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Valuation of VIX and target volatility options with affine GARCH models

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  • Hongkai Cao
  • Alexandru Badescu
  • Zhenyu Cui
  • Sarath Kumar Jayaraman

Abstract

In this paper we propose semiclosed‐form solutions, subject to an inversion of the Fourier transform, for the price of VIX options and target volatility options under affine GARCH models based on Gaussian and Inverse Gaussian distributions. We illustrate the advantage of the proposed analytic expressions by comparing them with those obtained from benchmark Monte–Carlo simulations. The empirical performance of the two affine GARCH models is tested using different calibration exercises based on historical returns and market quotes on VIX and SPX options.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:jfutmk:v:40:y:2020:i:12:p:1880-1917
    DOI: 10.1002/fut.22157
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    References listed on IDEAS

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    Cited by:

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    2. Liang Wang & Weixuan Xia, 2022. "Power‐type derivatives for rough volatility with jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1369-1406, July.
    3. 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.
    4. 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.
    5. Nagaraj Naik & Biju R. Mohan, 2021. "Stock Price Volatility Estimation Using Regime Switching Technique-Empirical Study on the Indian Stock Market," Mathematics, MDPI, vol. 9(14), pages 1-18, July.
    6. 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).
    7. Xu Gong & Yujing Jin & Chuanwang Sun, 2022. "Time‐varying pure contagion effect between energy and nonenergy commodity markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(10), pages 1960-1986, October.
    8. Christa Cuchiero & Guido Gazzani & Janka Moller & Sara Svaluto-Ferro, 2023. "Joint calibration to SPX and VIX options with signature-based models," Papers 2301.13235, arXiv.org, revised Jul 2024.
    9. Tong, Chen, 2024. "Pricing CBOE VIX in non-affine GARCH models with variance risk premium," Finance Research Letters, Elsevier, vol. 62(PA).

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