Enhanced policy iteration for American options via scenario selection

Kolodko & Schoenmakers and Bender & Schoenmakers introduced a policy iteration that allows the achievement of a tight lower approximation of the price for early exercise options via a nested Monte Carlo simulation in a Markovian setting. In this paper we enhance the algorithm by a scenario selection method. It is demonstrated by numerical examples that the scenario selection can significantly reduce the number of inner simulations actually performed, and thus can greatly speed up the method (by up to a factor of 15 in some examples).