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Analytical Upper Bounds for American Option Prices

Published online by Cambridge University Press:  06 April 2009

Ren-Raw Chen  and
Shih-Kuo Yeh
Ren-Raw Chen
Affiliation:
[email protected], Rutgers Business School, Rutgers University, 94 Rockafeller Road, Piscataway, NJ 08854
Shih-Kuo Yeh
Affiliation:
[email protected], Department of Financial Operations, National Kaohsiung First University of Science and Technology, 1 University Road, Kaohsiung, Taiwan 824.
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Abstract

American options require numerical methods, namely lattice models, to provide accurate price estimates. The computations can become expensive when more than one state variable is involved. Analytical upper bounds can therefore provide a useful guideline for how high American values can reach. In this paper, we derive analytical (closed-form) upper bounds for American option prices under stochastic interest rates, stochastic volatility, and jumps where American option prices are difficult to compute with accuracy. In a stochastic volatility model (Heston (1993) and Scott (1997)) that has two random factors, we demonstrate that the upper bound only takes a very small fraction of the time that the American option needs to compute.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 37 , Issue 1 , March 2002 , pp. 117 - 135
Copyright
Copyright © School of Business Administration, University of Washington 2002

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