The information content of implied volatility, skewness and kurtosis: empirical evidence from long‐term CAC 40 options
利用长期CAC 40期权价格，检验隐含波动率、偏度和峰度对未来收益分布的信息含量，发现高阶矩信息能改进Black-Scholes模型的定价表现。
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.