Robust bounds for the American Put

David Hobson and Dominykas Norgilas

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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 $T_1$ or $T_2$ 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 Beiglb\"{o}ck and Juillet.

Date: 2017-11, Revised 2018-05
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1711.06466

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