IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2002.05143.html
   My bibliography  Save this paper

Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness

Author

Listed:
  • Archil Gulisashvili

Abstract

We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. The main results obtained in the paper are sample path and small-noise large deviation principles for the log-price process in a time-inhomogeneous super rough Gaussian model under very mild restrictions. We use these results to study the asymptotic behavior of binary barrier options, exit time probability functions, and call options.

Suggested Citation

  • Archil Gulisashvili, 2020. "Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness," Papers 2002.05143, arXiv.org, revised Dec 2020.
    • Handle: RePEc:arx:papers:2002.05143
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2002.05143
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Archil Gulisashvili, 2017. "Large deviation principle for Volterra type fractional stochastic volatility models," Papers 1710.10711, arXiv.org, revised Aug 2018.
    2. Baldi, P. & Caramellino, L., 2011. "General Freidlin-Wentzell Large Deviations and positive diffusions," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1218-1229, August.
    3. Archil Gulisashvili & Frederi Viens & Xin Zhang, 2015. "Extreme-Strike Asymptotics for General Gaussian Stochastic Volatility Models," Papers 1502.05442, arXiv.org, revised Feb 2017.
    4. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    5. Josselin Garnier & Knut Solna, 2015. "Correction to Black-Scholes formula due to fractional stochastic volatility," Papers 1509.01175, arXiv.org, revised Mar 2017.
    6. Robertson, Scott, 2010. "Sample path Large Deviations and optimal importance sampling for stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 66-83, January.
    7. Archil Gulisashvili, 2018. "Gaussian stochastic volatility models: Scaling regimes, large deviations, and moment explosions," Papers 1808.00421, arXiv.org, revised Jun 2019.
    8. Archil Gulisashvili & Frederi Viens & Xin Zhang, 2019. "Extreme-strike asymptotics for general Gaussian stochastic volatility models," Annals of Finance, Springer, vol. 15(1), pages 59-101, March.
    9. Archil Gulisashvili & Frederi Viens & Xin Zhang, 2015. "Small-time asymptotics for Gaussian self-similar stochastic volatility models," Papers 1505.05256, arXiv.org, revised Mar 2016.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Archil Gulisashvili, 2020. "Large deviation principles for stochastic volatility models with reflection and three faces of the Stein and Stein model," Papers 2006.15431, arXiv.org.
    2. Christian Bayer & Fabian Andsem Harang & Paolo Pigato, 2020. "Log-modulated rough stochastic volatility models," Papers 2008.03204, arXiv.org, revised May 2021.
    3. Peter K. Friz & Paul Gassiat & Paolo Pigato, 2022. "Short-dated smile under rough volatility: asymptotics and numerics," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 463-480, March.
    4. Archil Gulisashvili, 2022. "Multivariate Stochastic Volatility Models and Large Deviation Principles," Papers 2203.09015, arXiv.org, revised Nov 2022.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Archil Gulisashvili, 2020. "Large deviation principles for stochastic volatility models with reflection and three faces of the Stein and Stein model," Papers 2006.15431, arXiv.org.
    2. 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.
    3. Archil Gulisashvili, 2018. "Gaussian stochastic volatility models: Scaling regimes, large deviations, and moment explosions," Papers 1808.00421, arXiv.org, revised Jun 2019.
    4. 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.
    5. Archil Gulisashvili, 2022. "Multivariate Stochastic Volatility Models and Large Deviation Principles," Papers 2203.09015, arXiv.org, revised Nov 2022.
    6. Giacomo Giorgio & Barbara Pacchiarotti & Paolo Pigato, 2023. "Short-Time Asymptotics for Non-Self-Similar Stochastic Volatility Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(3), pages 123-152, May.
    7. Antoine Jacquier & Alexandre Pannier, 2020. "Large and moderate deviations for stochastic Volterra systems," Papers 2004.10571, arXiv.org, revised Apr 2022.
    8. Giacomo Giorgio & Barbara Pacchiarotti & Paolo Pigato, 2023. "Short-Time Asymptotics for Non-Self-Similar Stochastic Volatility Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(3), pages 123-152, May.
    9. Jacquier, Antoine & Pannier, Alexandre, 2022. "Large and moderate deviations for stochastic Volterra systems," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 142-187.
    10. Christian Bayer & Peter K. Friz & Paul Gassiat & Jorg Martin & Benjamin Stemper, 2020. "A regularity structure for rough volatility," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 782-832, July.
    11. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    12. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Finance and Stochastics, Springer, vol. 26(4), pages 733-769, October.
    13. Eduardo Abi Jaber & Shaun & Li, 2024. "Volatility models in practice: Rough, Path-dependent or Markovian?," Papers 2401.03345, arXiv.org.
    14. Florian Bourgey & Stefano De Marco & Peter K. Friz & Paolo Pigato, 2023. "Local volatility under rough volatility," Mathematical Finance, Wiley Blackwell, vol. 33(4), pages 1119-1145, October.
    15. Marc Geha & Antoine Jacquier & Zan Zuric, 2021. "Large and moderate deviations for importance sampling in the Heston model," Papers 2111.00348, arXiv.org.
    16. Huy N. Chau & Duy Nguyen & Thai Nguyen, 2024. "On short-time behavior of implied volatility in a market model with indexes," Papers 2402.16509, arXiv.org, revised Apr 2024.
    17. Eduardo Abi Jaber, 2022. "The Laplace transform of the integrated Volterra Wishart process," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 309-348, January.
    18. Peter K. Friz & Thomas Wagenhofer, 2023. "Reconstructing volatility: Pricing of index options under rough volatility," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 19-40, January.
    19. Paul Gassiat, 2018. "On the martingale property in the rough Bergomi model," Papers 1811.10935, arXiv.org, revised Apr 2019.
    20. Florian Bourgey & Stefano De Marco & Peter K. Friz & Paolo Pigato, 2023. "Local volatility under rough volatility," Mathematical Finance, Wiley Blackwell, vol. 33(4), pages 1119-1145, October.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2002.05143. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.