Entropy-based implied volatility and its information content

This paper investigates the maximum entropy approach on estimating implied volatility. The entropy approach also allows to measure option implied skewness and kurtosis nonparametrically, and to construct confidence intervals. Simulations show that the en- tropy approach outperforms the Black-Scholes model and model-free method in backing out implied volatility, when the risk neutral distribution of the underlying asset deviates from log-normal distribution, and when the number of available options is limited. Using S&P500 index options, we apply the entropy method to obtain implied volatilities and their confidence intervals. We find that the entropy-based implied volatility subsumes all information in the Black-Scholes implied volatility and historical volatility. In addition, it has more predictive power than the model-free implied volatility, in both in-sample and out-of-sample setup. Entropy-based variance risk premium performs better than other alternatives in predicting future monthly market return in both in-sample and out-of-sample.