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This paper is concerned with evaluation of American options in discrete time, also called Bermudan options. We use the dual approach to derive upper bounds on the price of such options using only a reduced number of nested Monte Carlo steps. The key idea is to apply nonparametric regression to estimate continuation values and all other required conditional expectations and to combine the resulting estimate with another estimate computed by using only a reduced number of nested Monte Carlo steps. The expectation of the resulting estimate is an upper bound on the option price. It is shown that the estimates of the option prices are universally consistent, i.e., they converge to the true price regardless of the structure of the continuation values. The finite sample behavior is validated by experiments on simulated data.

Upper bounds for Bermudan options on Markovian data using nonparametric regression and a reduced number of nested Monte Carlo steps