VIX Futures Pricing with Affine Jump-GARCH Dynamics and Variance-Dependent Pricing Kernels

Abstract

Volatility Index (VIX) futures are among the most actively traded contracts at the Chicago Board Options Exchange, in response to the growing need for protection against volatility risk. We develop a new class of discrete-time and closed-form VIX futures pricing models, in which the S&P 500 returns follow the time-varying infinite-activity Normal Inverse Gaussian (NIG) and finite-activity compound Poisson (CP) jump-GARCH models, and which are risk-neutralized by the variance-dependent pricing kernel used by Christoffersen et al. (2013). We estimate these models using several data sets, including the S&P 500 returns, VIX Index, and VIX futures. The empirical results indicate that the time-varying NIG and CP jump-GARCH models significantly outperform the Heston-Nandi (HN) GARCH model in asset returns fitting and VIX futures pricing.