IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v11y2023i3p61-d1099372.html
   My bibliography  Save this article

Backward Deep BSDE Methods and Applications to Nonlinear Problems

Author

Listed:
  • Yajie Yu

    (Corporate Model Risk, Wells Fargo, New York, NY 10017, USA)

  • Narayan Ganesan

    (Corporate Model Risk, Wells Fargo, New York, NY 10017, USA)

  • Bernhard Hientzsch

    (Corporate Model Risk, Wells Fargo, New York, NY 10017, USA)

Abstract

We present a pathwise deep Backward Stochastic Differential Equation (BSDE) method for Forward Backward Stochastic Differential Equations with terminal conditions that time-steps the BSDE backwards and apply it to the differential rates problem as a prototypical nonlinear problem of independent financial interest. The nonlinear equation for the backward time-step is solved exactly or by a Taylor-based approximation. This is the first application of such a pathwise backward time-stepping deep BSDE approach for problems with nonlinear generators. We extend the method to the case when the initial value of the forward components X can be a parameter rather than fixed and similarly to also learn values at intermediate times. We present numerical results for a call combination and for a straddle, the latter comparing well to those obtained by Forsyth and Labahn with a specialized PDE solver.

Suggested Citation

  • Yajie Yu & Narayan Ganesan & Bernhard Hientzsch, 2023. "Backward Deep BSDE Methods and Applications to Nonlinear Problems," Risks, MDPI, vol. 11(3), pages 1-16, March.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:3:p:61-:d:1099372
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/11/3/61/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/11/3/61/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Haojie Wang & Han Chen & Agus Sudjianto & Richard Liu & Qi Shen, 2018. "Deep Learning-Based BSDE Solver for Libor Market Model with Application to Bermudan Swaption Pricing and Hedging," Papers 1807.06622, arXiv.org, revised Sep 2018.
    2. Warin Xavier, 2018. "Nesting Monte Carlo for high-dimensional non-linear PDEs," Monte Carlo Methods and Applications, De Gruyter, vol. 24(4), pages 225-247, December.
    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. Bernhard Hientzsch, 2023. "Reinforcement Learning and Deep Stochastic Optimal Control for Final Quadratic Hedging," Papers 2401.08600, arXiv.org.

    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. Jian Liang & Zhe Xu & Peter Li, 2019. "Deep Learning-Based Least Square Forward-Backward Stochastic Differential Equation Solver for High-Dimensional Derivative Pricing," Papers 1907.10578, arXiv.org, revised Oct 2020.
    2. Erhan Bayraktar & Qi Feng & Zhaoyu Zhang, 2022. "Deep Signature Algorithm for Multi-dimensional Path-Dependent Options," Papers 2211.11691, arXiv.org, revised Jan 2024.
    3. Bing Yu & Xiaojing Xing & Agus Sudjianto, 2019. "Deep-learning based numerical BSDE method for barrier options," Papers 1904.05921, arXiv.org.
    4. Lorenc Kapllani & Long Teng, 2024. "A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations," Papers 2404.08456, arXiv.org.
    5. Jori Hoencamp & Shashi Jain & Drona Kandhai, 2023. "A Semi-Static Replication Method for Bermudan Swaptions under an Affine Multi-Factor Model," Risks, MDPI, vol. 11(10), pages 1-41, September.
    6. Yajie Yu & Bernhard Hientzsch & Narayan Ganesan, 2020. "Backward Deep BSDE Methods and Applications to Nonlinear Problems," Papers 2006.07635, arXiv.org.
    7. Jiawei Huo, 2023. "Finite Difference Solution Ansatz approach in Least-Squares Monte Carlo," Papers 2305.09166, arXiv.org, revised Nov 2023.
    8. Jiefei Yang & Guanglian Li, 2024. "Gradient-enhanced sparse Hermite polynomial expansions for pricing and hedging high-dimensional American options," Papers 2405.02570, 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:gam:jrisks:v:11:y:2023:i:3:p:61-:d:1099372. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.