Option Pricing with the Realized GARCH Model: An Analytical Approximation Approach
Zhuo Huang (a) Tianyi Wang (b) Peter Reinhard Hansen(c)
(a)Peking University, National School of Development
(b) University of International Business and Economics,School of Banking and Finance
(c) University of North Carolina at Chapel Hill & CREATES
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 empiricalanalysis 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.
Realized GARCH, Analytical approximation, Edgeworth expansion,Option pricing, Realized variance.