Do Transaction Costs Affect the Optimal Exercise Strategy for American Put Options?

Abstract

In this paper we theoretically analyze the effect of proportional transaction costs in the underlying on the optimal exercise strategy for American put options. Interestingly the results offer a theoretical explanation above other results in the literature for two types of empirically observed (irrational) investor's behavior; "faulty exercise" (option is exercised when not optimal) and "failure to exercise" (option is not exercised, although it is optimal). We show that for determining the exercise strategy in the presence of proportion transaction costs it becomes crucial important that (a) actually the holder of the option is in charge to decide about exercising or not, and that (b) it is important according to which investment strategy the investor is holding the option. Using a model which explicitly takes proportional transaction costs into account, we show for a realistic parameterization that, conditional on the investor's investment strategy, it maybe optimal to postpone exercising of put options, or to exercise more often compared to the standard frictionless theory. We also quantify that an investor neglecting transaction costs when determining the exercise strategy will make considerable pricing errors.

Keywords: American Options, Transaction Costs, Optimal Exercise Strategy, Discrete Binomial Setup, Small Proportional Transaction Costs

JEL Classification: G13