Robust bounds for the American put

DOI10.1007/S00780-019-00385-4zbMATH Open1411.91558arXiv1711.06466OpenAlexW2963351743WikidataQ128268182 ScholiaQ128268182MaRDI QIDQ1739057

Dominykas Norgilas, David Hobson

Publication date: 24 April 2019

Published in: Finance and Stochastics (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1711.06466

zbMATH Keywords

optimal stopping martingale optimal transport model-independent pricing American put left-curtain coupling

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Stopping times; optimal stopping problems; gambling theory (60G40) Derivative securities (option pricing, hedging, etc.) (91G20)

Cites Work