IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-00567729.html
   My bibliography  Save this paper

A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options

Author

Listed:
  • Céline Labart

    (LAMA - Laboratoire de Mathématiques - USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc - CNRS - Centre National de la Recherche Scientifique)

  • Jérôme Lelong

    (MATHFI - Financial mathematics - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École des Ponts ParisTech - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12, MATHFI - Mathématiques financières - LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique)

Abstract

We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our algorithm based on Gobet and Labart (2010) exploits the link between BSDEs and non linear partial differential equations (PDEs in short) and hence enables to solve high dimensional non linear PDEs. In this work, we apply it to the pricing and hedging of American options in high dimensional local volatility models, which remains very computationally demanding. We have tested our algorithm up to dimension 10 on a cluster of 512 CPUs and we obtained linear speedups which proves the scalability of our implementation

Suggested Citation

  • Céline Labart & Jérôme Lelong, 2011. "A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options," Working Papers hal-00567729, HAL.
    • Handle: RePEc:hal:wpaper:hal-00567729
    Note: View the original document on HAL open archive server: https://hal.science/hal-00567729
    as

    Download full text from publisher

    File URL: https://hal.science/hal-00567729/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Pierre L'Ecuyer & Richard Simard & E. Jack Chen & W. David Kelton, 2002. "An Object-Oriented Random-Number Package with Many Long Streams and Substreams," Operations Research, INFORMS, vol. 50(6), pages 1073-1075, December.
    2. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    3. Bally, Vlad & Pagès, Gilles, 2003. "Error analysis of the optimal quantization algorithm for obstacle problems," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 1-40, July.
    4. Gilles Pag`es & Benedikt Wilbertz, 2011. "GPGPUs in computational finance: Massive parallel computing for American style options," Papers 1101.3228, arXiv.org.
    5. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    6. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    7. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    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. Lorenc Kapllani & Long Teng, 2020. "Deep learning algorithms for solving high dimensional nonlinear backward stochastic differential equations," Papers 2010.01319, arXiv.org, revised Jun 2022.
    2. Masaaki Fujii & Akihiko Takahashi, 2012. "Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method," CARF F-Series CARF-F-278, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2015.
    3. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen & Timo Welti, 2019. "Solving high-dimensional optimal stopping problems using deep learning," Papers 1908.01602, arXiv.org, revised Aug 2021.

    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. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen & Timo Welti, 2019. "Solving high-dimensional optimal stopping problems using deep learning," Papers 1908.01602, arXiv.org, revised Aug 2021.
    2. Ivan Guo & Nicolas Langren'e & Jiahao Wu, 2023. "Simultaneous upper and lower bounds of American option prices with hedging via neural networks," Papers 2302.12439, arXiv.org.
    3. Andrew Lesniewski & Anja Richter, 2016. "Managing counterparty credit risk via BSDEs," Papers 1608.03237, arXiv.org, revised Aug 2016.
    4. Ludkovski, Michael & Young, Virginia R., 2008. "Indifference pricing of pure endowments and life annuities under stochastic hazard and interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 14-30, February.
    5. Lokman A. Abbas-Turki & Ioannis Karatzas & Qinghua Li, 2014. "Impulse Control of a Diffusion with a Change Point," Papers 1404.1761, arXiv.org.
    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. Steven Kou & Xianhua Peng & Xingbo Xu, 2016. "EM Algorithm and Stochastic Control in Economics," Papers 1611.01767, arXiv.org.
    8. Berridge, S.J. & Schumacher, J.M., 2002. "An Irregular Grid Approach for Pricing High Dimensional American Options," Other publications TiSEM 416a6d43-3466-47e0-b656-d, Tilburg University, School of Economics and Management.
    9. Jérôme Lelong, 2020. "Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach," Post-Print hal-01983115, HAL.
    10. Ioannis Exarchos & Evangelos Theodorou & Panagiotis Tsiotras, 2019. "Stochastic Differential Games: A Sampling Approach via FBSDEs," Dynamic Games and Applications, Springer, vol. 9(2), pages 486-505, June.
    11. 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.
    12. D. Belomestny & M. Kaledin & J. Schoenmakers, 2019. "Semi-tractability of optimal stopping problems via a weighted stochastic mesh algorithm," Papers 1906.09431, arXiv.org.
    13. Berridge, S.J. & Schumacher, J.M., 2004. "Pricing High-Dimensional American Options Using Local Consistency Conditions," Other publications TiSEM 8c8de631-5039-4eec-a965-3, Tilburg University, School of Economics and Management.
    14. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, vol. 13(2), pages 177-217, July.
    15. Aïd, René & Campi, Luciano & Langrené, Nicolas & Pham, Huyên, 2014. "A probabilistic numerical method for optimal multiple switching problems in high dimension," LSE Research Online Documents on Economics 63011, London School of Economics and Political Science, LSE Library.
    16. Pierre del Moral & Peng Hu & Nadia Oudjane & Bruno Rémillard, 2010. "On the Robustness of the Snell envelope," Working Papers inria-00487103, HAL.
    17. Anne Mackay & Marie-Claude Vachon, 2023. "On an Optimal Stopping Problem with a Discontinuous Reward," Papers 2311.03538, arXiv.org, revised Nov 2023.
    18. Yingming Ge & Lingfei Li & Gongqiu Zhang, 2022. "A Fourier Transform Method for Solving Backward Stochastic Differential Equations," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 385-412, March.
    19. Giorgia Callegaro & Alessandro Gnoatto & Martino Grasselli, 2021. "A Fully Quantization-based Scheme for FBSDEs," Working Papers 07/2021, University of Verona, Department of Economics.
    20. Gilles Pag`es & Benedikt Wilbertz, 2011. "GPGPUs in computational finance: Massive parallel computing for American style options," Papers 1101.3228, 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:hal:wpaper:hal-00567729. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.