A matched asymptotic expansions approach to continuity corrections for discretely sampled options. Part 1: barrier options

Sam Howison and Mario Steinberg

OFRC Working Papers Series from Oxford Financial Research Centre

Abstract: We discuss the `continuity correction' that should be applied to relate the prices of discretely sampled barrier options and their continuously-sampled equivalents. Using a matched asymptotic expansions approach we show that the correction of Broadie, Glasserman \& Kou (\emph{Mathematical Finance} {\bf 7}, 325 (1997)) can be applied in a very wide variety of cases. We calculate the correction to higher order in terms of the expansion parameter (the scaled time between resets) and we show how to apply the correction in jump-diffusion and local volatility models.

Date: 2005
New Economics Papers: this item is included in nep-fin
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