This paper investigates the option implied risk measures by applying the principle of maximum entropy. The entropy approach allows to measure option implied volatility, skewness and kurtosis nonparametrically, and to construct confidence intervals. Simulations show that the entropy approach outperforms the Black-Scholes model and model-free method in backing out implied volatility, when the risk neutral distribution of the underlying asset possesses heavy tails and non-zero skewness. When estimating skewness and kurtosis, entropy approach is also slightly better than model-free approach, whereas both approaches have innegligible estimation errors. Using S&P500 index options, we apply the entropy method to calculate implied volatility 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 Bakshi and Madan (2003), in both in-sample and out-of-sample setup.

Discussant: Andrei Lalu (University of Amsterdam)