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

Abstract

This article investigates the performance of the GJR–GARCH process in pricing VIX futures. The authors first establish a theoretical relationship between VIX futures prices and the model implied VIX, from which an analytical approximation pricing formula is then obtained. The authors compare the pricing performance of the GJR–GARCH model with the Heston–Nandi model. The results show significant dominance of the GJR–GARCH model over the Heston–Nandi model 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 prices and the model implied VIX is established.

• • An analytical approximation pricing formula for VIX futures under the GJR–GARCH process 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.