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

Abstract

The problem of pricing Bermudan options using simulations and nonparametric regression is considered. We derive optimal non-asymptotic 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, 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 the required property.