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Instantaneous squared VIX and VIX derivatives

Xingguo Luo, Jin E. Zhang and Wenjun Zhang

Journal of Futures Markets, 2019, vol. 39, issue 10, 1193-1213

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.

Date: 2019
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