More on hedging American options under model uncertainty
Abstract
The purpose of this note is to reconcile two different results concerning the model-free upper bound on the price of an American option, given a set of European option prices. Neuberger (2007, `Bounds on the American option') and Hobson and Neuberger (2016, `On the value of being American') argue that the cost of the cheapest super-replicating strategy is equal to the highest model-based price, where we search over all models which price correctly the given European options. Bayraktar, Huang and Zhou (2015, `On hedging American options under model uncertainty', SIAM J. Financial Math ematics) argue that the cost of the cheapest super-replicating strategy can strictly exceed the highest model-based price. We show that the reason for the difference in conclusion is that Bayraktar et al do not search over a rich enough class of models.
Cite
@article{arxiv.1604.02274,
title = {More on hedging American options under model uncertainty},
author = {David Hobson and Anthony Neuberger},
journal= {arXiv preprint arXiv:1604.02274},
year = {2016}
}