Valuation of VIX Derivatives: Incorporating Larger Spikes in Volatility-of-Volatility Dynamics

The literature on direct VIX modeling highlights volatility-of-volatility as an important feature of VIX dynamics. Recent periods of financial market turbulence have been characterized by numerous uncertain events, leading to pronounced spikes in volatility-of-volatility. To capture this feature, this study proposes a new direct VIX model incorporating an additional spike process and derives an analytical characteristic function for pricing VIX derivatives. Our empirical results indicate that the additional spike component is statistically significant and helps capture large, transient spikes in volatility-of-volatility in an economically interpretable way.