On the value of being American

TL;DR

This paper quantifies the maximum value of American options under model uncertainty by deriving bounds based on European call prices, providing a robust hedging strategy that accounts for model error.

Contribution

It introduces a model-free bound on American option prices using European call prices, addressing the gap in literature that assumes away model uncertainty.

Findings

Derived a supremum price bound for American options under model uncertainty.

Developed a hedging strategy consistent with European call prices.

Demonstrated robustness of the bounds to model errors.

Abstract

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 no model is imposed on the data, but rather any model is required to be 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.