual achievements of the 20th century was the theory of option pricing. This is its story, and it’s absolutely fascinating. Options have been around since the buying and selling of tulips and the very first efforts of investors to control their downside risk. But the economic value of such protections was not finally understood until the Nobel Prize winning research of Fischer Black, Myron Scholes, and Robert Merton in the 1970’s. It could not have happened without 350 years of serious thinking by botanists, physicists, chemists, and mathematicians. Finally, by 1960 all the pieces were in place, and Black, Scholes, and Merton solved the puzzle. The book should be required reading of all first year PhD students in finance, and economics, simply to see what is needed for path-breaking research. For the rest of us with an interest in the origins of important ideas, this is a great read.”Sylvia Nasar, author of Grand Pursuit: The Story of Economic Genius and A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash “George Szpiro’s crisp prose, clever vignettes and refreshingly concise explanations make finance history go down like gelato on a summer’s day.”Andrew Lo, Harris & Harris Group Professor of Finance and Director of the Laboratory for Financial Engineering, Massachusetts Institute of Technology “This is a fascinating historical account of the origins of modern finance and the Black-Scholes/Merton option-pricing formula, by a consummate expositor who also happens to be a first-rate financial economist. Those who think finance is a science will be surprised by the serendipitous events that delayed the discovery of the option-pricing formula by 73 years; those who think finance is an art will be shocked by the deep connections between option-pricing, physics, and probability theory. No matter what your background, you’ll want to read this book slowly—like a rare vintage port, it’s meant to be sipped slowly and every drop savored.”Franklin Allen, Nippon Professor of Finance and Economics, The Wharton School of the University of Pennsylvania “George Szpiro has written a wonderful book. Often finance is viewed as one of the driest of fields. Szpiro makes the history of the option pricing formula fascinating at many levels. He starts with the history of options, bringing in the Tulipmania, the Dutch East India Company, the Amsterdam Bourse, Joseph de La Vega, John Law’s colorful life and on and on. The mathematical tools needed for deriving the formula and the people who developed them are also heroes of the tale. The climax is reached with Fisher Black, Myron Scholes and Robert Merton’s time together at MIT and the derivation of the formula that revolutionized finance. It is a book that is very difficult to put down. This will be true for beginning students of finance as well as the highest earning traders. I thoroughly recommend it!” About the Author George G. Szpiro is a mathematician, financial economist, and journalist. He is the Israel correspondent of the Swiss daily Neue Zürcher Zeitung and has published in Science, Nature, and the Jerusalem Report. He is the author of Kepler’s Conjecture, The Secret Life of Numbers, Poincaré’s Prize, and Numbers Rule. He lives in Switzerland.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐300 years of precursors to the Black-Scholes option pricing formula are traced via accounts of the lives and works of a dozen or so major characters and another dozen minor characters. This is nowadays a common format for popular science writing (used e.g. for Bayes rule in

⭐), and here it is executed well — the writing style and content is engaging and appropriately non-technical. The choice of topic is intrinsically cross-disciplinary (mathematics theory, economics theory, practical market speculation) and by incorporating also the author’s own physics background, a book emerges that is pleasingly different from other popular science accounts of these topics and characters (typically written from the viewpoint of one particular academic discipline, or none in the case of journalistic authors).Here is a precis of the relevant standard history, from a mathematician’s viewpoint. For various reasons [mathematicians couldn’t make it fit with the rest of math, and physicists perceived the world in terms of deterministic laws], in 1900 mathematical probability had not yet become a coherent discipline. In particular there is a fundamental mathematical “square root law” providing a rough description of the cumulative effect of purely random fluctuations. Before 1900 this had been observed and explained in various contexts but not appreciated as a widely-applicable fact. Over the first third of the 20th century this (quite simple) law, the associated “Normal approximation” and the more technically sophisticated notion of the Wiener process as the fundamental model of “purely random” continuous fluctuations, all became well understood. The Wiener process was subsequently recognized as a mathematically fundamental and interesting object, and studied deeply by mathematicians and in several applied disciplines. During this time period and previous centuries, the relevance of such probability models to finance (stock prices and options thereon) was repeatedly realized by scattered individuals, but their theories never were widely used by speculators nor joined any academic mainstream. Until in 1973 Black and Scholes published their explicit formula for fair option prices (based on the Wiener process model for price fluctuations), fortuitously at the time when the Chicago Board Options Exchange opened and when electronic calculators became available to use the formula quickly, and mathematical finance blasted off.The book does a fine job of adding color and Physics counterparts to this history, and of giving verbal explanations of some of the mathematics, though by emphasizing individual stories it may not leave the reader with a very accurate big picture.

⭐Pricing the Future has its merits. It brings to light much financial history and reminds us that many things we now take for granted were obscure in 1900 or even 1970. The problem is the author does exactly what he pans in 19th century economic theory: he avoids the math. You can’t really understand this stuff without the math. If he had assumed readers already had some exposure to differential equations or at least calculus, he could have explained the math, usuing equations, as it developed in history. Then, by the time we got to the actual options value equation, we would have been ready for it. Or he could have taken some of the words he used to describe trivial color in the lives of economists and instead taught the essentials needed for this particular subject. He does not even explain why the number e appears in the equation, much less how to solve the type of differential equation involved, or why the heat diffusion equation, mentioned in the book and presented with no explanation in the appendix, works mathematically.Still, I would recommend the book to amateur investors who are bombarded by people who want them to play the options market. The key take away is that options are almost always appropriately priced, so gambling on them is wasting your money in brokerage fees. There are many legitimate uses for stock and commodities options, but even the most savy, best funded traders are playing with fire when they use options as investments rather than hedges.

⭐Too many of us have learned options strategies and theory from texts that present it all in packages, now backed up by Excel spreadsheets with all the formulas embedded in them, that give no reference to where it all came from. Or, alternatively, we have been forced to study the Black-Scholes equation and the Merton replicating portfolio as if the underlying math also sprang full-blown from the creative minds of those three scholars. And too many of us who teach options choose one of those routes or the other, depending on our own tastes, without setting them in a broarder context than as a follow up to lectures on efficient frontiers and CAPM. George S. Szpiro has given us a readable account of how the theory of option pricing evolved to the point that Scholes and Merton (and Black, if he had lived longer) merited a Nobel Prize for their contibution to economics. Practically every element of the theory was built on great breakthroughs by individual mathematicians, physicists, biologists, and even other economists over centuries, including scholars who themselves earned Nobel Prizes in their fields. But the process was hardly linear, and many of the models soon proved to have serious flaws, which later scholars corrected. By giving us bigraphical highlights of dozens of scholars, Szpiro provides us with a vivid case study of how science moves forward. And in the end, he notes that even the Black-Scholes-Merton model didn’t account for fat tail risk, that there is more work to be done. Well, any one who is seeking to come up with a better model should read this book. For one, you may find that your approach has already been tried and found wanting. Or, better, you might find the kernel of an idea that all those great minds have not fully fleshed out.

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