A bias-reduction technique for Monte Carlo pricing of early-exercise options

We present a new method for reducing the bias present in Monte-Carlo estimators of the price of American-style contingent claims. At each exercise opportunity (in a time discretization), we assume there is an unbiased estimator of the claim value at the next exercise opportunity. We approximate the distribution of this statistic using the central limit theorem, and use this to derive an asymptotic expression for the bias. This expression is easily estimated in the context of a simulation, which allows for the straightforward computation of bias-reduced estimators of the claim value. We conclude by presenting a well-studied multivariate pricing example to show that this method offers significant improvements over the vanilla stochastic mesh technique, and that it is much more computationally efficient approach to reducing bias than nonparametric bootstrapping.