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

TL;DR

This paper establishes optimal convergence rates for nonparametric regression methods used to compute lower biased estimates in Bermudan option pricing, providing theoretical bounds and practical estimation techniques.

Contribution

It introduces non-asymptotic bounds for lower biased estimates in Bermudan option pricing using nonparametric regression, including local polynomial methods under regularity conditions.

Findings

Derived optimal non-asymptotic bounds for lower biased estimates

Demonstrated the effectiveness of local polynomial estimates

Provided conditions under which estimates have uniform deviation bounds

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.