A matched asymptotic expansions approach to continuity corrections for discretely sampled options. Part 2: Bermudan options

We discuss the `continuity correction' that should be applied to connect the prices of discretely sampled American put options (i.e.Bermudan options) and their continuously-sampled equivalents. Using a matched asymptotic expansions approach we compute the correction and relate it to that discussed by Broadie, Glasserman \& Kou (\emph{Mathematical Finance} {\bf 7}, 325 (1997)) for barrier options. In the Bermudan case, the continuity correction is an order of magnitude smaller than in the corresponding barrier problem. We also show that the optimal exercise boundary in the discrete case is slightly higher than in the continuously sampled case.