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Option Pricing with the Realized GARCH Model: An Analytical Approximation Approach

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  • Zhuo Huang
  • Tianyi Wang
  • Peter Reinhard Hansen

Abstract

We derive a pricing formula for European options for the Realized GARCH framework based on an analytical approximation using an Edgeworth expansion for the density of cumulative return. Existing approximations in this context are based on a Gram–Charlier expansion while the proper Edgeworth expansion is more accurate. In relation to existing discrete‐time option pricing models with realized volatility, our model is log‐linear, non‐affine, with a flexible leverage effect. We conduct an extensive empirical analysis on S&P500 index options and the results show that our computationally fast formula outperforms competing methods in terms of pricing errors, both in‐sample and out‐of‐sample. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:328–358, 2017

Suggested Citation

  • Zhuo Huang & Tianyi Wang & Peter Reinhard Hansen, 2017. "Option Pricing with the Realized GARCH Model: An Analytical Approximation Approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(4), pages 328-358, April.
    • Handle: RePEc:wly:jfutmk:v:37:y:2017:i:4:p:328-358
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    Cited by:

    1. Wu, Xinyu & Xia, Michelle & Zhang, Huanming, 2020. "Forecasting VaR using realized EGARCH model with skewness and kurtosis," Finance Research Letters, Elsevier, vol. 32(C).
    2. Martin, Vance L. & Tang, Chrismin & Yao, Wenying, 2021. "Forecasting the volatility of asset returns: The informational gains from option prices," International Journal of Forecasting, Elsevier, vol. 37(2), pages 862-880.
    3. Haibin Xie & Xinyu Wu & Pengying Fan, 2021. "Accelerating FHS Option Pricing Under Linear GARCH," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 395-411, August.
    4. Yan Liu & Xiong Zhang, 2023. "Option Pricing Using LSTM: A Perspective of Realized Skewness," Mathematics, MDPI, vol. 11(2), pages 1-21, January.
    5. Fang Liang & Lingshan Du & Zhuo Huang, 2023. "Option pricing with overnight and intraday volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(11), pages 1576-1614, November.
    6. 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.
    7. Wenjun Zhang & Jin E. Zhang, 2020. "GARCH Option Pricing Models and the Variance Risk Premium," JRFM, MDPI, vol. 13(3), pages 1-21, March.
    8. Mozumder, Sharif & Frijns, Bart & Talukdar, Bakhtear & Kabir, M. Humayun, 2024. "On practitioners closed-form GARCH option pricing," International Review of Financial Analysis, Elsevier, vol. 94(C).
    9. Peter Reinhard Hansen & Zhuo Huang & Chen Tong & Tianyi Wang, 2024. "Realized GARCH, CBOE VIX, and the Volatility Risk Premium," Journal of Financial Econometrics, Oxford University Press, vol. 22(1), pages 187-223.
    10. Peter Reinhard Hansen & Chen Tong, 2022. "Option Pricing with Time-Varying Volatility Risk Aversion," Papers 2204.06943, arXiv.org, revised Aug 2024.
    11. Gong, Xu & Lin, Boqiang, 2019. "Modeling stock market volatility using new HAR-type models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 194-211.
    12. Junting Liu & Qi Wang & Yuanyuan Zhang, 2024. "VIX option pricing through nonaffine GARCH dynamics and semianalytical formula," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1189-1223, July.
    13. Papantonis, Ioannis & Rompolis, Leonidas & Tzavalis, Elias, 2023. "Improving variance forecasts: The role of Realized Variance features," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1221-1237.
    14. 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.
    15. Chen Tong & Peter Reinhard Hansen & Zhuo Huang, 2022. "Option pricing with state‐dependent pricing kernel," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(8), pages 1409-1433, August.
    16. Zhang, Yuanyuan & Zhang, Qian & Wang, Zerong & Wang, Qi, 2024. "Option valuation via nonaffine dynamics with realized volatility," Journal of Empirical Finance, Elsevier, vol. 77(C).
    17. Moritz Jirak, 2021. "Edgeworth expansions for volatility models," Papers 2111.00529, arXiv.org, revised Sep 2022.
    18. Tianyi Wang & Sicong Cheng & Fangsheng Yin & Mei Yu, 2022. "Overnight volatility, realized volatility, and option pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1264-1283, July.
    19. Fang Liang & Lingshan Du, 2024. "Option pricing with dynamic conditional skewness," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1154-1188, July.
    20. Zargar, Faisal Nazir & Kumar, Dilip, 2020. "Heterogeneous market hypothesis approach for modeling unbiased extreme value volatility estimator in presence of leverage effect: An individual stock level study with economic significance analysis," The Quarterly Review of Economics and Finance, Elsevier, vol. 77(C), pages 271-285.
    21. Qiao, Gaoxiu & Yang, Jiyu & Li, Weiping, 2020. "VIX forecasting based on GARCH-type model with observable dynamic jumps: A new perspective," The North American Journal of Economics and Finance, Elsevier, vol. 53(C).
    22. Xie, Haibin & Yu, Chengtan, 2020. "Realized GARCH models: Simpler is better," Finance Research Letters, Elsevier, vol. 33(C).
    23. Qiao, Gaoxiu & Jiang, Gongyue & Yang, Jiyu, 2022. "VIX term structure forecasting: New evidence based on the realized semi-variances," International Review of Financial Analysis, Elsevier, vol. 82(C).
    24. Wu, Xinyu & Zhao, An & Liu, Li, 2023. "Forecasting VIX using two-component realized EGARCH model," The North American Journal of Economics and Finance, Elsevier, vol. 67(C).
    25. 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.

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