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

2016/04/15 by Bayraktar, Erhan, Zhou, Zhou · 2 citations
#FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR)

paper · doi:10.48550/arxiv.1604.04608

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∑_ic_iϕ^Q_i, where c_i ∈ ℝ₊ and the martingale measure Qⁱ are chosen such that ∑_i c_i=1 and ∑_i c_iQ_i prices the European options correctly, and ϕ^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.

Cited by

• Robust Pricing and Hedging of American Options in Continuous Time
• Robust Hedging of American Options via Aggregated Snell Envelopes

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