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

Primordial Seeds 
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the strike price. If a share of Google is trading at $100, and I have a 
contract that entitles me to buy a share of Google for $50, that option 
is worth at least $50 to me, since I can buy the share of Google at the 
discounted rate and then immediately sell it at a profit. conversely, if 
the option gives me the right to buy a share at $150, the option isn’t 
going to do me much good — unless, of course, Google’s stock price 
shoots up to above $150. But figuring out the precise relationship was a 
mystery. What should the right to do something in the future be worth 
now?
Bachelier’s answer was built on the idea of a fair bet. A bet is consid-
ered fair, in probability theory, if the average outcome for both people 
involved in the bet is zero. this means that, on average, over many re-
peated bets, both players should break even. An unfair bet, meanwhile, 
is when one player is expected to lose money in the long run. Bachelier 
argued that an option is itself a kind of bet. the person selling the op-
tion is betting that between the time the option is sold and the time it 
expires, the price of the underlying security will fall beneath the strike 
price. If that happens, the seller wins the bet — that is, makes a profit 
on the option. the option buyer, meanwhile, is betting that at some 
point the price of the underlying security will exceed the strike price, 
in which case the buyer makes a profit, by exercising the option and 
immediately selling the underlying security. So how much should an 
option cost? Bachelier reasoned that a fair price for an option would 
be the price that would make it a fair bet.
In general, to figure out whether a bet is fair, you need to know the 
probability of every given outcome, and you need to know how much 
you would gain (or lose) if that outcome occurred. How much you 
gain or lose is easy to work out, since it’s just the difference between 
the strike price on the option and the market price for the underly-
ing security. But with the random walk model in hand, Bachelier also 
knew how to calculate the probabilities that a given stock would ex-
ceed (or fail to exceed) the strike price in a given time window. Putting 
these two elements together, Bachelier showed just how to calculate 
the fair price of an option. Problem solved.
there’s an important point to emphasize here. one often hears 
that markets are unpredictable because they are random. there is a 

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sense in which this is right, and Bachelier knew it. Bachelier’s ran-
dom walk model indicates that you can’t predict whether a given stock 
is going to go up or down, or whether your portfolio will profit. But 
there’s another sense in which some features of markets are predictable 
precisely because they are random. It’s because markets are random 
that you can use Bachelier’s model to make probabilistic predictions, 
which, because of the law of large numbers — the mathematical result 
that Bernoulli discovered, linking probabilities with frequency — give 
you information about how markets will behave in the long run. this 
kind of prediction is useless for someone speculating on markets di-
rectly, because it doesn’t let the speculator pick which stocks will be 
the winners and which the losers. But that doesn’t mean that statisti-
cal predictions can’t help investors — just consider Bachelier’s options 
pricing model, where the assumption that markets for the underlying 
assets are random is the key to its effectiveness.
that said, even a formula for pricing options isn’t a guaranteed trip 
to the bank. You still need a way to use the information that the for-
mula provides to guide investment decisions and gain an edge on the 
market. Bachelier offered no clear insight into how to incorporate his 
options pricing model in a trading strategy. this was one reason why 
Bachelier’s options pricing model got less attention than his random 
walk model, even after his thesis was rediscovered by economists. A 
second reason was that options remained relatively exotic for a long 
time after he wrote his dissertation, so that even when economists in 
the fifties and sixties became interested in the random walk model, 
the options pricing model seemed quaint and irrelevant. In the United 
States, for instance, most options trading was illegal for much of the 
twentieth century. this would change in the late 1960s and again in 
the early 1970s. In the hands of others, Bachelier-style options pricing 
schemes would lay the foundations of fortunes.
Bachelier survived World War I. He was released from the military 
on the last day of 1918. on his return to Paris, he discovered that his 
position at the University of Paris had been eliminated. But overall, 
things were better for Bachelier after the war. Many promising young 
mathematicians had perished in battle, opening up university posi-
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