VIX Options Valuation via Continuous-Time Markov Chain Approximation and Ito-Taylor Expansion

We propose a novel analytical method to evaluate VIX options under the general class of affine and non-affine stochastic volatility models, which extends the current literature in particular to the realm of non-affine stochastic volatility models. The approach is based on a closed-form approximation of the VIX index through the Ito-Taylor expansion and the subsequent continuous-time Markov chain (CTMC) approximation to evaluate VIX options. The formula is in explicit closed-form and does not involve numerical (Fourier) inversions, in contrast to the existing literature. Numerical experiments with several stochastic volatility models demonstrate that it is accurate and efficient by comparing with benchmarks in the literature and Monte Carlo simulations. Empirical experiments demonstrate that in general non-affine stochastic volatility models provide better fit to the VIX options data.