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

We derive a pricing formula for European options for the Realized GARCH framework based on an analytical approximation using an Edgeworth expansion for the density of cumulative return. Existing approximations in this context are based on a Gram–Charlier expansion while the proper Edgeworth expansion is more accurate. 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.