Thursday, September 24, 2009


One thing I didn't like about "Panic" was the introduction by Michael Lewis which contained a confusing and in my view wrongheaded attack on the Black-Scholes option pricing formula.

Briefly Black and Scholes showed given a certain simplified model of the world in which stock prices move in continuous random walks then you could derive a formula for the value of stock options. Now it has always been known that this simplified model was not completely accurate. This is generally the case with models. The real world is very complicated and hard to understand. So we look at simplified models of the world which we can analyze. If chosen carefully such models can give us considerable insight into what is happening in the more complicated real world. But they will never match reality exactly and will increasingly diverge from reality as we move into domains where the simplified model assumptions break down. Still such models can be very useful.

But Lewis writes:

... At the end of 2006, according to the Bank for International Settlements, there was $415 trillion in derivatives-that is, $415 trillion in securities for which there is no completely satisfactory pricing model. ...

This is a silly objection. There is no completely satisfactory pricing model for stocks so why should there be one for stock options? In both cases the price is ultimately determined by the market, by the balance between supply and demand. The market price can be very wrong in retrospect. For instance during bubbles. But this is not the fault of the Black-Scholes formula. It just reflects the fact that it can be hard to think independently from the herd.

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