Asian options can be priced on the unrecombining binomial tree.Unfor-
tunately,without approximation,the running time is exponential.This pa-
per presents e fficient 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 -perio binomial tree,our algorithm runs
in O (kn 2 )time with a guaranteed error bound of O (X √n/k )for any positive
integer k .Parameter k can be adjusted for any esired trade-o ffbetween time
and accuracy.This basic algorithm is then mo i fied to give increasingly tighter
upper and lower bounds (or range bounds )that bracket the desired option
value while maintaining the same computational e fficiency.As the upper and
lower bounds are essentially numerically identical in practice,the proposed al-
gorithms can be said to price European-style Asian options exactly without
combinatorial explosion.Our results also imply for the first time in the lit-
erature that the popular Hull-White algorithms are upper-bound algorithms.
Extensive computer experiments are conducted to con firm the extreme accu-
racy of the algorithms and their competitiveness in comparison with alternative
schemes
