The Information Content of Implied Volatility, Skewness and Kurtosis: The Empirical Evidence from Long Term CAC 40 Options

Abstract

The implied standard deviation is widely believed to be the best available forecast of the volatility of the returns over the remaining contract life (Jorion 1995). In this paper, we generalize this result to the higher moments of the distribution (Skewness and Kurtosis) based on a Gram-Charlier series expansion of the normal distribution (Corrado and Su 1996) using long term CAC 40 option prices contract, named PXL. First, we find that implied first moments contain a substantial amount of information for realized future moments of CAC 40 returns although this amount is decreasing with respect to the moment's order. Second, we find that different shapes of the volatility smile are consistent with different distributions of the underlying returns. Based on these results, we also observe that including other implied moments significantly improve the out-of-sample pricing performance of the Black-Scholes (1973) model.

Keywords: Implied Density Function, Smile, Volatility, Skewness, Kurtosis.

JEL Classification: C14, C52, G12, G13, G14