Pricing VIX Futures under 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.