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-Ross-Rubinstein (1979) 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 (1993) 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 (1995) and Chalasani-Jha-Varikooty (1998). Our algorithms run in time proportional to the number of nodelets in the refined lattice, which is smaller than n4/20 for n > 14 periods.
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Chalasani, P., Jha, S., Egriboyun, F. et al. A Refined Binomial Lattice for Pricing American Asian Options. Review of Derivatives Research 3, 85–105 (1999). https://doi.org/10.1023/A:1009622231124
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DOI: https://doi.org/10.1023/A:1009622231124