A Refined Binomial Lattice for Pricing American Asian Options

We present simple and fast algorithms for computing very tight upper and lower bounds on the prices of American Asian options in the binomial model. We introduce a new refined version of the Cox-Ross-Rubinstein [4] binomial lattice of stock prices. Each node in the lattice is partitioned into "nodelets", each of which represents all paths arriving at the node with a specific geometric stock price average. The upper bound uses an interpolation idea similar to the Hull-White [6] method. From the backward-recursive upper-bound computation, we estimate a good exercise rule that is consistent with the refined lattice. This exercise rule is used to obtain a lower bound on the option price using a modification of a conditional-expectation based idea from Rogers-Shi [12] and Chalasani-Jha-Varikooty [3]. Our algorithms run in time proportional to the number of nodelets in the refined lattice, which is smaller than n 4 =20 for n periods