Wednesday, February 20, 2008

Misguided Derision of Black-Scholes


I just finished reading an article by Michael Lewis, of Liar's Poker fame, where he essentially blames Black-Scholes as the reason for catastrophic market failures, from 1987, to LTCM and even the current subprime debacle. I think he's gone a little far however.

Black-Scholes is a model which is supposed to give fairly accurate predictions of option prices. The problem that Lewis failed to understand is that the formula, in and of itself, is not necessarily faulty. The problem is that people have come to expect and use the model to actually price different securities instead of predicting the movements that result from dynamic variables.

This would not be the only time that traders/bankers/fund managers/etc. have used models as a means of pricing things in fact rather than in theory. Consider the write-downs from CDOs and other similar asset backed securities which presented themselves due to the inability to mark-to-market and the ensuing reliance on marking-to-model. In fact, I wrote the following for a research paper on CDOs, with regards to their pricing:

Interestingly, the Marshall-Olkin copula, the so-called “shock model” that accounted for successive catastrophic default events, was found to be a poor model of true market values of CDOs due to the fat-tails it created on the distributions of losses from defaults. This is interesting because the research was done in 2005, and the CDO market has actually trended toward fat-tail loss distributions and catastrophic default events in recent months. Obviously, such strict mathematical models should always be taken with a grain of salt, or at least with the understanding that such models should only be used as approximations for the price of an illiquid security. Instead, many investors (again, in the institutional sense) regarded the prices placed on the CDOs by their models to be the actual value, and in many cases felt that their models were still correct even in the face of a large divergence between the market prices and the model prices [1].


[1] X. Burtschell, J. Gregory, J.-P. Laurent. “A comparative analysis of CDO pricing models.”


It doesn't take college-level laboratory courses to see that theory does not always exactly match actuality or take into account the existence of outlying data points. For that reason, it seems that Lewis is misplacing the blame, at least to some degree. While Black-Scholes, or any market model, certainly comes with limitations and downfalls, it is the implementation of said models that determines their utlimate accuracy.

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