IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v34y2021i2d10.1007_s10959-020-00992-4.html
   My bibliography  Save this article

Pathwise Asymptotics for Volterra Type Stochastic Volatility Models

Author

Listed:
  • Miriana Cellupica

    (Poste Italiane)

  • Barbara Pacchiarotti

    (Università di Roma Tor Vergata)

Abstract

We study stochastic volatility models in which the volatility process is a positive continuous function of a continuous Volterra stochastic process. We state some pathwise large deviation principles for the scaled log-price.

Suggested Citation

  • Miriana Cellupica & Barbara Pacchiarotti, 2021. "Pathwise Asymptotics for Volterra Type Stochastic Volatility Models," Journal of Theoretical Probability, Springer, vol. 34(2), pages 682-727, June.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:2:d:10.1007_s10959-020-00992-4
    DOI: 10.1007/s10959-020-00992-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-020-00992-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-020-00992-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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, 2018. "Gaussian stochastic volatility models: Scaling regimes, large deviations, and moment explosions," Papers 1808.00421, arXiv.org, revised Jun 2019.
    3. Archil Gulisashvili, 2017. "Large deviation principle for Volterra type fractional stochastic volatility models," Papers 1710.10711, arXiv.org, revised Aug 2018.
    4. Tommi Sottinen & Lauri Viitasaari, 2016. "Stochastic Analysis of Gaussian Processes via Fredholm Representation," International Journal of Stochastic Analysis, Hindawi, vol. 2016, pages 1-15, July.
    5. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    6. Lucia Caramellino & Barbara Pacchiarotti & Simone Salvadei, 2015. "Large Deviation Approaches for the Numerical Computation of the Hitting Probability for Gaussian Processes," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 383-401, June.
    Full references (including those not matched with items on IDEAS)

    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. Eduardo Abi Jaber, 2022. "The Laplace transform of the integrated Volterra Wishart process," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 309-348, January.
    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. 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.
    4. 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.
    5. 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.
    6. Paul Gassiat, 2018. "On the martingale property in the rough Bergomi model," Papers 1811.10935, arXiv.org, revised Apr 2019.
    7. 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.
    8. Archil Gulisashvili, 2020. "Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness," Papers 2002.05143, arXiv.org, revised Dec 2020.
    9. Antoine Jacquier & Alexandre Pannier, 2020. "Large and moderate deviations for stochastic Volterra systems," Papers 2004.10571, arXiv.org, revised Apr 2022.
    10. Stefan Gerhold & Christoph Gerstenecker & Archil Gulisashvili, 2020. "Large deviations for fractional volatility models with non-Gaussian volatility driver," Papers 2003.12825, arXiv.org.
    11. 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.
    12. Josselin Garnier & Knut Sølna, 2018. "Option pricing under fast-varying and rough stochastic volatility," Annals of Finance, Springer, vol. 14(4), pages 489-516, November.
    13. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    14. Elisa Alòs & Maria Elvira Mancino & Tai-Ho Wang, 2019. "Volatility and volatility-linked derivatives: estimation, modeling, and pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 321-349, December.
    15. Carsten H. Chong & Viktor Todorov, 2023. "Asymptotic Expansions for High-Frequency Option Data," Papers 2304.12450, arXiv.org.
    16. Xiyue Han & Alexander Schied, 2022. "Robust Faber--Schauder approximation based on discrete observations of an antiderivative," Papers 2211.11907, arXiv.org, revised Oct 2024.
    17. Calypso Herrera & Florian Krach & Pierre Ruyssen & Josef Teichmann, 2021. "Optimal Stopping via Randomized Neural Networks," Papers 2104.13669, arXiv.org, revised Dec 2023.
    18. Zhu, Qinwen & Diao, Xundi & Wu, Chongfeng, 2023. "Volatility forecast with the regularity modifications," Finance Research Letters, Elsevier, vol. 58(PA).
    19. Bastien Baldacci, 2020. "High-frequency dynamics of the implied volatility surface," Papers 2012.10875, arXiv.org.
    20. Tommi Sottinen & Lauri Viitasaari, 2018. "Parameter estimation for the Langevin equation with stationary-increment Gaussian noise," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 569-601, October.

    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:spr:jotpro:v:34:y:2021:i:2:d:10.1007_s10959-020-00992-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.