Tight bounds for American options via multilevel Monte Carlo

This paper is an overview of recent results by Belomestny and Schoenmakers 2011 and Belomestny, Ladkau, and Schoenmakers 2012, on dual and primal Monte Carlo evaluation of American style derivatives using multilevel principles. It presents a novel and generic approach to reduce the complexity of nested simulations problems arising in Monte Carlo pricing of American options. The approach genuinely uses the multilevel idea where each level corresponds to a given number of inner simulations. A thorough complexity analysis of the respective nested dual algorithm and nested policy improvement algorithm shows that a significant complexity reduction can be achieved by using the multilevel versions of the algorithms.