Robust bounds for the American Put

2017/11/17 by Hobson, David, Norgilas, Dominykas
#60G40 #60G42 #91G20 #FOS: Economics and business #Mathematical Finance (q-fin.MF)

paper · doi:10.48550/arxiv.1711.06466

Abstract

We consider the problem of finding a model-free upper bound on the price of an American put given the prices of a family of European puts on the same underlying asset. Specifically we assume that the American put must be exercised at either T₁ or T₂ and that we know the prices of all vanilla European puts with these maturities. In this setting we find a model which is consistent with European put prices and an associated exercise time, for which the price of the American put is maximal. Moreover we derive a cheapest superhedge. The model associated with the highest price of the American put is constructed from the left-curtain martingale transport of Beiglböck and Juillet.

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