Large bets, rare fluctuations and derivative pricing

The market volatility during 3Q 1998 has resulted in spectacular and well-publicized losses, exemplified by the bailout of Long-Term Capital Management, and called into question the sophisticated trading models used in today's markets. Whether or not these models are to blame for these events, as the popular press would have us believe, there is little doubt that the Black-Scholes-Merton assumptions and their extensions are incapable of modeling large but rare fluctuations, or even the milder but statistically significant phenomena giving rise to the volatility smile and fat tails. This month's Off The Wall, contributed by Erik Aurell, Roberto Baviera, Maurizio Serva, Ola Hammarlid and Angelo Vulpiani, reports on their recent work which attempts to use large deviation theory to model rare fluctuations, while at the same time reducing to standard option pricing theory for small fluctuations. We know that these issues are of great interest to the readership of Off The Wall, and extend a warm welcome to our latest contributors.