VIX option pricing through nonaffine GARCH dynamics and semianalytical formula

Abstract

This paper develops analytical approximations for volatility index (VIX) option pricing under nonaffine generalized autoregressive conditional heteroskedasticity (GARCH) models as advocated by Christoffersen et al. We obtain the approximation formulae for pricing VIX options and then evaluate their performance with three expansions under four empirically well-tested models. Our numerical experiments find that the weighted ${ℒ}^2$ expansion generated by the fat-tailed weighting kernel can significantly reduce approximation error over the Gram-Charlier expansion; the Taylor expansion of conditional moments can lead to divergence for parameters with certain high persistence in the affine GARCH, nonlinear asymmetric GARCH, and Glosten-Jagannathan-Runkle GARCH models, while surviving during high persistence in the exponential GARCH.