I shall discuss the 'continuity correction' that should be applied to a discretely sampled barrier or Bermudan option. This problem has been analysed by Brodie, Glasserman and Kou, who calculated the barrier correction with an error inversely proportional to the number of sampling dates, but only for the constant parameter Black-Scholes model. I show how to use the method of matched asymptotic expansions to obtain the correction as accurately as desires, and how to extend the method to the case of non-constant parameters. I then show how to calculate the continuity correction for a Bermudan (discretely sampled American) option.

• Howison_Jan05.pdf

Please feel free to bring this to the attention of interested colleagues.