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Adaptive Simulation Algorithms for Pricing American and Bermudian Options by Local Analysis of Financial Market

Author

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  • Denis Belomestny
  • Grigori Milstein

Abstract

Here we develop an approach for efficient pricing discrete-time American and Bermudan options which employs the fact that such options are equivalent to the European ones with a consumption, combined with analysis of the market model over a small number of steps ahead. This approach allows constructing both upper and low bounds for the true price by Monte Carlo simulations. An adaptive choice of local low bounds and use of the kernel interpolation technique enhance efficiency of the whole procedure, which is supported by numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:hum:wpaper:sfb649dp2006-038
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-038.pdf
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    Cited by:

    1. 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.
    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. Denis Belomestny & Pavel V. Gapeev, 2006. "An Iteration Procedure for Solving Integral Equations Related to Optimal Stopping Problems," SFB 649 Discussion Papers SFB649DP2006-043, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    American and Bermudan options; Lower and Upper bounds; Monte Carlo simulation; Variance reduction;
    All these keywords.

    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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