IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v10y2006i1p27-49.html
   My bibliography  Save this article

Iterative construction of the optimal Bermudan stopping time

Author

Listed:
  • Anastasia Kolodko
  • John Schoenmakers

Abstract

We present an iterative procedure for computing the optimal Bermudan stopping time, hence the Bermudan Snell envelope. The method produces an increasing sequence of approximations of the Snell envelope from below, which coincide with the Snell envelope after finitely many steps. Then, by duality, the method induces a convergent sequence of upper bounds as well. In a Markovian setting the presented procedure allows to calculate approximative solutions with only a few nestings of conditional expectations and is therefore tailor-made for a plain Monte Carlo implementation. The method may be considered generic for all discrete optimal stopping problems. The power of the procedure is demonstrated for Bermudan swaptions in a full factor LIBOR market model. Copyright Springer-Verlag Berlin/Heidelberg 2006

Suggested Citation

  • Anastasia Kolodko & John Schoenmakers, 2006. "Iterative construction of the optimal Bermudan stopping time," Finance and Stochastics, Springer, vol. 10(1), pages 27-49, January.
    • Handle: RePEc:spr:finsto:v:10:y:2006:i:1:p:27-49
    DOI: 10.1007/s00780-005-0168-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00780-005-0168-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00780-005-0168-5?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christoph Reisinger & Rasmus Wissmann, 2012. "Numerical Valuation of Derivatives in High-Dimensional Settings via PDE Expansions," Papers 1209.1909, arXiv.org, revised Oct 2013.
    2. Denis Belomestny & G. Milstein & John Schoenmakers, 2010. "Sensitivities for Bermudan options by regression methods," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(2), pages 117-138, November.
    3. Christian Bayer & Denis Belomestny & Paul Hager & Paolo Pigato & John Schoenmakers, 2020. "Randomized optimal stopping algorithms and their convergence analysis," Papers 2002.00816, arXiv.org.
    4. Christian Bender & Anastasia Kolodko & John Schoenmakers, 2008. "Enhanced policy iteration for American options via scenario selection," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 135-146.
    5. repec:hum:wpaper:sfb649dp2006-051 is not listed on IDEAS
    6. Denis Belomestny & Christian Bender & John Schoenmakers, 2009. "True Upper Bounds For Bermudan Products Via Non‐Nested Monte Carlo," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 53-71, January.
    7. Joerg Kampen & Anastasia Kolodko & John Schoenmakers, 2008. "Monte Carlo Greeks for financial products via approximative transition densities," Papers 0807.1213, arXiv.org.
    8. Dan Andrei Iancu & Nikolaos Trichakis & Do Young Yoon, 2021. "Monitoring with Limited Information," Management Science, INFORMS, vol. 67(7), pages 4233-4251, July.
    9. Beveridge, Christopher & Joshi, Mark & Tang, Robert, 2013. "Practical policy iteration: Generic methods for obtaining rapid and tight bounds for Bermudan exotic derivatives using Monte Carlo simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1342-1361.
    10. Wei, Wei & Zhu, Dan, 2022. "Generic improvements to least squares monte carlo methods with applications to optimal stopping problems," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1132-1144.
    11. 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.
    12. 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.
    13. Krätschmer, Volker & Schoenmakers, John G. M., 2009. "Representations for optimal stopping under dynamic monetary utility functionals," SFB 649 Discussion Papers 2009-055, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    14. 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.
    15. Joshi, Mark & Tang, Robert, 2014. "Effective sub-simulation-free upper bounds for the Monte Carlo pricing of callable derivatives and various improvements to existing methodologies," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 25-45.
    16. Jeechul Woo & Chenru Liu & Jaehyuk Choi, 2024. "Leave‐one‐out least squares Monte Carlo algorithm for pricing Bermudan options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(8), pages 1404-1428, August.
    17. Soren Christensen & Albrecht Irle & Julian Peter Lemburg, 2021. "Flexible forward improvement iteration for infinite time horizon Markovian optimal stopping problems," Papers 2111.13443, arXiv.org.
    18. Christian Bender & Christian Gaertner & Nikolaus Schweizer, 2016. "Pathwise Iteration for Backward SDEs," Papers 1605.07500, arXiv.org, revised Jun 2016.
    19. Roberto Baviera & Lorenzo Giada, 2013. "A perturbative approach to Bermudan options pricing with applications," Quantitative Finance, Taylor & Francis Journals, vol. 13(2), pages 255-263, January.
    20. John Schoenmakers & Junbo Huang & Jianing Zhang, 2011. "Optimal dual martingales, their analysis and application to new algorithms for Bermudan products," Papers 1111.6038, arXiv.org, revised Feb 2012.
    21. Denis Belomestny & John Schoenmakers, 2021. "From optimal martingales to randomized dual optimal stopping," Papers 2102.01533, arXiv.org.
    22. John Schoenmakers, 2012. "A pure martingale dual for multiple stopping," Finance and Stochastics, Springer, vol. 16(2), pages 319-334, April.
    23. Denis Belomestny & John Schoenmakers & Fabian Dickmann, 2013. "Multilevel dual approach for pricing American style derivatives," Finance and Stochastics, Springer, vol. 17(4), pages 717-742, October.

    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:spr:finsto:v:10:y:2006:i:1:p:27-49. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.