Robust pricing-hedging duality for American options in discrete time financial markets
Deng, Shuoqing; Tan, Xiaolu; Aksamit, Anna; Obloj , Jan (2017), Robust pricing-hedging duality for American options in discrete time financial markets. https://basepub.dauphine.fr/handle/123456789/17090
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-01429550
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
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Abstract (EN)We aim to generalize the duality results of Bouchard & Nutz  to the case of American options. By introducing an enlarged canonical space, we reformulate the superhedging problem for American options as a problem for European options. Then in a discrete time market with finitely many liquid options, we show that the minimum superhedging cost of an American option equals to the supremum of the expectation of the payoff at all (weak) stopping times and under a suitable family of martingale measures. Moreover, by taking the limit on the number of liquid options, we obtain a new class of martingale optimal transport problems as well as a Kantorovich duality result.
Subjects / KeywordsSuper-replication; American option; nondominated model; martingale; optimal transport; Kantorovich duality
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