Formulas for pricing American VIX options under the generalized mixture volatility models

Abstract

This study considers the American VIX option pricing problem under the models of mixing the 3/2, and 1/2 classes of volatility processes. The pricing formulas for the perpetual American VIX call are provided for the generalized 1/2 volatility model, the generalized 3/2 volatility model and the model mixing these two processes. For these models, we derive approximate formulas for the finite-lived American VIX call option by the quadratic approximation approach. Then, we illustrate the influence of the varied parameters on the free boundaries and the corresponding continuation regions through numerical analysis. Finally, in the real application, we obtain the price for the finite-lived American VIX call option using the CBOE volatility index.