Volatility Components, Affine Restrictions, and Nonnormal Innovations

Here we assess the return fitting and option valuation performance of generalized autoregressive conditional heteroscedasticity (GARCH) models. We compare component versus GARCH(1, 1) models, affine versus nonaffine GARCH models, and conditionally normal versus nonnormal GED models. We find that nonaffine models dominate affine models in terms of both fitting returns and option valuation. For the affine models, we find strong evidence in favor of the component structure for both returns and options; for the nonaffine models, the evidence is less convincing in option valuation. The evidence in favor of the nonnormal GED models is strong when fitting daily returns, but not when valuing options.