Sunday, January 4, 2009

BS v. BS: Black Swans against Black-Scholes

On December 30, the Economist's website posted an anonymous column about the Black-Scholes-Merton options pricing formula. Access it here if you please.

The columnist observes that BSM has come under attack of late, and it has even been used as a prime example of why the Nobel Prize in Economics ought to be discontinued. Scholes and Merton received that august prize in 1997 for their work on this model in articles published in 1973 [Fischer Black had died in 1995 and the award is never given posthumously.]

The critics of the BSM model to whom the Economist alludes include Nassim Nicholas Taleb, the author of Fooled by Randomness (2001) and The Black Swan (2007), who attributes much of the recent financial dislocation to what he sees as the fallacious view of financial risk and risk management of which the BSM model is an important part.

In 2005, Taleb and co-author Emanuel Derman wrote "The illusions of dynamic replication," in the journal Quantitative Finance. This was a brief nerdy paper in quant jargon. In essence, "dynamic replication" refers to the replication of the value of a derivative by the continuous ("dynamic") trading of its underlyings.

Presumably, dynamic replication would render the derivative itself redundant, and this fact allows for the determination of its value by means of the no-arbitrage principle.

The Derman-Taleb paper made the case that dynamic replication is much too complicated—there are simpler ways to get the results. The most important of these simpler ways is static replication. Their idea was to drop the principle of continuous trading and construct a portfolio consisting of a long position in a call and a short position in a put. The traditionally discounted expected value of their payoffs must replicate a forward contract.

The Black-Scholes option pricing formula could have been discovered much more rapidly than it was, Taleb and Derman maintained, had this simpler route to that goal been adopted.

In 2006, the same journal published a responsive comment from two students of Robert Merton, Doriana Ruffino and Jonathan Treussard, who took issue with the Derman-Taleb reasoning. Ms. Ruffino and Mr. Treussard wrote in their paper that although it's conceivable the same result could have been reached by mathematicians making use of put-call parity without dynamic replication, it would have been a fluke, a "matter of pure chance."

In 2007, Taleb changed partners and somewhat changed his line of attack. He wrote a paper with Espen Haug entitled "Why We Have Never Used the Black-Scholes-Merton Options Pricing Formula." They proposed that the name "Black-Scholes" itself be relegated to the dustbins. They would call the options pricing formula Bachelier-Thorp, after the early stochastic-process theorist Louis Bachelier and blackjack-sharp hedge-fund pioneer Ed Thorp.

The Taleb-Haug paper attracted more attention than did its Derman-Taleb precursor. I wrote about the controversy myself at that point.

On December 7, 2008, the Financial Times ran an opinion column by Taleb and another co-author, Pablo Triana, using the intervening market chaos to reinforce their argument against contemporary financial risk management in general and the BSM model in particular.

"Ask for the Nobel prize in economics to be withdrawn from the authors of these theories," they urged their readers. "Boycott professional associations that give certificates in financial analysis that promoted these methods. The fraud can be displaced only by shaming people, by boycotting the orthodox financial economics establishment and the institutions that allowed this to happen."

So it was that the same Pablo Triana wrote an open letter to the Swedish central bank, which gives out the Nobel Prize in this field (it isn't one of the real Nobel Prizes, instituted by the old peace-loving dynamiter of that name.) Triana said: "Stop doing this! You only encourage theorists who come up with these terrible ideas that lead us all off a cliff!" -- that my paraphrase of his letter, but I submit it's a fair one.

And so we come back to the column in The Economist, which takes issue with Triana and with the whole campaign, contending that the BSM model has been "a force for good," i.e. that the world is much better off in terms of how risks are managed than it would have been had the three authors written nothing at all.

So much for the history of this dispute. I'll wade into it (unworthily, for I'm a humble scribe who has just named several people all of whom are much smarter than am I) tomorrow.

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