Pricing VIX Futures under the GJR–GARCH Process: An Analytical Approximation Method

Abstract

This article investigates the performance of GJR-GARCH in pricing VIX futures. We first establish a theoretical relationship between VIX futures price and the model implied VIX, from which an analytical approximation pricing formula is then obtained. We compare the pricing performance of the GJR-GARCH model with the Heston-Nandi model. The results show significant dominance of the GJR-GARCH over the Heston-Nandi in both in-sample and out-of-sample VIX futures pricing. TOPICS:Futures and forward contracts, options Key Findings • A theoretical relationship between VIX futures price and the model implied VIX is established. • An analytical approximation pricing formula for VIX futures under the GJR-GARCH is obtained. • The empirical results show that the analytical approximation pricing method under GJR-GARCH outperforms the analytical pricing method under the Heston-Nandi model.