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Gatheral double stochastic volatility model with Skorokhod reflection

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  • Yuliya Mishura
  • Andrey Pilipenko
  • Kostiantyn Ralchenko

Abstract

We investigate the Gatheral model of double mean-reverting stochastic volatility, in which the drift term itself follows a mean-reverting process, and the overall model exhibits mean-reverting behavior. We demonstrate that such processes can attain values arbitrarily close to zero and remain near zero for extended periods, making them practically and statistically indistinguishable from zero. To address this issue, we propose a modified model incorporating Skorokhod reflection, which preserves the model's flexibility while preventing volatility from approaching zero.

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  • Yuliya Mishura & Andrey Pilipenko & Kostiantyn Ralchenko, 2025. "Gatheral double stochastic volatility model with Skorokhod reflection," Papers 2505.09184, arXiv.org.
    • Handle: RePEc:arx:papers:2505.09184
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    References listed on IDEAS

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    1. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    2. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    3. Giulia Di Nunno & Kęstutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From Constant to Rough: A Survey of Continuous Volatility Modeling," Mathematics, MDPI, vol. 11(19), pages 1-35, October.
    4. Liu Chang & Shouting Chen & Ailin Zhu, 2015. "Properties of the Cox–Ingersoll–Ross Interest Rate Processes with Two-sided Reflections," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(4), pages 657-670, February.
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    6. Shi, Yiwei & Shu, Huisheng & Wang, Chunyang & Zhang, Xuekang, 2025. "Parameter estimation for Cox–Ingersoll–Ross process with two-sided reflections," Statistics & Probability Letters, Elsevier, vol. 221(C).
    7. Christian Bayer & Jim Gatheral & Morten Karlsmark, 2013. "Fast Ninomiya--Victoir calibration of the double-mean-reverting model," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1813-1829, November.
    8. Mishura, Yuliya & Ralchenko, Kostiantyn & Dehtiar, Olena, 2022. "Parameter estimation in CKLS model by continuous observations," Statistics & Probability Letters, Elsevier, vol. 184(C).
    9. Olena Dehtiar & Yuliya Mishura & Kostiantyn Ralchenko, 2022. "Two methods of estimation of the drift parameters of the Cox–Ingersoll–Ross process: Continuous observations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(19), pages 6818-6833, October.
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