The Sensitivity of American Options to Suboptimal Exercise Strategies

42 Pages Posted: 29 Mar 2008 Last revised: 24 Jan 2009

Date Written: January 21, 2009

Abstract

The value of American options depends on the exercise policy followed by option holders. Market frictions, risk aversion, a misspecified model, or an inaccurate algorithm 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. Precisely, "if B is the optimal exercise price, but exercise is either brought forward when or delayed until a price B has been reached, the cost of suboptimal exercise is given by "(1/2)xL(B)x(B-B)2," where L(B) denotes the American option Gamma." Therefore, American options with small Gamma are less sensitive to suboptimal exercise, if B and B are not far away, which has a quadratic cost. This result provides new insights on American options.

Keywords: American Options, suboptimal exercise, cost of suboptimal exercise, optimal exercise boundary, swaptions

JEL Classification: G12, G13, G14

Suggested Citation

Ibañez, Alfredo and Paraskevopoulos, Ioannis, The Sensitivity of American Options to Suboptimal Exercise Strategies (January 21, 2009). Available at SSRN: https://ssrn.com/abstract=1022541 or http://dx.doi.org/10.2139/ssrn.1022541

Alfredo Ibañez (Contact Author)

Comillas Pontifical University ( email )

Alberto Aguilera 21
Madrid, Madrid 28015
Spain

Ioannis Paraskevopoulos

Bankia ( email )

Torre Caja Madrid
P. de la Castellana, 189
Madrid, 28046
Spain
+34618969259 (Phone)

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