The optimal method for pricing Bermudan options by simulation

Pricing Bermudan options by simulation has attracted a lot of interest, since many securities contain early-exercise features and depend on several factors. Longstaff and Schwartz (2001) develop a practical approach, which is based on least-squares and simulation. This paper prices Bermudan options from Merton's (1973) model for perpetual American options which, fi rst, derives the option price for a given policy and, second, optimizes between a family of policies. The first-order conditions associated to this discrete-time optimal stopping-time problem are orthogonality conditions, which are easily implemented by "local" least-squares and simulation. Consistent with this optimality, the reported prices (or lower bounds) of this extension improve upon other methods. So, in the optimal method, Longstaff and Schwartz "local" least-squares approach meets Merton.