Comparing optimal convergence rate of stochastic mesh and least squares method for Bermudan option pricing

We analyze the stochastic mesh method (SMM) as well as the least squares method (LSM) commonly used for pricing Bermudan options using the standard two phase methodology. For both the methods, we determine the decay rate of mean square error of the estimator as a function of the computational budget allocated to the two phases and ascertain the order of the optimal allocation in these phases. We conclude that with increasing computational budget, while SMM estimator converges at a slower rate compared to LSM estimator, it converges to the true option value whereas LSM estimator, with fixed number of basis functions, usually converges to a biased value