Articlegreen2016

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

Zhuo Huang · Tianyi Wang · Peter Reinhard Hansen

58 citations0/0 files storedJournal of Futures Markets

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

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

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References

1991Conditional Heteroskedasticity in Asset Returns: A New Approach 1993On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks 2003Modeling and Forecasting Realized Volatility 1993Measuring and Testing the Impact of News on Volatility 2006Realized Variance and Market Microstructure Noise 2000A Closed-Form GARCH Option Valuation Model 2011Realized GARCH: a joint model for returns and realized measures of volatility 1982Approximate option valuation for arbitrary stochastic processes

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