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. 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].
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