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Under the assumption of no-arbitrage, the pricing of American and Bermudanoptions can be casted into optimal stopping problems. We propose a new adaptivesimulation based algorithm for the numerical solution of optimal stoppingproblems in discrete time. Our approach is to recursively compute the so-calledcontinuation values. They are defined as regression functions of the cash flow,which would occur over a series of subsequent time periods, if the approximatedoptimal exercise strategy is applied. We use nonparametric least squaresregression estimates to approximate the continuation values from a set ofsample paths which we simulate from the underlying stochastic process. Theparameters of the regression estimates and the regression problems are chosenin a data-dependent manner. We present results concerning the consistency andrate of convergence of the new algorithm. Finally, we illustrate itsperformance by pricing high-dimensional Bermudan basket options withstrangle-spread payoff based on the average of the underlying assets.

A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options