James Owen Weatherall's The Physics of Wall Street: A Brief History of Predicting the Unpredictable (Houghton Mifflin Harcourt, 2013) is an engrossing book. Even though I was familiar with many of the stories the author recounts, at no point was I tempted to skip a page. Coming from me, that's high praise indeed.
In the first chapter Weatherall takes the reader on a journey from sixteenth- and seventeenth-century attempts at a systematic theory of probability (Cardano, de Méré, Pascal, and Fermat) through Bachelier's 1900 dissertation, A Theory of Speculation. Bachelier is credited with having come up with the random walk model/efficient market hypothesis. Like many quants, he was ahead of his time. "In a just world, Bachelier would be to finance what Newton is to physics. But Bachelier's life was a shambles, in large part because academia couldn't countenance so original a thinker." (p. 27)
It wasn't until Maury Osborne's 1959 paper entitled "Brownian Motion in the Stock Market," similar in both topic (predicting stock prices) and solution to Bachelier's thesis, that people began to understand that physics could make a substantial contribution to finance. By then, as Osborne said, "Physicists essentially could do no wrong." (p. 28) Scientists were in demand in industry, research facilities, and government. Pre-The Graduate, think nylon and the Manhattan Project.
Osborne found that stock prices don't follow a normal distribution as Bachelier had suggested; rather, the rate of return on a stock (the "average percentage by which the price changes each instant") is normally distributed. "Since price and rate of return are related by a logarithm, Osborne's model implies that prices should be log-normally distributed."
The plots "show what these two distributions look like at some time in the future, for a stock whose price is $10 now. Plot (a) is an example of a normal distribution over rates of return, and plot (b) is the associated log-normal distribution for the prices, given those probabilities for rates of return." (p. 37)
Osborne later modified his Brownian motion model, which had assumed that prices are equally likely to move up or down. "Osborne showed that if a stock went up a little bit, its next motion was much more likely to be a move back down than another move up. Likewise, if a stock went down, it was much more likely to go up in value in its next change. That is, from moment to moment the market is much more likely to reverse itself than to continue on a trend. But there was another side to this coin. If a stock moved in the same direction twice, it was much more likely to continue in that direction than if it had moved in a given direction only once. Osborne argued that the infrastructure of the trading floor was responsible for this kind of non-randomness, and Osborne went on to suggest a model for how prices change that took this kind of behavior into account." (p. 46)
Osborne's methodology (though not his model), Weatherall maintains, is worth emulating. First, you study the data and "make simplifying assumptions to derive simple models." Then "you check carefully to find places where your simplifying assumptions break down and try to figure out, again by focusing on the data, how these failures of your assumptions produce problems for the model's predictions. … For instance, Osborne showed that price changes aren't independent. This is especially true during market crashes, when a series of downward ticks makes it very likely that prices will continue to fall. When this kind of herding effect is present, even Osborne's extended Brownian motion model is going to be an unreliable guide." (p. 47)
These few paragraphs are just a taste of what's in The Physics of Wall Street. We meet Benoît Mandelbrot, Ed Thorp, Fischer Black, James Doyne Farmer and Norman Packard of the Prediction Company, Didier Sornette, and finally Pia Malaney and Eric Weinstein.
Weatherall defends quants and argues, with Weinstein and Malaney, that there are ways to make economic and financial models better by using "more powerful mathematics to avoid having to make strong assumptions about people and markets." (p. 211) Whether you agree with him or not, he makes a thoroughly enjoyable and beautifully teased out case.