Global Journal of Business Management

Global Journal of Business Management ISSN 6731-4538 Vol. 6 (7), pp. 001-008, July, 2012. © International Scholars Journals

Full Length Research Paper

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

Chi-Tai Lin¹ and Yen-Hsien Lee^2*

¹Department of Banking and Finance, TamKang University No.151, Ying-Chuan Rd., Danshuei Township, Taipei County 251, Taiwan.

²Department of Finance, Chung Yuan Christian University 200,Chung Pei Rd., Chung Li, Taiwan 320, R. O. C., Taiwan.

Accepted 11 April, 2012

Abstract

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.

Key words: VIX, CBP-GARCH model, jump-diffusion process.