Efficiently pricing European–Asian options—ultimate implementation and analysis of the AMO algorithm

Abstract

We propose an efficient and accurate randomized approximation algorithm for pricing a European-Asian option on the binomial tree model. For an option with the strike price X on an n-step binomial tree and any positive integer k, our algorithm runs in O(kn 2) time with the error bound O(X/k) which is independent of n. Our algorithm is a modification of the approximation algorithm developed by Aingworth, Motwani, and Oldham (2000) into a randomized algorithm, which improves the accuracy theoretically as well as practically.