Pricing Bermudan optionsusing regression: optimalrates of convergence forlower estimates

The problem of pricing Bermudan options using Monte Carlo anda nonparametric regression is considered. We derive optimal nonasymptoticbounds for a lower biased estimate based on the suboptimalstopping rule constructed using some estimates of continuationvalues. These estimates may be of different nature, they may be localor global, with the only requirement being that the deviations of theseestimates from the true continuation values can be uniformly boundedin probability.