Super-hedging American Options with Semi-static Trading Strategies under Model Uncertainty

TL;DR

This paper characterizes the super-hedging price of American options in a discrete-time market with both dynamic stock trading and static European option trading under model uncertainty, showing it equals the supremum over randomized models.

Contribution

It generalizes the model uncertainty framework for American options by expressing the super-hedging price as a supremum over a set of randomized models, extending prior work.

Findings

Super-hedging price equals the supremum over randomized models.

The result extends the model uncertainty pricing framework.

Provides a new representation for American option prices under uncertainty.

Abstract

We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price $\pi$ is given by the supremum over the prices of the American option under randomized models. That is, $\pi=\sup_{(c_i,Q_i)_i}\sum_ic_i\phi^{Q_i}$, where $c_i \in \mathbb{R}_+$ and the martingale measure $Q^i$ are chosen such that $\sum_i c_i=1$ and $\sum_i c_iQ_i$ prices the European options correctly, and $\phi^{Q_i}$ is the price of the American option under the model $Q_i$. Our result generalizes the example given in ArXiv:1604.02274 that the highest model based price can be considered as a randomization over models.