The Impact of Jump Distributions on the Implied Volatility of Variance

We consider a tractable affine stochastic volatility model that generalizes the seminal Heston model by augmenting it with jumps in the instantaneous variance process. In this framework, we consider both realized variance options and VIX options, and we examine the impact of the distribution of jumps on the associated implied volatility smile. We provide sufficient conditions for the asymptotic behavior of the implied volatility of variance for small and large strikes. In particular, by selecting alternative jump distributions, we show that one can obtain fundamentally different shapes of the implied volatility of variance smile some clearly at odds with the upward-sloping volatility skew observed in variance markets.