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Option Pricing with the Realized GARCH Model: An Analytical Approximation Approach.

posted Sep 1, 2016, 6:46 PM by Peter Hansen   [ updated Mar 3, 2017, 7:13 AM ]
Journal of Futures Markets Vol. 37 pp. 328–358 (2017) with Z. Huang and T. Wang.

Abstract:   We derive a pricing formula for European options for the Realized GARCH framework. The formula is based on an analytical approximation using an Edgeworth expansion for the density of cumulative return. Existing approximations in this context that were labeled Edgeworth are, in fact, based on a Gram-Charlier expansion. The distinction is important because the proper Edgeworth expansion offers a more accurate approximation. In relation to existing discrete-time option pricing models with realized volatility, our model is log-linear, non-affine, with a flexible leverage effect. We conduct an extensive empirical analysis on S&P500 index options and the results show that our computationally fast formula outperforms competing methods in terms of pricing errors, both in-sample and out-of-sample.

Keywords:  Realized GARCH, Analytical approximation, Edgeworth expansion, Option pricing, Realized variance.

JEL Classification:  

Author(s): Zhuo Huang and Tianyi Wang and Peter Reinhard Hansen.

Peter Hansen,
Sep 1, 2016, 6:46 PM