Extremely Accurate and Efficient Algorithms for European-Style Asian Options with Range Bounds

Asian options can be priced on the unrecombining binomial tree. Unfortunately, without approximation, the running time is exponential. This paper presents efficient and extremely accurate approximation algorithms for European-style Asian options on the binomial tree. For a European-style Asian option with strike price X on an n-period binomial tree, our algorithm runs in O(kn2) time with a guaranteed error bound of O(X √ n/k) for any positive integer k. Parameter k can be adjusted for any desired trade-off between time and accuracy. This basic algorithm is then modified to give increasingly tighter upper and lower bounds (or range bounds) that bracket the desired option value while maintaining the same computational efficiency. As the upper and lower bounds are essentially numerically identical in practice, the proposed algorithms can be said to price European-style Asian options exactly without combinatorial explosion. Our results also imply for the first time in the literature that the popular Hull-White algorithms are upper-bound algorithms. Extensive computer experiments are conducted to confirm the extreme accuracy of the algorithms and their competitiveness in comparison with alternative schemes.