IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb649/sfb649dp2007-048.html
   My bibliography  Save this paper

Sensitivities for Bermudan options by regression methods

Author

Listed:
  • Belomestny, Denis
  • Milstein, Grigori N.
  • Schoenmakers, John G. M.

Abstract

In this article we propose several pathwise and finite difference based methods for calculating sensitivities of Bermudan options using regression methods and Monte Carlo simulation. These methods rely on conditional probabilistic representations which allow, in combination with a regression approach, for efficient simultaneous computation of sensitivities at many initial positions. Assuming that the price of a Bermudan option can be evaluated sufficiently accurate, we develop a method for constructing deltas based on least squares. We finally propose a testing procedure for assessing the performance of the developed methods.

Suggested Citation

  • Belomestny, Denis & Milstein, Grigori N. & Schoenmakers, John G. M., 2007. "Sensitivities for Bermudan options by regression methods," SFB 649 Discussion Papers 2007-048, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
  • Handle: RePEc:zbw:sfb649:sfb649dp2007-048
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/25220/1/558608590.PDF
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Anastasia Kolodko & John Schoenmakers, 2006. "Iterative construction of the optimal Bermudan stopping time," Finance and Stochastics, Springer, vol. 10(1), pages 27-49, January.
    3. Denis Belomestny, 2009. "Pricing Bermudan options using nonparametric regression: optimal rates of convergence for lower estimates," Papers 0907.5599, arXiv.org.
    4. Joerg Kampen & Anastasia Kolodko & John Schoenmakers, 2008. "Monte Carlo Greeks for financial products via approximative transition densities," Papers 0807.1213, 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. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    8. Belomestny, Denis & Milstein, Grigori N., 2006. "Adaptive simulation algorithms for pricing American and Bermudan options by local analysis of financial market," SFB 649 Discussion Papers 2006-038, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    9. Belomestny, Denis, 2009. "Pricing Bermudan options using regression: Optimal rates of convergence for lower estimates," SFB 649 Discussion Papers 2009-023, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    10. 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.
    11. Denis Belomestny & Grigori N. Milstein, 2006. "Monte Carlo Evaluation Of American Options Using Consumption Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 455-481.
    12. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    13. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    14. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    15. Vladimir V. Piterbarg, 2004. "Risk Sensitivities Of Bermuda Swaptions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 465-509.
    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. repec:hum:wpaper:sfb649dp2007-060 is not listed on IDEAS
    2. Werner Hürlimann, 2012. "Valuation of fixed and variable rate mortgages: binomial tree versus analytical approximations," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 35(2), pages 171-202, November.
    3. 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.
    4. Perederiy, Volodymyr, 2007. "Kombinierte Liquiditäts- und Solvenzkennzahlen und ein darauf basierendes Insolvenzprognosemodell für deutsche GmbHs," SFB 649 Discussion Papers 2007-060, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. Nan Chen & Yanchu Liu, 2014. "American Option Sensitivities Estimation via a Generalized Infinitesimal Perturbation Analysis Approach," Operations Research, INFORMS, vol. 62(3), pages 616-632, June.

    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. 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.
    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. Ammann, Manuel & Kind, Axel & Wilde, Christian, 2008. "Simulation-based pricing of convertible bonds," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 310-331, March.
    4. Mark Broadie & Menghui Cao, 2008. "Improved lower and upper bound algorithms for pricing American options by simulation," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 845-861.
    5. 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.
    6. John Schoenmakers, 2012. "A pure martingale dual for multiple stopping," Finance and Stochastics, Springer, vol. 16(2), pages 319-334, April.
    7. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    8. 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.
    9. Fabian Dickmann & Nikolaus Schweizer, 2014. "Faster Comparison of Stopping Times by Nested Conditional Monte Carlo," Papers 1402.0243, arXiv.org.
    10. 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.
    11. 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.
    12. 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.
    13. Bradley Sturt, 2021. "A nonparametric algorithm for optimal stopping based on robust optimization," Papers 2103.03300, arXiv.org, revised Mar 2023.
    14. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    15. Zbigniew Palmowski & Tomasz Serafin, 2020. "A Note on Simulation Pricing of π -Options," Risks, MDPI, vol. 8(3), pages 1-19, August.
    16. Nan Chen & Yanchu Liu, 2014. "American Option Sensitivities Estimation via a Generalized Infinitesimal Perturbation Analysis Approach," Operations Research, INFORMS, vol. 62(3), pages 616-632, June.
    17. Christian Fries & Joerg Kampen, 2010. "Global existence, regularity and a probabilistic scheme for a class of ultraparabolic Cauchy problems," Papers 1002.5031, arXiv.org, revised Oct 2012.
    18. Chen Liu & Henry Schellhorn & Qidi Peng, 2019. "American Option Pricing With Regression: Convergence Analysis," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-31, December.
    19. Joerg Kampen & Anastasia Kolodko & John Schoenmakers, 2008. "Monte Carlo Greeks for financial products via approximative transition densities," Papers 0807.1213, arXiv.org.
    20. 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.

    More about this item

    Keywords

    American and Bermudan options; Optimal stopping times; Monte Carlo simulation; Deltas; Conditional probabilistic representations; Regression methods;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    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:zbw:sfb649:sfb649dp2007-048. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sohubde.html .

    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.