Why Models Work [?]
Posted At : August 8, 2006 3:37 AM | Posted By : Emanuel Derman
Related Categories: Models
A student at another university recently sent me a question which I've often wondered about myself:
"Any introductory economics course in college will introduce the student to simple supply and demand curves; the forces of the market that determine the price of a good. If that is the case, why is there such an effort in pricing financial instruments or (as you mention in one of your interviews) trying to understand the price of a stock? Shouldnât these prices simply be dictated by the supply and demand of the market?"
Off the bat, I had two answers.
1. The world, physical or mental, doesnât just have to have a description on only one level. You can describe water as a bunch of molecules or as a liquid or as something without which your body dies. All descriptions are true. Similarly you can think of a person as chemistry or biology or as a mind and a body, and all of those have some validity. It depends what facets of the person you want to talk about. So far this argument isnât an argument about why the financial laws are right, but rather about why they donât have to be wrong.
2. More deeply, people who supply or demand often themselves use various kinds of models to figure out value. For example, when you buy a house you first look at the market's implied cost per square foot and then see if that produces a reasonable estimate of the value of the house you're interested in. Then you adjust the price about that theoretical value. In other words, price per square foot is a model, like yield to maturity for bonds, that many of the participants in the market are using, some more rigorously, some more intuitively.
In the same way, the supply and demand for options probably depend on intuitive estimates of future volatility, and then those prices lead to an implied volatility that does indeed reflect estimates of future volatility. People, even naïve people, are often using some version of the financial strategists sophisticated model too.
Supply and demand is one way of looking at things; models are a complementary view of the same phenomenon. Often, but not always, they are related, not in conflict. Fischer Black once said that the market is efficient when prices are with a factor of 1/2 and 2 of the fair value.....
One other thing I came back to add: Models are very useful when they are the only way to communicate value, and then drive supply and demand for financial assets. The value of an option is hard to estimate, almost impossible, without a model. Black-Scholes takes a linear quantity like volatility, which you can estimate with intuition and thought, and translates it into a nonlinear price, which you couldn't.
nitro