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Regression methods in pricing American and Bermudan options using consumption processes

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Listed:
  • Denis Belomestny
  • Grigori N. Milstein
  • Vladimir Spokoiny

Abstract

Here we develop methods for e±cient pricing multidimensional discrete-time American and Bermudan options by using regression based algorithms together with a new approach towards constructing upper bounds for the price of the option. Applying the sample space with payoffs at the optimal stopping times, we propose sequential estimates for continuation values, values of the consumption process, and stopping times on the sample paths. The approach admits constructing both low and upper bounds for the price by Monte Carlo simulations. The methods are illustrated by pricing Bermudan swaptions and snowballs in the Libor market model.

Suggested Citation

  • Denis Belomestny & Grigori N. Milstein & Vladimir Spokoiny, 2006. "Regression methods in pricing American and Bermudan options using consumption processes," SFB 649 Discussion Papers SFB649DP2006-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2006-051
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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," 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. Vladislav Kargin, 2005. "Lattice Option Pricing By Multidimensional Interpolation," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 635-647.
    5. 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.
    6. 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.
    7. Kolodko A. & Schoenmakers J., 2004. "Upper Bounds for Bermudan Style Derivatives," Monte Carlo Methods and Applications, De Gruyter, vol. 10(3-4), pages 331-343, December.
    8. Anastasia Kolodko & John Schoenmakers, 2006. "Iterative construction of the optimal Bermudan stopping time," Finance and Stochastics, Springer, vol. 10(1), pages 27-49, January.
    9. Denis Belomestny & Grigori Milstein, 2006. "Adaptive Simulation Algorithms for Pricing American and Bermudian Options by Local Analysis of Financial Market," SFB 649 Discussion Papers SFB649DP2006-038, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
    11. 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.
    12. 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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    Cited by:

    1. Denis Belomestny, 2011. "Pricing Bermudan options by nonparametric regression: optimal rates of convergence for lower estimates," Finance and Stochastics, Springer, vol. 15(4), pages 655-683, December.
    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. 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.
    4. John Schoenmakers, 2012. "A pure martingale dual for multiple stopping," Finance and Stochastics, Springer, vol. 16(2), pages 319-334, April.
    5. 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.

    More about this item

    Keywords

    American and Bermudan options; Low and Upper bounds; Monte Carlo simulations; Consumption process; Regression methods; Optimal stopping times;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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