The optimal method for pricing bermudan options by simulation

Longstaff and Schwartz (2001) least-squares approach is the de facto method for pricing Bermudan options by simulation. We address the optimal method for pricing Bermudan options, by deriving the cost function associated to suboptimal exercise. From the first order conditions, the optimal estimator is a local least-squares estimator, where only small and significant value-matching errors (i.e., the difference between continuation and intrinsic values) are orthogonal to the regressors. Therefore, this estimator has two key properties: First, it is a linear estimator, which iterates a few local, instead of one, regressions. And second, it estimates the (most significant part of the) exercise boundary, which is, precisely, characterized by the value-matching property. In addition, we show why a simple quadratic basis of functions for the regressors works well in practice. We prove the convergence of the local least-squares method and our numerical exercise confirms that it is easy to implement and yields the best prices.