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Generalized Analytical Upper Bounds for American Option Prices

Published online by Cambridge University Press:  06 April 2009

San-Lin Chung  and
Hsieh-Chung Chang
San-Lin Chung
Affiliation:
chungs@management.ntu.edu.tw, National Taiwan University, Department of Finance, 85, Section 4, Roosevelt Road, Taipei 106
Hsieh-Chung Chang
Affiliation:
s1428007@cc.ncu.edu.tw, National Central University, Department of Finance, 300, Chungda Road, Chungli 320, Taiwan
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Abstract

This paper generalizes and tightens Chen and Yeh's (2002) analytical upper bounds for American options under stochastic interest rates, stochastic volatility, and jumps, where American option prices are difficult to compute with accuracy. We first generalize Theorem 1 of Chen and Yeh (2002) and apply it to derive a tighter upper bound for American calls when the interest rate is greater than the dividend yield. Our upper bounds are not only tight, but also converge to accurate American call option prices when the dividend yield or strike price is small or when volatility is large. We then propose a general theorem that can be applied to derive upper bounds for American options whose payoffs depend on several risky assets. As a demonstration, we utilize our general theorem to derive upper bounds for American exchange options and American maximum options on two risky assets.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 42 , Issue 1 , March 2007 , pp. 209 - 227
Copyright
Copyright © School of Business Administration, University of Washington 2007

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