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

Physics Hits the Street 
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was failing to properly account for extreme events. And so Greenbaum 
built a team of risk managers and mathematicians to figure out how 
to improve on the Black-Scholes model. one of o’connor’s first em-
ployees was an eighteen-year-old whiz kid named clay Struve, who 
had worked for Greenbaum at first options in a summer job, and 
who worked for fischer Black as an undergraduate at MIt during the 
school year. during 1977 and 1978, Greenbaum, Struve, and a small 
team of proto-quants worked out a modified Black-Scholes model that 
took into account things like sudden jumps in prices, which can lead 
to fat tails.
o’connor was famously successful, first in options and then in 
other derivatives — in part because the modified Black-Scholes model 
tended to outperform the standard one. remarkably, according to 
Struve, o’connor was aware of the volatility smile from very early on. 
that is, even before the crash of 1987, there were small, potentially ex-
ploitable discrepancies between the Black-Scholes model and market 
prices. Later, when the 1987 crash did occur, o’connor survived.
there’s another, deeper concern about the market revolution initi-
ated by Black and his followers that many people worried about in 1987 
and that has become quite stark in the wake of the most recent crisis. 
take the 2008 crash as an example. during the financial meltdown, 
even sophisticated investors, such as the banks that produced securi-
tized loans in the first place, appear to have been mistaken about how 
risky these products were. In other words, the models that were sup-
posed to make these products risk-free for their manufacturers failed, 
utterly. Models have failed in other market disasters as well — perhaps 
most notably when Long-term capital Management (LtcM), a small 
private investment firm whose strategy team included Myron Scholes 
among others, imploded. LtcM had a successful run from its found-
ing in 1994 until the early summer of 1998, when russia defaulted on 
its state debts. then, in just under four months, LtcM lost $4.6 bil-
lion. By September, its assets had disappeared. the firm was heavily 
invested in derivatives markets, with obligations to every major bank 
in the world, totaling about $1 trillion. Yet at the close of trading on 
September 22, its market positions were worth about $500 million — a 
tiny fraction of what they had been worth a few months before, and far 

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too little to cover the company’s loans. A feather’s weight would have 
led to a default on hundreds of billions of dollars of debt, leading to an 
immediate international panic, had the government not stepped in to 
resolve the crisis.
the mathematical models underlying dynamic hedging strategies 
specifically, and derivatives trading more generally, are not perfect. 
Bachelier’s, osborne’s, and Mandelbrot’s stories go a long way toward 
making clear just why this is. their models, and the models that have 
come since, are based on rigorous reasoning that, in a very real sense, 
cannot be wrong. But even the best mathematical models can be mis-
applied, often in subtle and difficult-to-detect ways. In order to make 
complicated financial markets tractable, Bachelier, osborne, thorp, 
Black, and even Mandelbrot introduced idealizations and often strong 
assumptions about how markets work. As osborne in particular em-
phasized, the models that resulted were only as good as the assump-
tions that went in. Sometimes assumptions that are usually excellent 
quickly become lousy as market conditions change.
for this reason, the o’connor story has an important moral. Many 
histories suggest that the 1987 crash rocked the financial world because 
it was so entirely unexpected — impossible to anticipate, in fact, given 
the prevailing market models. the sudden appearance of the volatil-
ity smile is taken as evidence that models can work for a while and 
then suddenly stop working, which in turn is supposed to undermine 
the reliability of the whole market-modeling enterprise. If models that 
work today can break tomorrow, with no warning and no explana-
tion, why should anyone ever trust physicists on Wall Street? But this 
just isn’t right. By carefully thinking through the simplest model and 
complicating it as appropriate — in essence, by accounting for fat tails
— o’connor was able to anticipate the conditions under which Black-
Scholes would break down, and to adopt a strategy that allowed the 
firm to weather an event like the 1987 crash.
the story that I have told so far, from Bachelier to Black, goes a long 
way toward showing that financial modeling is an evolving process, 
one that proceeds in iterative fashion as mathematicians, statisticians, 
economists, and quite often physicists attempt to figure out the short-
comings of the best models and identify ways of improving them. In 
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t h e p h y s i c s o f wa l l s t r e e t

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