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SUPER-HEDGING AMERICAN OPTIONS WITH SEMI-STATIC TRADING STRATEGIES UNDER MODEL UNCERTAINTY

Erhan Bayraktar and Zhou Zhou ()
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Zhou Zhou: Institute for Mathematics and its Applications, University of Minnesota, 207 Church Street, SE, Minneapolis, MN 55455, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2017, vol. 20, issue 06, 1-10

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 π is given by the supremum over the prices of the American option under randomized models. That is, π =sup(ci,Qi)i∑iciϕQi, where ci ∈ ℝ+ and the martingale measure Qi are chosen such that ∑ici = 1 and ∑iciQi prices the European options correctly, and ϕQi is the price of the American option under the model Qi. Our result generalizes the example given in Hobson & Neuberger (2016) that the highest model-based price can be considered as a randomization over models.

Keywords: American options; super-hedging; model uncertainty; semi-static trading strategies; randomized models (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S0219024917500364

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