Option Implied Risk Measures: A Maximum Entropy Approach
37 Pages Posted: 22 Aug 2014
Date Written: August 21, 2014
This paper investigates option implied risk measures (volatility, skewness and kurtosis) by applying the principle of maximum entropy. Compared to parametric models, e.g. Black Scholes model, this method is free of parametric assumptions. Compared to model-free methods such as that in Bakshi and Madan (2003), this method does not require a large number of options with strike prices covering the entire support of the return distribution and can be used to construct confidence interval for option implied moments. Given different underlying risk neutral distributions, we find that the entropy approach outperforms the Black Scholes model and the model-free methods, particularly when the risk neutral distribution possesses heavy tails and non-zero skewness. Using S\&P500 index options, we apply our method to obtain implied volatilities and test its forecasting performance. We show that the implied volatilities obtained from our method subsumes all information in the Black-Schole implied volatility and historical volatility. In addition, it has more predictive power than the model-free implied volatility following Bakshi and Madan (2003), in both in-sample and out-of-sample setup.
Keywords: volatility, skewness, kurtosis, nonparametric estimation, risk neutral distribution
JEL Classification: C14, G13, G17
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