On the binomial tree method and other issues in connection with pricing Bermudan and American options

Joshi and Staunton [<italic>Quantit. Finance</italic>, 2012, <bold>12</bold>, 17--20] have commented on the paper by Prékopa and Szántai [<italic>Quantit. Finance</italic>, 2010, <bold>10</bold>, 59-74] and criticized the statement that the binomial tree method overestimates the option price, under some condition. In this paper we present our more detailed reasoning that clarifies some property of the mechanism behind the binomial tree method, and further numerical results. We also comment on the use of Richardson extrapolation, in this context, and other issues mentioned by Joshi and Staunton.