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.

中文翻译：

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GJR-GARCH过程下的VIX期货定价：一种分析逼近方法

本文研究了在VIX期货定价中GJR–GARCH流程的性能。作者首先建立了VIX期货价格与模型隐含VIX之间的理论关系，然后从中获得了解析近似定价公式。作者将GJR–GARCH模型与Heston–Nandi模型的定价性能进行了比较。结果表明，在样本内和样本外VIX期货定价中，GJR–GARCH模型相对于Heston–Nandi模型具有显着优势。主题：期货和远期合约，期权主要发现•建立了VIX期货价格与VIX隐含模型之间的理论关系。•获得了在GJR–GARCH流程下VIX期货的分析近似定价公式。