Financial Markets as Adaptive Ecosystems

Abstract:     
Options markets offer an interesting example of the adaptation of a population to a complex environment, through trial and error and by 'natural' selection. Guided by the Black-Scholes theory but constrained by the fact that mispricing leads to arbitrage opportunities, options markets agree on prices which are close but significantly and systematically different from those given by the Black- Scholes formula. We re-examine the informational content of option prices in the light of the notion of implied kurtosis, analogous to that of implied volatility but taking into account the non-Gaussian character of the fluctuations of the underlying asset. We conclude by a detailed empirical study of market prices for options on German Bund futures, showing very good agreement between implied kurtosis calculated from option prices and empirical kurtosis calculated using prices of the underlying asset. Our results show that the market has adapted itself to incorporate more information on the statistical properties of returns than that conveyed by the Black-Scholes model.

JEL Classification: G10, G13

working papers series