IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v156y2023icp156-195.html
   My bibliography  Save this article

Sensitivity analysis with respect to a stochastic stock price model with rough volatility via a Bismut–Elworthy–Li formula for singular SDEs

Author

Listed:
  • Coffie, Emmanuel
  • Duedahl, Sindre
  • Proske, Frank

Abstract

In this paper, we show the existence of unique Malliavin differentiable solutions to SDE‘s driven by a fractional Brownian motion with Hurst parameter H<12 and singular, unbounded drift vector fields, for which we also prove a stability result. Further, using the latter results, we propose a stock price model with rough and correlated volatility, which also allows for capturing regime switching effects. Finally, we derive a Bismut–Elworthy–Li formula with respect to our stock price model for certain classes of vector fields.

Suggested Citation

  • Coffie, Emmanuel & Duedahl, Sindre & Proske, Frank, 2023. "Sensitivity analysis with respect to a stochastic stock price model with rough volatility via a Bismut–Elworthy–Li formula for singular SDEs," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 156-195.
    • Handle: RePEc:eee:spapps:v:156:y:2023:i:c:p:156-195
    DOI: 10.1016/j.spa.2022.11.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922002332
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.11.001?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. D. Baños & T. Meyer-Brandis & F. Proske & S. Duedahl, 2017. "Computing deltas without derivatives," Finance and Stochastics, Springer, vol. 21(2), pages 509-549, April.
    2. Catellier, R. & Gubinelli, M., 2016. "Averaging along irregular curves and regularisation of ODEs," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2323-2366.
    3. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    4. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux, 2001. "Applications of Malliavin calculus to Monte-Carlo methods in finance. II," Finance and Stochastics, Springer, vol. 5(2), pages 201-236.
    5. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394, arXiv.org.
    6. David Baños & Salvador Ortiz-Latorre & Andrey Pilipenko & Frank Proske, 2022. "Strong Solutions of Stochastic Differential Equations with Generalized Drift and Multidimensional Fractional Brownian Initial Noise," Journal of Theoretical Probability, Springer, vol. 35(2), pages 714-771, June.
    7. Nualart, David & Ouknine, Youssef, 2002. "Regularization of differential equations by fractional noise," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 103-116, November.
    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. Maria Elvira Mancino & Simona Sanfelici, 2020. "Nonparametric Malliavin–Monte Carlo Computation of Hedging Greeks," Risks, MDPI, vol. 8(4), pages 1-17, November.
    2. Anne Laure Bronstein & Gilles Pagès & Jacques Portès, 2013. "Multi-asset American Options and Parallel Quantization," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 547-561, September.
    3. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    4. Arturo Kohatsu-Higa & Miquel Montero, 2001. "An application of Malliavin Calculus to Finance," Papers cond-mat/0111563, arXiv.org.
    5. Hyungbin Park, 2018. "Sensitivity analysis of long-term cash flows," Finance and Stochastics, Springer, vol. 22(4), pages 773-825, October.
    6. Bally Vlad & Caramellino Lucia & Zanette Antonino, 2005. "Pricing and hedging American options by Monte Carlo methods using a Malliavin calculus approach," Monte Carlo Methods and Applications, De Gruyter, vol. 11(2), pages 97-133, June.
    7. Ruzong Fan & Hong-Bin Fang, 2022. "Stochastic functional linear models and Malliavin calculus," Computational Statistics, Springer, vol. 37(2), pages 591-611, April.
    8. David Baños & Salvador Ortiz-Latorre & Andrey Pilipenko & Frank Proske, 2022. "Strong Solutions of Stochastic Differential Equations with Generalized Drift and Multidimensional Fractional Brownian Initial Noise," Journal of Theoretical Probability, Springer, vol. 35(2), pages 714-771, June.
    9. Michael C. Fu, 2008. "What you should know about simulation and derivatives," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(8), pages 723-736, December.
    10. W. Ackooij & X. Warin, 2020. "On conditional cuts for stochastic dual dynamic programming," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(2), pages 173-199, June.
    11. Montero, Miquel & Kohatsu-Higa, Arturo, 2003. "Malliavin Calculus applied to finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 548-570.
    12. Iksanov, Alexander & Pilipenko, Andrey, 2023. "On a skew stable Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 44-68.
    13. Robert J. Elliott & Tak Kuen Siu, 2023. "Hedging options in a hidden Markov‐switching local‐volatility model via stochastic flows and a Monte‐Carlo method," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(7), pages 925-950, July.
    14. Gassiat, Paul & Mądry, Łukasz, 2023. "Perturbations of singular fractional SDEs," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 137-172.
    15. Akihiko Takahashi & Toshihiro Yamada, 2012. "A Remark on Approximation of the Solutions to Partial Differential Equations in Finance," CIRJE F-Series CIRJE-F-842, CIRJE, Faculty of Economics, University of Tokyo.
    16. Koike, Takaaki & Saporito, Yuri & Targino, Rodrigo, 2022. "Avoiding zero probability events when computing Value at Risk contributions," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 173-192.
    17. Elisa Alòs & Christian-Olivier Ewald, 2005. "A note on the Malliavin differentiability of the Heston volatility," Economics Working Papers 880, Department of Economics and Business, Universitat Pompeu Fabra.
    18. Yeliz Yolcu-Okur & Tilman Sayer & Bilgi Yilmaz & B. Alper Inkaya, 2018. "Computation of the Delta of European options under stochastic volatility models," Computational Management Science, Springer, vol. 15(2), pages 213-237, June.
    19. John Armstrong & Andrei Ionescu, 2023. "Gamma Hedging and Rough Paths," Papers 2309.05054, arXiv.org, revised Mar 2024.
    20. Yuri F. Saporito, 2020. "Pricing Path-Dependent Derivatives under Multiscale Stochastic Volatility Models: a Malliavin Representation," Papers 2005.04297, 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:eee:spapps:v:156:y:2023:i:c:p:156-195. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.