IDEAS home Printed from https://ideas.repec.org/p/ise/remwps/wp03102024.html
   My bibliography  Save this paper

Pseudo rough vol-of-vol through Markovian approximation

Author

Listed:
  • Henrique Guerreiro
  • João Guerra

Abstract

We discuss a possible framework for a (pseudo) rough vol-of-vol model through a multi-factor Markovian approximation of the vol-ofvol process. We identify a key martingale condition which may allow to express the VIX in terms of the solution of a certain Riccati ordinary dierential equation. We derive this equation and provide sucient conditions for the existence of solutions. We also provide some partial results regarding the martingale condition. In particular, we verify a local martingale condition.

Suggested Citation

  • Henrique Guerreiro & João Guerra, 2024. "Pseudo rough vol-of-vol through Markovian approximation," Working Papers REM 2024/0310, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    • Handle: RePEc:ise:remwps:wp03102024
    as

    Download full text from publisher

    File URL: https://rem.rc.iseg.ulisboa.pt/wps/pdf/REM_WP_0310_2024.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    2. Giulia Livieri & Saad Mouti & Andrea Pallavicini & Mathieu Rosenbaum, 2018. "Rough volatility: Evidence from option prices," IISE Transactions, Taylor & Francis Journals, vol. 50(9), pages 767-776, September.
    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. Blanka Horvath & Antoine Jacquier & Aitor Muguruza & Andreas Søjmark, 2024. "Functional central limit theorems for rough volatility," Finance and Stochastics, Springer, vol. 28(3), pages 615-661, July.
    2. 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.
    3. Tetsuya Takaishi, 2019. "Rough volatility of Bitcoin," Papers 1904.12346, arXiv.org.
    4. Fabio Baschetti & Giacomo Bormetti & Silvia Romagnoli & Pietro Rossi, 2020. "The SINC way: A fast and accurate approach to Fourier pricing," Papers 2009.00557, arXiv.org, revised May 2021.
    5. Horvath, Blanka & Jacquier, Antoine & Muguruza, Aitor & Søjmark, Andreas, 2024. "Functional central limit theorems for rough volatility," LSE Research Online Documents on Economics 122848, London School of Economics and Political Science, LSE Library.
    6. Takaishi, Tetsuya, 2020. "Rough volatility of Bitcoin," Finance Research Letters, Elsevier, vol. 32(C).
    7. 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.
    8. 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.
    9. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    10. 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.
    11. 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.
    12. Huy N. Chau & Miklos Rasonyi, 2016. "On optimal investment with processes of long or negative memory," Papers 1608.00768, arXiv.org, revised Mar 2017.
    13. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    14. Blanka Horvath & Josef Teichmann & Žan Žurič, 2021. "Deep Hedging under Rough Volatility," Risks, MDPI, vol. 9(7), pages 1-20, July.
    15. Calypso Herrera & Florian Krach & Pierre Ruyssen & Josef Teichmann, 2021. "Optimal Stopping via Randomized Neural Networks," Papers 2104.13669, arXiv.org, revised Dec 2023.
    16. Masaaki Fukasawa & Tetsuya Takabatake & Rebecca Westphal, 2019. "Is Volatility Rough ?," Papers 1905.04852, arXiv.org, revised May 2019.
    17. Eduardo Abi Jaber & Shaun & Li, 2024. "Volatility models in practice: Rough, Path-dependent or Markovian?," Papers 2401.03345, arXiv.org.
    18. Andrey Itkin, 2023. "The ATM implied skew in the ADO-Heston model," Papers 2309.15044, arXiv.org.
    19. Liang Wang & Weixuan Xia, 2022. "Power‐type derivatives for rough volatility with jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1369-1406, July.
    20. Henrique Guerreiro & Jo~ao Guerra, 2022. "VIX pricing in the rBergomi model under a regime switching change of measure," Papers 2201.10391, arXiv.org.

    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:ise:remwps:wp03102024. 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: Sandra Araújo (email available below). General contact details of provider: https://rem.rc.iseg.ulisboa.pt/ .

    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.