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The Sensitivity of American Options to Suboptimal Exercise Strategies

Published online by Cambridge University Press:  21 September 2010

Alfredo Ibáñez  and
Ioannis Paraskevopoulos
Alfredo Ibáñez
Affiliation:
Caja Madrid, Torre Caja Madrid, Po de la Castellana, 189, 3a planta, 28046 Madrid, Spain. [email protected]
Ioannis Paraskevopoulos
Affiliation:
Caja Madrid, Torre Caja Madrid, Po de la Castellana, 189, 3a planta, 28046 Madrid, Spain. [email protected]
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Abstract

The value of American options depends on the exercise policy followed by option holders. Market frictions, risk aversion, or a misspecified model, for example, can result in suboptimal behavior. We study the sensitivity of American options to suboptimal exercise strategies. We show that this measure is given by the Gamma of the American option at the optimal exercise boundary. More precisely, “if B is the optimal exercise price, but exercise is either brought forward when or delayed until a price B̃ has been reached, the cost of suboptimal exercise is given by ½ × Γ(B) × (B − B̃)2, where Γ(B) denotes the American option Gamma.” Therefore, the cost of suboptimal exercise is second-order in the bias of the exercise policy and depends on Gamma. This result provides new insights on American options.

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 45 , Issue 6 , December 2010 , pp. 1563 - 1590
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2010

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