Abstract: A barrier option is a derivative contract that is activated or extinguished when the price of the underlying asset crosses a certain level. Most models assume continuous monitoring of the barrier. However in practice most, if not all, barrier options traded in markets are discretely monitored. Unlike their continuous counterparts, there is essentially no closed form solution available, and even numerical pricing is difficult. This paper extends an approximation by Broadie, Glasserman and Kou (1997) for discretely monitored barrier options by covering more cases and giving a simpler proof. The techniques used here come from sequential analysis, particularly Siegmund and Yuh (1982) and Siegmund (1985).
Key words and phrases: Girsanov theorem, level crossing probabilities, Siegmund's corrected diffusion approximation.