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Pricing Bermudan options using nonparametric 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 non-asymptotic 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. As an illustration, we discuss a class of local polynomial estimates which, under some regularity conditions, yield continuation values estimates possessing this property.

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File URL: http://arxiv.org/pdf/0907.5599
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0907.5599.

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Date of creation: Jul 2009
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Handle: RePEc:arx:papers:0907.5599

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Web page: http://arxiv.org/

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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, vol. 33(2), pages 117-138, November.
  2. Denis Belomestny & Fabian Dickmann & Tigran Nagapetyan, 2013. "Pricing American options via multi-level approximation methods," Papers 1303.1334, arXiv.org, revised Dec 2013.
  3. Fabian Dickmann & Nikolaus Schweizer, 2014. "Faster Comparison of Stopping Times by Nested Conditional Monte Carlo," Papers 1402.0243, arXiv.org.

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