Super-hedging American Options with Semi-static Trading Strategies under Model 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, $\pi ={\sup }_{(c_i,Q_i{)}_i}{\sum }_i{c}_i{\varphi }^{Q_i}$, where $c_i\in {\mathbb{R}}_{+}$ and the martingale measure $Q^i$ are chosen such that ${\sum }_i{c}_i=1$ and ${\sum }_i{c}_i{Q}_i$ prices the European options correctly, and ${\varphi }^{Q_i}$ 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.

arXiv commentFinal version. To appear in the International Journal of Theoretical and Applied Finance. Keywords: American options, super-hedging, model uncertainty, semi-static trading strategies, randomized models