Wall Street's Sexiest Model
About George Szpiro - GeorgeSzpiro.com
www.georgeszpiro.com/index.asp?page=about.htm
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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 called 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 the Chicago Board Options Exchange). Szpiro, interviewed from his home in Jerusalem, explains why he still trusts models but why we should keep a close eye on the people who use them:
FORBES: How did you get interested in the Black-Scholes equation, and what is it meant to do?
George Szpiro (photo by Noga Szpiro)
The Black Scholes-equation was meant to elicit the correct value of an option. Before Black, Scholes and Merton, values were based on gut feeling. Black Scholes ended the guessing game. Of course, in any model in physics and economics, there are assumptions. If the assumptions do not hold, the result is incorrect. For example, Newtonian physics ignores relativistic effects. Many other models assume that friction is zero, for example. So the model is only a starting point. Once one has the model, one can search further.
SZPIRO: The first person to really use mathematical formulation to describe options was Louis Bachelier, who did his Ph.D at the Sorbonne in Paris, in 1900. His work was lost and only re-discovered by Paul Samuelson in the 1960s. Other people who are important to the story are Robert Brown (of Brownian motion fame), the 19th century French accountants Jules Regnault and Henri Levefre, and also Albert Einstein, the MIT-mathematician Norbert Wiener, the Russion probabilist Andrei Kolmogorov, the French mathematician turned soldier Wolfgang Döblin (who committed suicide rather than fall into the hands of the Nazis), the Japanese mathematician Kiyoshi Ito, and a host of physicists, chemists and mathematicians.
FORBES: What was the greatest achievement of the equation?
SZPIRO: It made it possible to efficiently trade options, thus allowing people to buy and sell risk as if it were a commodity.
FORBES: How has Black-Scholes failed, or gone awry?
SZPIRO: I don’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 stock’s volatility; it is very hard to estimate that. Also, the equation is based on the Gaussian “bell” 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 it’s not, that’s a recipe for disaster. To me that’s an argument to rely less on math, more on common sense. Wouldn’t you agree?
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 Newton’s Laws of Motion for car accidents. It is the drivers who are at fault, not Newton’s equations.
FORBES: We have rules of the road for drivers. Do we need similar rules for mathematical models?
FORBES: How?
SZPIRO: Strict enforcement of existing laws, creation of new laws if necessary, elimination of incentives that ignore long-term risks. Maybe institute a “malus” system to punish reckless managers, or at least keep their bonuses in escrow for a number of years to make sure that there were no hidden risks.
FORBES: What gives you this confidence in math?
SZPIRO: One must not use mathematical models blindly. One should make use of models to get an idea of the workings of the market and then use common sense when doing actual trading.
FORBES: Do you trade?
SZPIRO: No, I do not trade myself. I am interested in the history of ideas.
FORBES: Is Black-Scholes the sexiest model on Wall Street?
SZPIRO: As models go, Black-Scholes is very appealing. But I think the Bell Curve is also quite shapely… especially if it does not have fat tails.
This article originally said John Brown is he of Brownian motion fame. It has been corrected to say Robert Brown. Sorry about that, Robert.
