Entropy-based implied moments

This paper investigates the maximum entropy method for estimating the option implied volatility, skewness and kurtosis.The maximum entropy method allows for non-parametric estimation of the risk neutral distribution and construction of confidence intervals around the implied volatility. Numerical study shows that the maximum entropy method outperforms the existing methods such as the Black-Scholes model and model-free method when the underlying risk neutral distribution exhibits heavy tail and skewness. By applying this method to the S&P 500 index options, we find that the entropy-based implied volatility outperforms the Black-Scholes implied volatility and model-free implied volatility, in terms of in-sample fit and out-of-sample predictive power. The differences between entropy based and model-free implied moments can be explained by the level of the higher-order implied moments of the underlying distribution. 
 
Keywords: Option pricing, risk neutral distribution, higher order moments.
JEL classifications: C14, G13, G17.

 

Working paper no. 581