Entropy-Based Implied Moments

54 Pages Posted: 29 Dec 2017

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: December 27, 2017

Abstract

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 Classification: C14, G13, G17

Suggested Citation

Xiao, Xiao and Zhou, Chen, Entropy-Based Implied Moments (December 27, 2017). De Nederlandsche Bank Working Paper No. 581. Available at SSRN: https://ssrn.com/abstract=3094246 or http://dx.doi.org/10.2139/ssrn.3094246

Xiao Xiao

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 (Contact Author)

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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