Extension of the corrected barrier approximation by Broadie, Glasserman, and Kou (Q1424714)

This paper continues the work initiated by \textit{M. Broadie}, \textit{P. Glasserman} and \textit{S. G. Kou} [Math. Finance 7, No. 4, 325--349 (1997; Zbl 1020.91020)] and determines formulas for estimating the price of discrete up-and-out/in calls, down-and-out/in puts and double barrier options, where the barrier is monitored only at specific dates. In contrast to continuous barrier options, the price of discrete barrier option does not in general possess a closed form price formula, and the aim of the paper is to give estimates of prices of single and double barrier options. It is assumed that the underlying asset evolves under the risk-neutral martingale measure according to the price \[ S_t=S_0e^{(r-q-\sigma^2/2)t}+\sigma w_t,\;t\geq 0. \] The estimates of prices are given in terms of constants \(S_0, r, q, \sigma\) and some functions constructed by the standard normal distribution function. Accuracies in the pricing formulas are given in numerical examples both for single and double barrier options.