Model uncertainty and the pricing of American options

The virtue of an American option is that it can be exercised at any time. This right is particularly valuable when there is model uncertainty. Yet almost all the extensive literature on American options assumes away model uncertainty. This paper quantifies the potential value of this flexibility by identifying the supremum on the price of an American option when we do not impose a model, but rather consider the class of all models which are consistent with a family of European call prices. The bound is enforced by a hedging strategy involving these call options which is robust to model error.