Electronic copy available at: http://ssrn.com/abstract=1526765 Bermudan Option Pricing with Monte-Carlo Methods Raphaºl Douady  January 30, 2002 Abstract We explain, compare and improve two algorithms to compute American or Bermudan options by Monte-Carlo. The rst one is based on threshold optimisation in the exercise strategy (Andersen 1999). The notion of fuzzy threshold is introduced to ease optimisation. The second one uses a linear regression to get an estimate of the option price at intermediary dates and determine the exercise strategy (Carriere 1997, Longsta/-Schwartz 1999). We thoroughly study the convergence of these two approaches, including a mixture of both. 1. Introduction American and Bermudan option pricing in a Monte-Carlo framework is, in theory, impossible because it requires the value of the option at intermediary dates  in order to decide whether to exercise or to keep it  an information that is usually not provided. Actually, rather than the value of the option, one needs an optimal exercise strategy, that is, for each trajectory, an optimal date when to exercise the option. In this situation, the word optimal means that it maximizes the price of the option  which is computed as usual by averaging the pay-out, including early exercise  among all acceptable strategies (probabilists use the word adapted ).  C.N.R.S. and Ecole Normale SupØrieure, C.M.L.A., 61 av. du Pdt Wilson, 94235 Cachan Cedex, France. E-mail: rdouady@cmla.ens-cachan.fr