IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2301.08232.html
   My bibliography  Save this paper

Efficient Pricing and Hedging of High Dimensional American Options Using Recurrent Networks

Author

Listed:
  • Andrew Na
  • Justin Wan

Abstract

We propose a deep Recurrent neural network (RNN) framework for computing prices and deltas of American options in high dimensions. Our proposed framework uses two deep RNNs, where one network learns the price and the other learns the delta of the option for each timestep. Our proposed framework yields prices and deltas for the entire spacetime, not only at a given point (e.g. t = 0). The computational cost of the proposed approach is linear in time, which improves on the quadratic time seen for feedforward networks that price American options. The computational memory cost of our method is constant in memory, which is an improvement over the linear memory costs seen in feedforward networks. Our numerical simulations demonstrate these contributions, and show that the proposed deep RNN framework is computationally more efficient than traditional feedforward neural network frameworks in time and memory.

Suggested Citation

  • Andrew Na & Justin Wan, 2023. "Efficient Pricing and Hedging of High Dimensional American Options Using Recurrent Networks," Papers 2301.08232, arXiv.org.
    • Handle: RePEc:arx:papers:2301.08232
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2301.08232
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:dau:papers:123456789/4273 is not listed on IDEAS
    2. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    3. Yangang Chen & Justin W. L. Wan, 2021. "Deep neural network framework based on backward stochastic differential equations for pricing and hedging American options in high dimensions," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 45-67, January.
    4. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," CIRJE F-Series CIRJE-F-1069, CIRJE, Faculty of Economics, University of Tokyo.
    5. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    6. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
    7. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," CARF F-Series CARF-F-423, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    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. Jiefei Yang & Guanglian Li, 2024. "A deep primal-dual BSDE method for optimal stopping problems," Papers 2409.06937, 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. Yangang Chen & Justin W. L. Wan, 2019. "Deep Neural Network Framework Based on Backward Stochastic Differential Equations for Pricing and Hedging American Options in High Dimensions," Papers 1909.11532, arXiv.org.
    2. Christian Beck & Lukas Gonon & Arnulf Jentzen, 2024. "Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations," Partial Differential Equations and Applications, Springer, vol. 5(6), pages 1-47, December.
    3. Martin Hutzenthaler & Arnulf Jentzen & Thomas Kruse & Tuan Anh Nguyen, 2020. "A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations," Partial Differential Equations and Applications, Springer, vol. 1(2), pages 1-34, April.
    4. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2018. "Bitcoin technical trading with artificial neural network," CARF F-Series CARF-F-430, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. 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.
    6. F Bourgey & S de Marco & Emmanuel Gobet & Alexandre Zhou, 2020. "Multilevel Monte-Carlo methods and lower-upper bounds in Initial Margin computations," Post-Print hal-02430430, HAL.
    7. F Bourgey & S de Marco & Emmanuel Gobet & Alexandre Zhou, 2020. "Multilevel Monte-Carlo methods and lower-upper bounds in Initial Margin computations," Working Papers hal-02430430, HAL.
    8. Lukas Gonon, 2022. "Deep neural network expressivity for optimal stopping problems," Papers 2210.10443, arXiv.org.
    9. Bourgey Florian & De Marco Stefano & Gobet Emmanuel & Zhou Alexandre, 2020. "Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations," Monte Carlo Methods and Applications, De Gruyter, vol. 26(2), pages 131-161, June.
    10. Ron Kaniel & Stathis Tompaidis & Alexander Zemlianov, 2008. "Efficient Computation of Hedging Parameters for Discretely Exercisable Options," Operations Research, INFORMS, vol. 56(4), pages 811-826, August.
    11. Jiefei Yang & Guanglian Li, 2024. "A deep primal-dual BSDE method for optimal stopping problems," Papers 2409.06937, arXiv.org.
    12. 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.
    13. Jiefei Yang & Guanglian Li, 2024. "Gradient-enhanced sparse Hermite polynomial expansions for pricing and hedging high-dimensional American options," Papers 2405.02570, arXiv.org.
    14. Hendrik Kohrs & Hermann Mühlichen & Benjamin R. Auer & Frank Schuhmacher, 2019. "Pricing and risk of swing contracts in natural gas markets," Review of Derivatives Research, Springer, vol. 22(1), pages 77-167, April.
    15. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2018. "Bitcoin technical trading with artificial neural network," CIRJE F-Series CIRJE-F-1078, CIRJE, Faculty of Economics, University of Tokyo.
    16. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen, 2020. "Pricing and Hedging American-Style Options with Deep Learning," JRFM, MDPI, vol. 13(7), pages 1-12, July.
    17. Lukas Gonon, 2024. "Deep neural network expressivity for optimal stopping problems," Finance and Stochastics, Springer, vol. 28(3), pages 865-910, July.
    18. Ivan Guo & Nicolas Langren'e & Jiahao Wu, 2023. "Simultaneous upper and lower bounds of American-style option prices with hedging via neural networks," Papers 2302.12439, arXiv.org, revised Nov 2024.
    19. Chinonso Nwankwo & Nneka Umeorah & Tony Ware & Weizhong Dai, 2022. "Deep learning and American options via free boundary framework," Papers 2211.11803, arXiv.org, revised Dec 2022.
    20. Nakano, Masafumi & Takahashi, Akihiko & Takahashi, Soichiro, 2018. "Bitcoin technical trading with artificial neural network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 587-609.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:2301.08232. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.