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Instantaneous squared VIX and VIX derivatives

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  • Xingguo Luo
  • Jin E. Zhang
  • Wenjun Zhang

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.

Suggested Citation

  • Xingguo Luo & Jin E. Zhang & Wenjun Zhang, 2019. "Instantaneous squared VIX and VIX derivatives," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(10), pages 1193-1213, October.
    • Handle: RePEc:wly:jfutmk:v:39:y:2019:i:10:p:1193-1213
    DOI: 10.1002/fut.22037
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    Cited by:

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    2. Zhiqiang Zhou & Wei Xu & Alexey Rubtsov, 2024. "Joint calibration of S&P 500 and VIX options under local stochastic volatility models," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(1), pages 273-310, January.
    3. Jing, Bo & Li, Shenghong & Ma, Yong, 2021. "Consistent pricing of VIX options with the Hawkes jump-diffusion model," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
    4. Qiang Liu & Yuhan Jiao & Shuxin Guo, 2022. "GARCH pricing and hedging of VIX options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(6), pages 1039-1066, June.
    5. Chen Tong & Zhuo Huang & Tianyi Wang, 2022. "Do VIX futures contribute to the valuation of VIX options?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(9), pages 1644-1664, September.
    6. Chen Tong & Zhuo Huang, 2021. "Pricing VIX options with realized volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(8), pages 1180-1200, August.
    7. Venter, Pierre J & Maré, Eben, 2022. "Price discovery in the volatility index option market: A univariate GARCH approach," Finance Research Letters, Elsevier, vol. 44(C).
    8. Fangsheng Yin & Yang Bian & Tianyi Wang, 2021. "A short cut: Directly pricing VIX futures with discrete‐time long memory model and asymmetric jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(4), pages 458-477, April.
    9. Hongkai Cao & Alexandru Badescu & Zhenyu Cui & Sarath Kumar Jayaraman, 2020. "Valuation of VIX and target volatility options with affine GARCH models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(12), pages 1880-1917, December.

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