Abstract
Implied standard deviation is widely believed to be the best available forecast of the volatility of returns over the remaining contract life (Jorion, 1995). In this paper, we take this result two steps further 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 found that implied first moments contain a substantial amount of information for future moments of CAC 40 returns although this amount decreases with respect to the moment’s order. Secondly, we found that the different shapes of the volatility smile are consistent with different distribution of the underlying returns. Based on these results, we also observed that including other implied moments significantly improves the out‐of‐sample pricing performance of the Black–Scholes, (1973) model.