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Regression methods in pricing American and Bermudan options using consumption processes

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Author Info
Denis Belomestny
Grigori N. Milstein
Vladimir Spokoiny

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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.

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Publisher Info
Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-051.

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Length: 30 pages
Date of creation: Jul 2006
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Handle: RePEc:hum:wpaper:sfb649dp2006-051

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

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Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 14(1), pages 113-47.
  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. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. Vladislav Kargin, 2003. "Lattice Option Pricing By Multidimensional Interpolation," Finance 0309003, EconWPA, revised 29 Oct 2004. [Downloadable!]
    Other versions:
  5. Anastasia Kolodko & John Schoenmakers, 2006. "Iterative construction of the optimal Bermudan stopping time," Finance and Stochastics, Springer, vol. 10(1), pages 27-49, 01. [Downloadable!] (restricted)
  6. 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. [Downloadable!]
  7. Vlad Bally & Gilles Pagès & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Blackwell Publishing, vol. 15(1), pages 119-168. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

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  4. Zdenek Hlavka & Michal Pesta, 2006. "Constrained General Regression in Pseudo-Sobolev Spaces with Application to Option Pricing," SFB 649 Discussion Papers SFB649DP2006-069, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  9. Dirk Temme & Lutz Hildebrandt, 2006. "Formative Measurement Models in Covariance Structure Analysis: Specification and Identification," SFB 649 Discussion Papers SFB649DP2006-083, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  11. Ying Chen & Wolfgang Härdle & Vladimir Spokoiny, 2006. "GHICA - Risk Analysis with GH Distributions and Independent Components," SFB 649 Discussion Papers SFB649DP2006-078, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  12. Carsten Trenkler & Pentti Saikkonen & Helmut Lütkepohl, 2006. "Testing for the Cointegrating Rank of a VAR Process with Level Shift and Trend Break," SFB 649 Discussion Papers SFB649DP2006-067, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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