THE VALUATION OF AMERICAN OPTIONS ON MULTIPLE ASSETS

In this paper we provide valuation formulas for several types of Ameri can options on two or more assets. Our contribution is twofold. First, we characterize the optimal exercise regions and provide valuation fo rmulas for a number of American option contracts on multiple underlyin g assets with convex payoff functions. Examples include options on the maximum of two assets, dual strike options, spread options, exchange options, options on the product and powers of the product, and options on the arithmetic average of two assets. Second, we derive results fo r American option contracts with nonconvex payoffs, such as American c apped exchange options. For this option we explicitly identify the opt imal exercise boundary and provide a decomposition of the price in ter ms of a capped exchange option with automatic exercise at the cap and an early exercise premium involving the benefits of exercising prior t o reaching the cap. Besides generalizing the current literature on Ame rican option valuation our analysis has implications for the theory of investment under uncertainty. A specialization of one of our models a lso provides a new representation formula for an American capped optio n on a single underlying asset.