Wall Street’s Sexiest Model: Black-Scholes
Blame Disaster on Bad Inputs. Black-Scholes Works.
The last few years have given us plenty of reasons to hate financial models. Models that promised to increase efficiency and manage risk became substitutes for common sense and justifications for greed. The real estate bubble was of course justified by them.
Yet people at hedge funds and trading firms, using models to mint money, remain passionate believers. Another supporter is George Szpiro, a mathematician turned writer who recently released a book calledÂ Pricing The Future, about the history of the Black-Scholes equation, the most famous model in finance and the one that launched this quantitative revolution (plus theÂ ChicagoÂ BoardÂ OptionsÂ Exchange). Forbes recently interviewed Szpiro from his home in Jerusalem, pressing him to name faults in the model. Â Szpiro won’t, and instead passionately and convincingly explains why he still trusts modelsâ€”but why we should keep a close eye on the people who use them:
People are suspicious of models.
FORBES: How has Black-Scholes failed, or gone awry?
SZPIRO: I donâ€™t think Black-Scholes failed as such. The equation is correct. The problem is that it has many parameters that need to be estimated. And when the estimates that are used are incorrect, the result is garbage (garbage in, garbage out). For example, one of the inputs is a stockâ€™s volatility; it is very hard to estimate that. Also, the equation is based on the Gaussian â€śbellâ€ť curve. But stock prices do not behave strictly as the bell curve says they should. Catastrophic events (bankruptcies, tsunamis, bubbles) are more common than the Gaussian bell curve would have us believe.
FORBES: That sounds like a major failing to me. If you have a model that assumes data is correct, and itâ€™s not, thatâ€™s a recipe for disaster. To me thatâ€™s an argument to rely less on math, more on common sense. Wouldnâ€™t you agree?
SZPIRO: The model did not fail. It correctly describes the workings of the market. But you are right: if the data one uses is incorrect, the result is rubbish. It is a failing of the people who made inappropriate use of the model, who used incorrect data, not of the model itself. Regarding common sense: a resounding YES.
FORBES: Have the credit crisis, and risk models behaving badly, caused you to see Black-Scholes differently?
SZPIRO: No. The equation is totally correct. See above about garbage inputs. Also, many people use a calculator to compute the value of a stock option without knowing what they are doing. And then there is greed: brokers and banks are interested in their commissions, and do not always take the real risks into account.
One must not rely blindly on any model but make use of it wisely. Models should serve as a reference point. I also remind you of my previous answer concerning the inputs: garbage in, garbage out.
FORBES: What do you think of the fact a model meant to contain risk has created more of it? Was this all just a futile exercise?
SZPIRO: Again, the model as such has not increased risk. People who abuse the model created additional risk. This would be like faulting Isaac Newtonâ€™s Laws of Motion for car accidents. It is the drivers who are at fault, not Newtonâ€™s equations.
Point taken. Â But are there any other models as cool as Black-Scholes?
Szpiro opines: Â “I think the Bell Curve is also quite shapelyâ€¦ especially if it does not have fat tails.”