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Pricing VIX Futures Under a Markov‐Switching GARCH Framework

Author

Listed:
  • Fangsheng Yin
  • Yiling You
  • Tianyi Wang
  • Mei Yu

Abstract

We propose a Markov‐switching GARCH framework to describe the VIX series. Unlike previous studies on derivatives pricing, both the conditional mean and conditional variance here are allowed to vary with the market state described by a hidden Markov chain process. This switching framework preserves the good properties, under which we derive the analytical pricing formula for the VIX futures. In addition, to make it feasible in practice, we design a novel analytical algorithm that can efficiently filter out all the unobserved variables in the model. The empirical studies show that adding the Markov‐switching terms can significantly improve the fit of the underlying VIX series and the pricing performance of the VIX futures both in‐ and out‐of‐sample. Our research highlights the importance of incorporating regime switches that can be viewed as an additional risk factor into the model framework.

Suggested Citation

  • Fangsheng Yin & Yiling You & Tianyi Wang & Mei Yu, 2025. "Pricing VIX Futures Under a Markov‐Switching GARCH Framework," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 45(12), pages 2262-2281, December.
    • Handle: RePEc:wly:jfutmk:v:45:y:2025:i:12:p:2262-2281
    DOI: 10.1002/fut.70041
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    References listed on IDEAS

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    1. Chao‐Chun Chen & Ming‐Yang Hung, 2010. "Option pricing under Markov‐switching GARCH processes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(5), pages 444-464, May.
    2. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat, 2012. "Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options," Journal of Financial Economics, Elsevier, vol. 106(3), pages 447-472.
    3. Pan, Zhiyuan & Wang, Yudong & Wu, Chongfeng & Yin, Libo, 2017. "Oil price volatility and macroeconomic fundamentals: A regime switching GARCH-MIDAS model," Journal of Empirical Finance, Elsevier, vol. 43(C), pages 130-142.
    4. Franc Klaassen, 2002. "Improving GARCH volatility forecasts with regime-switching GARCH," Empirical Economics, Springer, vol. 27(2), pages 363-394.
    5. 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.
    6. Ekaterini Panopoulou & Theologos Pantelidis, 2015. "Regime-switching models for exchange rates," The European Journal of Finance, Taylor & Francis Journals, vol. 21(12), pages 1023-1069, September.
    7. Donald Aingworth & Sanjiv Das & Rajeev Motwani, 2006. "A simple approach for pricing equity options with Markov switching state variables," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 95-105.
    8. Andrew Ang & Geert Bekaert & Min Wei, 2008. "The Term Structure of Real Rates and Expected Inflation," Journal of Finance, American Finance Association, vol. 63(2), pages 797-849, April.
    9. Xin Zang & Jun Ni & Jing-Zhi Huang & Lan Wu, 2017. "Double-jump diffusion model for VIX: evidence from VVIX," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 227-240, February.
    10. Tianyi Wang & Sicong Cheng & Fangsheng Yin & Mei Yu, 2022. "Directly pricing VIX futures: the role of dynamic volatility and jump intensity," Applied Economics, Taylor & Francis Journals, vol. 54(32), pages 3678-3694, July.
    11. Calvet, Laurent E. & Fearnley, Marcus & Fisher, Adlai J. & Leippold, Markus, 2015. "What is beneath the surface? Option pricing with multifrequency latent states," Journal of Econometrics, Elsevier, vol. 187(2), pages 498-511.
    12. Robert J. Elliott & Tak Kuen Siu & Leunglung Chan, 2006. "Option Pricing For Garch Models With Markov Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(06), pages 825-841.
    13. Park, Yang-Ho, 2016. "The effects of asymmetric volatility and jumps on the pricing of VIX derivatives," Journal of Econometrics, Elsevier, vol. 192(1), pages 313-328.
    14. Ardia, David & Bluteau, Keven & Boudt, Kris & Catania, Leopoldo, 2018. "Forecasting risk with Markov-switching GARCH models:A large-scale performance study," International Journal of Forecasting, Elsevier, vol. 34(4), pages 733-747.
    15. Gerrit Reher & Bernd Wilfling, 2016. "A nesting framework for Markov-switching GARCH modelling with an application to the German stock market," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 411-426, March.
    16. Segnon, Mawuli & Gupta, Rangan & Wilfling, Bernd, 2024. "Forecasting stock market volatility with regime-switching GARCH-MIDAS: The role of geopolitical risks," International Journal of Forecasting, Elsevier, vol. 40(1), pages 29-43.
    17. Cui, Zhenyu & Lee, Chihoon & Liu, Yanchu, 2018. "Single-transform formulas for pricing Asian options in a general approximation framework under Markov processes," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1134-1139.
    18. Jiqian Wang & Feng Ma & Chao Liang & Zhonglu Chen, 2022. "Volatility forecasting revisited using Markov‐switching with time‐varying probability transition," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(1), pages 1387-1400, January.
    19. Billio, Monica & Casarin, Roberto & Osuntuyi, Anthony, 2018. "Markov switching GARCH models for Bayesian hedging on energy futures markets," Energy Economics, Elsevier, vol. 70(C), pages 545-562.
    20. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
    21. Herrera, Ana María & Hu, Liang & Pastor, Daniel, 2018. "Forecasting crude oil price volatility," International Journal of Forecasting, Elsevier, vol. 34(4), pages 622-635.
    22. Gongyue Jiang & Gaoxiu Qiao & Feng Ma & Lu Wang, 2022. "Directly pricing VIX futures with observable dynamic jumps based on high‐frequency VIX," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(8), pages 1518-1548, August.
    23. Augustyniak, Maciej, 2014. "Maximum likelihood estimation of the Markov-switching GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 61-75.
    24. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    25. Song‐Ping Zhu & Guang‐Hua Lian, 2012. "An analytical formula for VIX futures and its applications," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(2), pages 166-190, February.
    26. Bhat, Harish S. & Kumar, Nitesh, 2012. "Option pricing under a normal mixture distribution derived from the Markov tree model," European Journal of Operational Research, Elsevier, vol. 223(3), pages 762-774.
    27. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
    28. 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).
    29. Maddalena Cavicchioli, 2022. "Markov Switching Garch Models: Higher Order Moments, Kurtosis Measures, and Volatility Evaluation in Recessions and Pandemic," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1772-1783, October.
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