The Physics of Wall Street: a brief History of Predicting the Unpredictable

Epilogue: Send Physics, Math, and Money! 
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only under the very unusual circumstances that prevailed at the Paris 
Bourse, where there was very little variation in prices. correcting this 
problem led to osborne’s hypothesis that returns, not prices, are nor-
mally distributed. Mandelbrot’s realization that normal and log-nor-
mal distributions cannot capture the full wildness of financial markets, 
then, didn’t represent some crisis at the foundations of financial theory, 
despite his and others’ claims to the contrary — rather, it was the first 
recognition of how osborne’s version of the random walk hypothesis 
would run aground. that most economists (and physicists interested 
in such things) now believe that Mandelbrot, too, wasn’t quite right is 
simply another iteration still.
thorp and Black showed investors how to use the tools developed 
by Bachelier, osborne, and Mandelbrot in day-to-day trading — by 
drawing on still more sophisticated ideas from physics. In some sense, 
these two scientists are the most important in this book, both because 
of their pivotal role in putting cutting-edge theory into practice and 
because they reveal what is involved in using one set of models to build 
new ones. the options pricing models that thorp and Black and Scho-
les developed were based on osborne’s version of the random walk 
hypothesis, not on Mandelbrot’s. this meant that these options pricing 
models should have been recognized, from the very beginning, as tools 
with a limited range of applicability. from a physicist’s point of view, 
or an engineer’s, starting with osborne’s model made perfect sense. 
It was far better understood than Mandelbrot’s, and so, by adopting a 
simpler approximation of how market returns really work, thorp and 
Black and Scholes were able to turn an extremely difficult problem into 
a tractable one.
But there was little doubt, even from the beginning, about how these 
early options pricing models would fail, given Mandelbrot’s work: they 
would misprice extreme events. (Black seemed to recognize the short-
comings of his model as well as anyone — in a 1988 article called “the 
Holes in Black-Scholes,” Black explicitly listed the unrealistic assump-
tions that went into deriving his formula and described how each of 
these could lead to errors.) careful investors, like Michael Greenbaum 
and clay Struve at o’connor and Associates, were able to use their un-

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derstanding of when the Black-Scholes model would fail to profit and, 
even more importantly, to protect themselves during the 1987 market 
crash.
Yet still, the process continues. Both the scientists behind the Pre-
diction company and didier Sornette show how new developments in 
physics can be used to fill in gaps in the random walk, efficient markets 
thinking behind the Black-Scholes model. the Prediction company 
did this by using black box models to identify local, short-term inef-
ficiencies and capitalize on them as quickly as possible — essentially 
using physics to be the most sophisticated investors in the market. Sor-
nette, meanwhile, has taken Mandelbrot’s observation that in wildly 
random markets, extreme events like market crashes have dominating 
effects, and asked whether it is possible to predict these catastrophes. 
the tools he has adapted from seismology go a long way toward show-
ing that dragon kings can be seen from afar.
It is tempting when writing a work of history to try to force the 
pieces into an overarching narrative. Here, I think, there is a narrative
— but it would be a mistake to push it too far. the Prediction com-
pany and Sornette represent two natural and important ways to move 
forward from the still-dominant Black-Scholes-style thinking. But de-
spite the successes of such models, they are hardly the end of the story. 
Instead, they are just two examples of particularly fruitful ideas about 
financial markets — ideas that themselves should be subjected to care-
ful testing and analysis. It’s not easy to say what the next major advance 
will look like: it might be a new way of understanding and anticipating 
extreme events; it might equally well be a novel test for when the pre-
dictions of models are “robust” against inherent market uncertainty; 
or perhaps it will be a breakthrough in our ability to identify the un-
derlying chaotic patterns lurking in market data. What we do know 
for sure is that there will be a next major advance, and that when we 
figure out where Sornette’s models fail, or where the kind of black box 
modeling the Prediction company developed runs aground, we will 
understand markets more clearly than we do today.
If physicists have been successful at improving our understanding of 
finance, it is because they have approached problems in a novel way, 

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