The Value of an Option to Exchange One Asset for Another

In this paper I develop a model for the pricing of a European-type option to exchange one asset for another. I prove that a similar American-type option is never exercised until the last possible moment. Thus, the formula for the value of the American-type option is the same as that for the European-type option. This sort of option is not only a call option on the one asset, but also a put option on the other. Thus, the formula gives a closed-form expression for a special sort of American put option, and one can derive a put-call parity theorem for options of this sort. I also show how the model applies to four real-world financial arrangements; the investment advisor’s performance incentive fee, the general margin account, the corporate exchange offer, and the standby commitment.