Iterative construction of the optimal Bermudan stopping time

We present an iterative procedure for computing the optimal Bermudan stopping time, hence the Bermudan Snell envelope. The method produces an increasing sequence of approximations of the Snell envelope from below, which coincide with the Snell envelope after finitely many steps. Then, by duality, the method induces a convergent sequence of upper bounds as well. In a Markovian setting the presented iterative procedure allows to calculate approximative solutions with only a few nestings of conditionals expectations and is therefore tailor-made for a plain Monte-Carlo implementation. The method presented may be considered generic for all discrete optimal stopping problems. The power of the procedure is demonstrated at Bermudan swaptions in a full factor LIBOR market model.