Double-jump stochastic volatility model for VIX: evidence from VVIX

TL;DR

This paper introduces a double-jump stochastic volatility model for VIX, leveraging VVIX as a proxy for volatility, and demonstrates the significance of jumps and their impact on VIX dynamics through empirical analysis.

Contribution

It develops a novel double-jump stochastic volatility model for VIX using VVIX as a volatility proxy and provides empirical evidence of jump significance and state dependence.

Findings

Jumps in VIX and volatility are statistically significant.

Jump intensity depends on the current state.

The model improves understanding of VIX dynamics.

Abstract

The paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jump in logarithm of VIX, we derive a linear relation between the stochastic volatility factor and VVIX index. We detect the existence of co-jump of VIX and VVIX and put forward a double-jump stochastic volatility model for VIX through its joint property with VVIX. With VVIX index as a proxy for the stochastic volatility, we use MCMC method to estimate the dynamics of VIX. Comparing nested models on VIX, we show the jump in VIX and the volatility factor is statistically significant. The jump intensity is also statedependent. We analyze the impact of jump factor on the VIX dynamics.