Double-jump Diffusion Model for VIX: Evidence from VVIX
38 Pages Posted: 24 Jun 2015 Last revised: 23 Jul 2016
Date Written: November 26, 2015
This 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 jumps in the logarithm of VIX, we derive a linear relationship between the stochastic volatility factor and the VVIX index. We detect the existence of a co-jump of VIX and VVIX and put forward a double-jump stochastic volatility model for VIX through its joint property with VVIX. Using the VVIX index as a proxy for stochastic volatility, we use the MCMC method to estimate the dynamics of VIX. Comparing nested models of VIX, we show that the jump in VIX and the volatility factor are statistically significant. The jump intensity is also stochastic. We analyze the impact of the jump factor on VIX dynamics.
Keywords: Volatility indices, Volatility proxy, Cojump, Monte Carlo Markov chain, Bayesian analysis
JEL Classification: C11, C13, C15
Suggested Citation: Suggested Citation