Efficient Out-of-Sample Pricing of VIX Futures

Abstract

The authors propose the first closed-form price formulas for VIX futures under the widely used discrete-time symmetric GARCH(1, 1) and asymmetric Glosten–Jagannathan–Runkle (GJR) GARCH(1, 1) models. For VIX futures expired before July 21, 2017, the proposed methods, which are truly simple, perform reasonably well in out-of-sample pricing. In regard to pricing errors and efficiency, the new methods significantly outperform a continuous-time benchmark based on the Heston volatility model and a discrete-time benchmark based on the Heston–Nandi GARCH(1, 1). Empirically, GJR is the most “potent”—a term the authors apply to the ability of the model to successfully price VIX futures in the data set. The GJR potency in this study is as high as 96.6%. The novel GARCH approaches are unique with the implication of applicability in real time. Finally, an insight is gained into the research of pricing, namely, that potency is an important gauge of a pricing method. TOPICS: Futures and forward contracts, derivatives, factor-based models Key Findings • Closed-form price formulas for VIX futures under GARCH(1,1) and GJR GARCH(1,1) models are proposed. • The novel approaches are shown to be really competitive for out-of-sample, and more importantly imply applicability in real time, pricing of VIX futures. • Potency, as a gauge of the success rate of pricing, is proposed.