The Term Structure of VIX

Authors

  • Xingguo Luo,

    Corresponding author
    • Xingguo Luo is an Assistant Professor at the College of Economics and Academy of Financial Research, Zhejiang University, Hangzhou, China
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  • Jin E. Zhang

    1. Jin E. Zhang is an Associate Professor at the School of Economics and Finance, The University of Hong Kong, Hong Kong and Department of Accountancy and Finance, School of Business, University of Otago, New Zealand
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  • We are grateful for helpful comments from Bob Webb (editor), an anonymous referee, Charles Cao (the FMA Asian discussant), Michael Chng, Hitesh Doshi, Du Du, Joseph K. W. Fung, Gerard L. Gannon, Xiaohui Gao, Jingzhi Huang, Byoung Kang, Tse-Chun Lin, Dan Luo, Antonio Mele, Rujing Meng, Norman Seeger (the Financial Management Association [FMA] European discussant), Dragon Tang, Christopher Ting, Zhen Wang, Zhiguang Wang, Lixin Wu, Xianming Zhou, Jie Zhu, and seminar participants at the 2010 International Risk Management Conference in Italy, the 2010 FMA European Conference in Hamburg, the 2010 FMA Asian Conference in Singapore, the AsianFA 2011 International Conference in Macau, the 22nd Annual Asia-Pacific Futures Research Symposium in Shanghai, Central University of Finance and Economics, Shanghai University of Finance and Economics, Southwestern University of Finance and Economics, Sun Yat-sen University, Zhejiang University, and Zhongnan University of Economics and Law. Xingguo Luo has been supported by the Small Project Funding from the University of Hong Kong (project no. 201109176233). Jin E. Zhang has been supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (project no. HKU 7549/09H).

Correspondence author, College of Economics and Academy of Financial Research, Zhejiang University, Hangzhou 310027, China. Tel: +86-571-87953210, Fax: +86-571-87953937, e-mail: xingguoluo@gmail.com

Abstract

In this study, we extend the Chicago Board Options Exchange volatility index, VIX, from 30-day to any arbitrary time-to-maturity, and study the term structure of VIX. We propose new concepts of instantaneous and long-term squared VIXs as the limits at the short and long ends of the term structure respectively. Modeling the volatility process with instantaneous and long-term squared VIXs, we establish a parsimonious approach to capture information contained in the term structure of VIX. Our study provides an efficient setup to further study the pricing of VIX derivatives and their relation with S&P 500 options.

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