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VIX term structure and VIX futures pricing with realized volatility

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  • Zhuo Huang
  • Chen Tong
  • Tianyi Wang

Abstract

Using an extended LHARG model proposed by Majewski et al. (2015, J Econ, 187, 521–531), we derive the closed‐form pricing formulas for both the Chicago Board Options Exchange VIX term structure and VIX futures with different maturities. Our empirical results suggest that the quarterly and yearly components of lagged realized volatility should be added into the model to capture the long‐term volatility dynamics. By using the realized volatility based on high‐frequency data, the proposed model provides superior pricing performance compared with the classic Heston–Nandi GARCH model under a variance‐dependent pricing kernel, both in‐sample and out‐of‐sample. The improvement is more pronounced during high volatility periods.

Suggested Citation

  • Zhuo Huang & Chen Tong & Tianyi Wang, 2019. "VIX term structure and VIX futures pricing with realized volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(1), pages 72-93, January.
    • Handle: RePEc:wly:jfutmk:v:39:y:2019:i:1:p:72-93
    DOI: 10.1002/fut.21955
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    1. Cheng, Hung-Wen & Chang, Li-Han & Lo, Chien-Ling & Tsai, Jeffrey Tzuhao, 2023. "Empirical performance of component GARCH models in pricing VIX term structure and VIX futures," Journal of Empirical Finance, Elsevier, vol. 72(C), pages 122-142.
    2. Wang, Yajing & Liang, Fang & Wang, Tianyi & Huang, Zhuo, 2020. "Does measurement error matter in volatility forecasting? Empirical evidence from the Chinese stock market," Economic Modelling, Elsevier, vol. 87(C), pages 148-157.
    3. Shi Yafeng & Yanlong Shi & Ying Tingting, 2024. "Can technical indicators based on underlying assets help to predict implied volatility index," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(1), pages 57-74, January.
    4. 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.
    5. Wang, Qi & Wang, Zerong, 2020. "VIX valuation and its futures pricing through a generalized affine realized volatility model with hidden components and jump," Journal of Banking & Finance, Elsevier, vol. 116(C).
    6. Wenjun Zhang & Jin E. Zhang, 2020. "GARCH Option Pricing Models and the Variance Risk Premium," JRFM, MDPI, vol. 13(3), pages 1-21, March.
    7. Qi Wang & Zerong Wang, 2021. "VIX futures and its closed‐form pricing through an affine GARCH model with realized variance," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(1), pages 135-156, January.
    8. Hongkai Cao & Rupak Chatterjee & Zhenyu Cui, 2019. "Options valuation and calibration for leveraged exchange-traded funds with Heston–Nandi and inverse Gaussian GARCH models," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(03), pages 1-37, September.
    9. Albers, Stefan, 2023. "The fear of fear in the US stock market: Changing characteristics of the VVIX," Finance Research Letters, Elsevier, vol. 55(PA).
    10. Xu Gong & Mingchao Wang & Liuguo Shao, 2022. "The impact of macro economy on the oil price volatility from the perspective of mixing frequency," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(4), pages 4487-4514, October.
    11. 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.
    12. 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).
    13. 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.
    14. 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.
    15. Chen, Xiaoyi & Feng, JianFen & Wang, Tianyi, 2023. "Pricing VIX futures: A framework with random level shifts," Finance Research Letters, Elsevier, vol. 52(C).
    16. 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.
    17. 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.
    18. Mora-Valencia, Andrés & Rodríguez-Raga, Santiago & Vanegas, Esteban, 2021. "Skew index: Descriptive analysis, predictive power, and short-term forecast," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
    19. 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).
    20. 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).
    21. 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.
    22. 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.

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