Bermudan option pricing

We explain, compare and improve two algorithms to compute American or Bermudan options by Monte-Carlo. The first 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, Longstaff-Schwartz 1999). We thoroughly study the convergence of these two approaches, including a mixture of both.