A Refined Binomial Lattice for Pricing American Asian Options

Authors: Chalasani P.¹; Jha S.²; Egriboyun F.³; Varikooty A.³

Source: Review of Derivatives Research, Volume 3, Number 1, 1999 , pp. 85-105(21)

Publisher: Springer

Buy & download fulltext article:

Price: $47.00 plus tax (Refund Policy)

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 n^4/20for n > 14 periods.

Keywords: American options; Asian options; path-dependent options; binomial model; stopping times

Language: English

Document Type: Regular paper

Affiliations: 1: Computer Science Dept, Arizona State University, Tempe, AZ 85287 2: Computer Science Dept, Carnegie Mellon University, Pittsburgh, PA 15213 3: CS First Boston, NY

Publication date: 1999-01-01