Double-jump diffusion model for VIX: evidence from VVIX
研究了VIX指数与VVIX指数的共同跳跃特性，提出了一个双跳随机波动率模型，并用MCMC方法估计了VIX的动态，发现跳跃因子显著影响VIX。
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 analyse the impact of the jump factor on VIX dynamics.