Are American options European after all?

Sören Christensen (Hamburg University)

with Jan Kallsen, Matthias Lenga

This talk addresses one of the fundamental problems in mathematical finance: pricing of American type options. Although the underlying theory is discussed in every introductory textbook, both the mathematical and applied treatment is challenging even in unrealistically simplified models. This is a fundamental difference to European style options. We discuss a non-standard approach to treating American options. We call a given option representable if there exists a European claim which dominates the American payoff at any time and such that the values of the two options coincide in the continuation region of the American option. This concept has interesting implications from a probabilistic, analytic, financial, and numeric point of view. Relying, inter alia, on convex duality, we make a first step towards verifying representability of American options. This opens the door to a very efficient method for treating American options in both theory and practice.