Robust bounds for the American put

David Hobson () and Dominykas Norgilas ()
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David Hobson: University of Warwick
Dominykas Norgilas: University of Warwick

Finance and Stochastics, 2019, vol. 23, issue 2, No 3, 359-395

Abstract: 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 $T_{1}$ or T 2 $T_{2}$ 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, together with an associated exercise time, for which the price of the American put is maximal. Moreover, we derive the cheapest superhedge. The model associated with the highest price of the American put is constructed from the left-curtain martingale coupling of Beiglböck and Juillet (Ann. Probab. 44:42–106, 2016).

Keywords: Model-independent pricing; American put; Martingale optimal transport; Left-curtain coupling; Optimal stopping; 60G40; 60G42; 91G20 (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00780-019-00385-4

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