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

by Sam Howison

Abstract

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.

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