IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-03436046.html
   My bibliography  Save this paper

Pricing Bermudan options using regression trees/random forests

Author

Listed:
  • Zineb El Filali Ech-Chafiq

    (DAO - Données, Apprentissage et Optimisation - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes, Natixis)

  • Pierre Henry Labordère

    (Natixis)

  • Jérôme Lelong

    (DAO - Données, Apprentissage et Optimisation - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes)

Abstract

The value of an American option is the maximized value of the discounted cash flows from the option. At each time step, one needs to compare the immediate exercise value with the continuation value and decide to exercise as soon as the exercise value is strictly greater than the continuation value. We can formulate this problem as a dynamic programming equation, where the main difficulty comes from the computation of the conditional expectations representing the continuation values at each time step. In (Longstaff and Schwartz, 2001), these conditional expectations were estimated using regressions on a finite-dimensional vector space (typically a polynomial basis). In this paper, we follow the same algorithm; only the conditional expectations are estimated using Regression trees or Random forests. We discuss the convergence of the LS algorithm when the standard least squares regression is replaced with regression trees. Finally, we expose some numerical results with regression trees and random forests. The random forest algorithm gives excellent results in high dimensions.

Suggested Citation

  • Zineb El Filali Ech-Chafiq & Pierre Henry Labordère & Jérôme Lelong, 2023. "Pricing Bermudan options using regression trees/random forests," Post-Print hal-03436046, HAL.
  • Handle: RePEc:hal:journl:hal-03436046
    DOI: 10.1137/21M1460648
    Note: View the original document on HAL open archive server: https://hal.science/hal-03436046v2
    as

    Download full text from publisher

    File URL: https://hal.science/hal-03436046v2/document
    Download Restriction: no

    File URL: https://libkey.io/10.1137/21M1460648?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
    ---><---

    References listed on IDEAS

    as
    1. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    2. 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.
    3. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    4. Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.
    5. Vlad Bally & Gilles Pagès & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 119-168, January.
    6. Dragos Florin Ciocan & Velibor V. Mišić, 2022. "Interpretable Optimal Stopping," Management Science, INFORMS, vol. 68(3), pages 1616-1638, March.
    7. Philip Protter & Emmanuelle Clément & Damien Lamberton, 2002. "An analysis of a least squares regression method for American option pricing," Finance and Stochastics, Springer, vol. 6(4), pages 449-471.
    8. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2019. "Variance Reduction Applied to Machine Learning for Pricing Bermudan/American Options in High Dimension," Papers 1903.11275, arXiv.org, revised Dec 2019.
    9. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    10. 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.
    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. Lukas Gonon, 2024. "Deep neural network expressivity for optimal stopping problems," Finance and Stochastics, Springer, vol. 28(3), pages 865-910, July.

    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. Zineb El Filali Ech-Chafiq & Pierre Henry-Labordere & Jérôme Lelong, 2021. "Pricing Bermudan options using regression trees/random forests," Working Papers hal-03436046, HAL.
    2. Denis Belomestny & Grigori Milstein & Vladimir Spokoiny, 2009. "Regression methods in pricing American and Bermudan options using consumption processes," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 315-327.
    3. Belomestny, Denis & Milstein, Grigori N. & Spokoiny, Vladimir, 2006. "Regression methods in pricing American and Bermudan options using consumption processes," SFB 649 Discussion Papers 2006-051, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. Zineb El Filali Ech-Chafiq & Pierre Henry-Labordere & J'er^ome Lelong, 2021. "Pricing Bermudan options using regression trees/random forests," Papers 2201.02587, arXiv.org, revised Jun 2023.
    5. 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.
    6. Jérôme Lelong, 2019. "Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach," Working Papers hal-01983115, HAL.
    7. 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, revised Apr 2024.
    8. Bradley Sturt, 2021. "A nonparametric algorithm for optimal stopping based on robust optimization," Papers 2103.03300, arXiv.org, revised Mar 2023.
    9. Burcu Aydoğan & Ümit Aksoy & Ömür Uğur, 2018. "On the methods of pricing American options: case study," Annals of Operations Research, Springer, vol. 260(1), pages 79-94, January.
    10. J'er^ome Lelong, 2019. "Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach," Papers 1901.05672, arXiv.org, revised Jul 2020.
    11. Maximilian Mair & Jan Maruhn, 2013. "On the primal-dual algorithm for callable Bermudan options," Review of Derivatives Research, Springer, vol. 16(1), pages 79-110, April.
    12. Jain, Shashi & Oosterlee, Cornelis W., 2015. "The Stochastic Grid Bundling Method: Efficient pricing of Bermudan options and their Greeks," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 412-431.
    13. Jin, Xing & Yang, Cheng-Yu, 2016. "Efficient estimation of lower and upper bounds for pricing higher-dimensional American arithmetic average options by approximating their payoff functions," International Review of Financial Analysis, Elsevier, vol. 44(C), pages 65-77.
    14. Volker Krätschmer & Marcel Ladkau & Roger J. A. Laeven & John G. M. Schoenmakers & Mitja Stadje, 2018. "Optimal Stopping Under Uncertainty in Drift and Jump Intensity," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1177-1209, November.
    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. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    17. Garcia, Diego, 2003. "Convergence and Biases of Monte Carlo estimates of American option prices using a parametric exercise rule," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1855-1879, August.
    18. 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.
    19. Louis Bhim & Reiichiro Kawai, 2018. "Smooth Upper Bounds For The Price Function Of American Style Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-38, February.
    20. Vijay V. Desai & Vivek F. Farias & Ciamac C. Moallemi, 2012. "Pathwise Optimization for Optimal Stopping Problems," Management Science, INFORMS, vol. 58(12), pages 2292-2308, December.

    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:journl:hal-03436046. 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.