Instantaneous squared VIX and VIX derivatives |
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| Authors: | Xingguo Luo Jin E Zhang Wenjun Zhang |
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| Institution: | 1. Department of Finance, School of Economics and Academy of Financial Research, Zhejiang University, Hangzhou, P.R. China;2. Department of Accountancy and Finance, Otago Business School, University of Otago, Dunedin, New Zealand;3. Department of Mathematical Sciences, School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, Auckland, New Zealand |
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| Abstract: | In this paper, we propose a parsimonious and efficient model to price derivatives written on VIXs with different horizons. Our model is built on Luo and Zhang's (2012, J Futures Markets, 32, 1092–1123) concept of the instantaneous squared VIX (ISVIX) that is the sum of instantaneous diffusive and jump variances of the SPX return. Modeling the ISVIX as a mean-reverting jump-diffusion process with a stochastic long-term mean, we obtain analytical formulas for VIX options and futures. Estimation with VIX term structure and calibration with VIX options data show that our model performs well in matching both time series and cross-sectional VIX derivatives market prices. |
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| Keywords: | instantaneous squared VIX VIX VIX futures VIX option |
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