Abstract

. 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-RossRubinstein [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 [5] 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 [11] 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. Keywords: American Options, Asian Options, Path-depend...

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