Double-jump Diffusion Model for VIX: Evidence from VVIX

38 Pages Posted: 24 Jun 2015 Last revised: 23 Jul 2016

See all articles by Xin Zang

Xin Zang

Peking University

Jun Ni

Pennsylvania State University - Department of Mathematics

Jingzhi Huang

Pennsylvania State University - Department of Finance

Lan Wu

Peking University

Date Written: November 26, 2015

Abstract

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

Zang, Xin and Ni, Jun and Huang, Jingzhi and Wu, Lan, Double-jump Diffusion Model for VIX: Evidence from VVIX (November 26, 2015). Available at SSRN: https://ssrn.com/abstract=2622164 or http://dx.doi.org/10.2139/ssrn.2622164

Xin Zang (Contact Author)

Peking University ( email )

School of Mathematical Sciences, Peking University
Beijing, Beijing 100871
China

Jun Ni

Pennsylvania State University - Department of Mathematics ( email )

University Park, PA 16802
United States

Jingzhi Huang

Pennsylvania State University - Department of Finance ( email )

University Park, PA 16802
United States

Lan Wu

Peking University ( email )

No. 38 Xueyuan Road
Haidian District
Beijing, Beijing 100871
China

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