Option Implied Risk Measures: A Maximum Entropy Approach

37 Pages Posted: 22 Aug 2014

See all articles by Xiao Xiao

Xiao Xiao

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE); Erasmus Research Institute of Management (ERIM)

Chen Zhou

De Nederlandsche Bank; Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE)

Date Written: August 21, 2014

Abstract

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

Suggested Citation

Xiao, Xiao and Zhou, Chen, Option Implied Risk Measures: A Maximum Entropy Approach (August 21, 2014). 27th Australasian Finance and Banking Conference 2014 Paper. Available at SSRN: https://ssrn.com/abstract=2484847

Xiao Xiao (Contact Author)

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE) ( email )

P.O. Box 1738
3000 DR Rotterdam, NL 3062 PA
Netherlands

Erasmus Research Institute of Management (ERIM) ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Chen Zhou

De Nederlandsche Bank ( email )

PO Box 98
1000 AB Amsterdam
Amsterdam, 1000 AB
Netherlands

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE) ( email )

P.O. Box 1738
3000 DR Rotterdam, NL 3062 PA
Netherlands

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