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

Abstract

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. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:328–358, 2017

A short cut: Directly pricing VIX futures with discrete‐time long memory model and asymmetric jumps

“…That means our simplification does not undermine the model performance. These findings are also related to literature studying the economic value of realized measures (Christoffersen et al, 2014; Huang et al, 2017, and others). Unlike an overwhelming amount of papers that advocate the value of realized measures, our results suggest that such economic value might depend on the modeling strategy, at least for this specific application.…”

Capturing volatility persistence: a dynamically complete realized EGARCH-MIDAS model

“…By estimating γ, for a given weighting function and choice of K, the term K k=1 Γ k γ y t−1,k zero mean, µ = 0, is imposed for simplicity and may in fact generate better out-of-sample performance . However, in option-pricing applications a GARCH-in-Mean specification is usually employed, see, e.g., Huang, Wang, and Hansen (2017).…”

An analytical approximation of option prices via TGARCH model

“…Following this research, Duan et al (2006) provided analytical formulae via the EGARCH and GJR-GARCH models. Furthermore, Huang et al (2017) derived the option pricing formula via the Realized GARCH model with more terms in the Edgeworth expansion. Duan et al (1999) developed an analytical approximation for option pricing by computing an option price as a Black-Scholes formula adjusted by skewness and kurtosis of cumulative asset return with GARCH model under LRNVR.…”