Other positions of parameters in the asymptotic expansions of Knock-in barrier option prices

Abstract

Joshi's general method for computing the asymptotic expansions of european options was conceived by placing the strike price at the center of the binomial tree [6]. This set-up showed that the errors in approximating the continuous pricing models bydiscrete ones through asymptotic expansion is of order 1/n. In this paper, we find other positions, aside from the center, for the parameters K (strike price) and B (barrier level) in the asymptotic expansions of Knock-in barrier option prices under Joshi's general method. This has been shown to be possible for the case of an Up-and-In Put(UIP) barrier option in the paper done by Llemit and Escaner [1].