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Sensitivities for Bermudan options by regression methods

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    9. Anastasia Kolodko & John Schoenmakers, 2006. "Iterative construction of the optimal Bermudan stopping time," Finance and Stochastics, Springer, vol. 10(1), pages 27-49, January.
    10. Denis Belomestny, 2009. "Pricing Bermudan options using nonparametric regression: optimal rates of convergence for lower estimates," Papers 0907.5599, arXiv.org.
    11. Joerg Kampen & Anastasia Kolodko & John Schoenmakers, 2008. "Monte Carlo Greeks for financial products via approximative transition densities," Papers 0807.1213, arXiv.org.
    12. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    13. 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.
    14. 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.
    15. 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.
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    Citations

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    Cited by:

    1. 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.
    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. repec:hum:wpaper:sfb649dp2007-060 is not listed on IDEAS
    4. 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.
    5. 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.

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    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

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