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Large deviations for fractional volatility models with non-Gaussian volatility driver

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  • Gerhold, Stefan
  • Gerstenecker, Christoph
  • Gulisashvili, Archil

Abstract

We study non-Gaussian fractional stochastic volatility models. The volatility in such a model is described by a positive function of a stochastic process that is a fractional transform of the solution to an SDE satisfying the Yamada–Watanabe condition. Such models are generalizations of a fractional version of the Heston model considered in Bäuerle and Desmettre (2020). We establish sample path and small-noise large deviation principles for the log-price process in a non-Gaussian model. We also illustrate how to compute the second order Taylor expansion of the rate function, in a simplified example.

Suggested Citation

  • Gerhold, Stefan & Gerstenecker, Christoph & Gulisashvili, Archil, 2021. "Large deviations for fractional volatility models with non-Gaussian volatility driver," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 580-600.
    • Handle: RePEc:eee:spapps:v:142:y:2021:i:c:p:580-600
    DOI: 10.1016/j.spa.2021.09.010
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    References listed on IDEAS

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    1. Hult, Henrik, 2003. "Approximating some Volterra type stochastic integrals with applications to parameter estimation," Stochastic Processes and their Applications, Elsevier, vol. 105(1), pages 1-32, May.
    2. Archil Gulisashvili, 2017. "Large deviation principle for Volterra type fractional stochastic volatility models," Papers 1710.10711, arXiv.org, revised Aug 2018.
    3. Li, Yumeng & Wang, Ran & Yao, Nian & Zhang, Shuguang, 2017. "A moderate deviation principle for stochastic Volterra equation," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 79-85.
    4. Josselin Garnier & Knut Solna, 2015. "Correction to Black-Scholes formula due to fractional stochastic volatility," Papers 1509.01175, arXiv.org, revised Mar 2017.
    5. Gulisashvili, Archil, 2020. "Gaussian stochastic volatility models: Scaling regimes, large deviations, and moment explosions," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3648-3686.
    6. Gulisashvili, Archil, 2021. "Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 37-79.
    7. C. Bayer & P. K. Friz & A. Gulisashvili & B. Horvath & B. Stemper, 2019. "Short-time near-the-money skew in rough fractional volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 19(5), pages 779-798, May.
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    Cited by:

    1. Archil Gulisashvili, 2022. "Multivariate Stochastic Volatility Models and Large Deviation Principles," Papers 2203.09015, arXiv.org, revised Nov 2022.

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