Saturday, January 26, 2008

No option

There is an excellent article in today’s Guardian by the author John Lanchester, who turns out to have a surprisingly (but after all, why not?) thorough understanding of the derivatives market. Lanchester’s piece is motivated by the extraordinary losses chalked up by rogue trader Jérôme Kerviel of the French bank Société Générale. Kerviel’s exploits seem to be provoking the predictable shock-horror about the kind of person entrusted with the world’s finances (as though the last 20 years had never happened). I suspect it was Lanchester’s intention to leave it unstated, but one can’t read his piece without a mounting sense that the derivatives market is one of humankind’s more deranged inventions. To bemoan that is not in itself terribly productive, since it is not clear how one legislates against the situation where one person bets an insane amount of (someone else's) money on an event of which he (not she, on the whole) has not the slightest real idea of the outcome, and another person says ‘you’re on!’. All the same, it is hard to quibble with Lanchester’s conclusion that “If our laws are not extended to control the new kinds of super-powerful, super-complex, and potentially super-risky investment vehicles, they will one day cause a financial disaster of global-systemic proportions.”

All this makes me appreciate that, while I have been a small voice among many to have criticized the conventional models of economics, in fact economists are only the poor chaps trying to make sense of the lunacy that is the economy. Which brings me to Fischer Black and Myron Scholes, who, Lanchester explains, published a paper in 1973 that gave a formula for how to price derivatives (specifically, options). What Lanchester doesn’t mention is that this Nobel-winning work made the assumption that the volatility of the market – the fluctuations in prices – follows the form dictated by a normal or Gaussian distribution. The problem is that it doesn’t. This is what I said about that in my book Critical Mass:

“Options are supposed to be relatively tame derivatives—thanks to the Black-Scholes model, which has been described as ‘the most successful theory not only in finance but in all of economics’. Black and Scholes considered the question of strategy: what is the best price for the buyer, and how can both the buyer and the writer minimize the risks? It was assumed that the buyer would be given a ‘risk discount’ that reflects the uncertainty in the stock price covered by the option he or she takes out. Scholes and Black proposed that these premiums are already inherent in the stock price, since riskier stock sells for relatively less than its expected future value than does safer stock.
Based on this idea, the two went on to devise a formula for calculating the ‘fair price’ of an option. The theory was a gift to the trader, who had only to plug in appropriate numbers and get out the figure he or she should pay.
But there was just one element of the model that could not be readily specified: the market volatility, or how the market fluctuates. To calculate this, Black and Scholes assumed that the fluctuations were gaussian.
Not only do we know that this is not true, but it means that the Black-Scholes formula can produce nonsensical results: it suggests that option-writing can be conducted in a risk-free manner. This is a potentially disastrous message, imbuing a false sense of confidence that can lead to huge losses. The shortcoming arises from the erroneous assumption about market variability, showing that it matters very much in practical terms exactly how the fluctuations should be described.
The drawbacks of the Scholes-Black theory are known to economists, but they have failed to ameliorate them. Many extensions and modifications of the model have been proposed, yet none of them guarantees to remove the risks. It has been estimated that the deficiencies of such models account for up to 40 percent of the 1997 losses in derivatives trading, and it appears that in some cases traders’ rules of thumb do better than mathematically sophisticated models.”

Just a little reminder that, say what you will about the ‘econophysicists’ who are among those to be working on this issue, there are some rather important lacunae remaining in economic theory.

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