The jump-diffusion process for the VIX and the S&P 500 index

This paper applies the CBP-GARCH model of Chan (2003) to analyze the discontinuous jump and the time-varying correlated jump intensity for the changes in the VIX and the S&P 500 returns over the period extending from January 15, 2001 to December 31, 2009. The empirical results provide evidence of the significant jump-diffusion process and the causal relationships in the bi-directions between the S&P 500 returns and the changes in the VIX. In addition, the relationships between the S&P 500 returns and the changes in the VIX exhibit joint jump behavior are not time varying.