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Pricing Bermudan options using regression: optimal rates of convergence for lower estimates

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  • Denis Belomestny

Abstract

The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal nonasymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some estimates of continuation values. These estimates may be of different nature, they may be local or global, with the only requirement being that the deviations of these estimates from the true continuation values can be uniformly bounded in probability.

Suggested Citation

  • Denis Belomestny, 2009. "Pricing Bermudan options using regression: optimal rates of convergence for lower estimates," SFB 649 Discussion Papers SFB649DP2009-023, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2009-023
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2009-023.pdf
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    Citations

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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 & John Schoenmakers & Fabian Dickmann, 2013. "Multilevel dual approach for pricing American style derivatives," Finance and Stochastics, Springer, vol. 17(4), pages 717-742, October.

    More about this item

    Keywords

    Bermudan options; Regression; Boundary condition;
    All these keywords.

    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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