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, 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 <italic>B</italic> is the optimal exercise price, but exercise is either <italic>brought forward when</italic> or <italic>delayed until</italic> a price <italic>B̃</italic> has been reached, the cost of suboptimal exercise is given by ½ × <italic>Γ</italic>(<italic>B</italic>) × (<italic>B</italic> − <italic>B̃</italic>)<sup>2</sup>, where <italic>Γ</italic>(<italic>B</italic>) 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.
