Convergence of the Stochastic Mesh Estimator for Pricing Bermudan Options

Broadie and Glasserman proposed a Monte Carlo algorithm they named stochastic mesh for pricing high-dimensional Bermudan options. Based on simulated states of the assets underlying the option at each exercise opportunity, the method produces an estimator of the option value at each sampled state. We derive an asymptotic upper bound on the probability of error of the mesh estimator under the mild assumption of the finiteness of certain moments. Both the error size and the probability bound are functions that vanish with increasing sample size. Moreover, we report the mesh method's empirical performance on test problems taken from the recent literature. We find that the mesh estimator has large positive bias that decays slowly with the sample size.