Volatility Components, Affine Restrictions and Non-Normal Innovations

Abstract

Recent work by Engle and Lee (1999) shows that allowing for long-run and short-run components greatly enhances a GARCH model's ability to fit daily equity return dynamics. Using the risk-neutralization in Duan (1995), we assess the option valuation performance of the Engle-Lee model and compare it to the standard one-component GARCH(1,1) model. We also compare these non-affine GARCH models to one- and two- component models from the class of affine GARCH models developed in Heston and Nandi (2000). Using the option pricing methodology in Duan (1999), we then compare the four conditionally normal GARCH models to four conditionally non-normal versions. As in Hsieh and Ritchken (2005), we find that non-affine models dominate affine models both in terms of fitting return and in terms of option valuation. For the affine models, we find strong evidence in favor of the component structure for both returns and options; for the non-affine models, the evidence is somewhat less convincing in option valuation. The evidence in favor of the non-normal GED models is strong when fitting daily returns, but the non-normal models do not provide much improvement when valuing options.

Keywords: Volatility, Component Model, GARCH, Long Memory, Option Valuation, Affine, Normality

JEL Classification: C22, G13