Financial Models Must Be Clean and Simple

(page 2 of 2)

All that's left at the end is a single model variable: "the default correlation," which represents the probability that, on average, any one future loan default will be accompanied by another.

Other than the future growth in housing prices (which was almost always overestimated), it is the value of this variable alone that determines the CDO price. Worse, the simplistic model gives no indication of the CDO's risk.

What makes a good model, then? We think the best ones use only a few variables and are explicit about their assumptions. In this regard, we believe that the Black-Scholes model for options valuation—now often maligned—is a model for models. It is clear and robust. Clear because it is based on true engineering: It gives you a method for manufacturing an option out of stocks and bonds, and it tells you what, under ideal circumstances, the option should be worth. (To picture how the model works, imagine Del Monte figuring out the offering price of a can of its tropical fruit salad from the cost of the individual fruits, labor, and transportation.) The world of markets doesn't exactly fulfill the ideal conditions Black-Scholes requires. But the model allows an intelligent trader to see what real-world dirt has been swept under the rug—and to adjust his or her risk estimates accordingly.

Financial markets are alive. A model, however beautiful, is an artifice. To confuse the model with the world is to embrace a future disaster in the belief that humans obey mathematical principles.

How can we get our fellow modelers to give up their fantasy of perfection? We propose, not entirely in jest, a model makers' Hippocratic Oath:

• I will remember that I didn't make the world and that it doesn't satisfy my equations.

• Though I will use models boldly to estimate value, I will not be overly impressed by mathematics.

• I will never sacrifice reality for elegance without explaining why I have done so. Nor will I give the people who use my model false comfort about its accuracy. Instead, I will make explicit its assumptions and oversights.

• I understand that my work may have enormous effects on society and the economy, many of them beyond my comprehension.

Emanuel Derman, author of several widely used financial models and of My Life as a Quant (Wiley, 2004), is a professor at Columbia University and a principal at Prisma Capital Partners. Paul Wilmott runs a number of finance-related businesses and is an author, most recently of Paul Wilmott on Quantitative Finance (Wiley, 2006).