The sensitivity of American options to suboptimal exercise strategies

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.