VIX Option Pricing in a Jump-Diffusion Model

We first discuss the positive volatility skew observed in the implied volatilities of VIX options. To model this feature, we apply the square root stochastic variance model with variance jumps for the evolution of the S&P500 index volatility. Then we develop a robust method for unified pricing and hedging of different volatility products on the implied and realized variance of the S&P500 index and show how to apply this formula for pricing the VIX futures and options