Super-hedging American options with semi-static trading strategies under model uncertainty. (English) Zbl 1396.91716
Summary: 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 \(\sum_ic_i=1\) and \(\sum_ic_iQ_i\) 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 [D. Hobson and A. Neuberger, “More on hedging American options under model uncertainty”, Preprint, arXiv:1604.0227] that the highest model-based price can be considered as a randomization over models.
MSC:
91G20 | Derivative securities (option pricing, hedging, etc.) |
60G40 | Stopping times; optimal stopping problems; gambling theory |
60G42 | Martingales with discrete parameter |
Keywords:
American options; super-hedging; model uncertainty; semi-static trading strategies; randomized modelsReferences:
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