A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options

This paper discusses 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 it is shown that the correction of Broadie, Glasserman & Kou (Mathematical Finance 7, 325 (1997)) can be applied in a very wide variety of cases. The correction to higher order is calculated in terms of the expansion parameter (the scaled time between resets) and it is shown how to apply the correction in jump-diffusion and local volatility models.