Finance and Stochastics

, Volume 15, Issue 4, pp 655–683 | Cite as

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

Article

Abstract

The problem of pricing Bermudan options using simulations and nonparametric regression is considered. We derive optimal nonasymptotic bounds for the low biased estimate based on a suboptimal stopping rule constructed from some estimates of the optimal continuation values. These estimates may be of different nature, 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 the required property.

Keywords

Bermudan options Nonparametric regression Boundary condition Suboptimal stopping rules 

Mathematics Subject Classification (2000)

62G08 65C05 60G40 

JEL Classification

G10 G12 G13 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

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