  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.
