GARCH Pricing and Hedging of VIX Options

We are the first to study the pricing and hedging of VIX options via Monte Carlo (MC) under GARCH(1,1) and Glosten–Jagannathan–Runkle GARCH(1,1) models. Our pricing is ab initio and out‐of‐sample and can be implemented in real time. Importantly, we propose the so‐called single‐option hedge error, a better measure than that of Bakshi-Cao-Chen, and suggest several techniques to expedite MC by over 1000 times, which rivals the potential speedup of quantum computers. Empirically, our proposed approach outperforms two types of benchmarks; further, the asymmetric Glosten–Jagannathan–Runkle outperforms the symmetric GARCH. Overall, our paperhas both theoretical and practical implications