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April 2022 Are American options European after all?
Sören Christensen, Jan Kallsen, Matthias Lenga
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Ann. Appl. Probab. 32(2): 853-892 (April 2022). DOI: 10.1214/21-AAP1698

Abstract

We call a given American option representable if there exists a European claim which dominates the American payoff at any time and such that the values of the two options coincide in the continuation region of the American option. This concept has interesting implications from a probabilistic, analytic, financial, and numeric point of view. Relying on methods from (Math. Finance 24 (2014) 156–172; Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001) 1–17; Ann. Appl. Probab. 12 (2002) 196–223) and convex duality, we make a first step towards verifying representability of American options.

Acknowledgements

The authors thank Josef Teichmann for fruitful discussions and for bringing the papers [7, 8] to their attention. Thanks are also due to an anonymous referee for his/her very useful comments.

Citation

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Sören Christensen. Jan Kallsen. Matthias Lenga. "Are American options European after all?." Ann. Appl. Probab. 32 (2) 853 - 892, April 2022. https://doi.org/10.1214/21-AAP1698

Information

Received: 1 February 2020; Revised: 1 March 2021; Published: April 2022
First available in Project Euclid: 28 April 2022

Digital Object Identifier: 10.1214/21-AAP1698

Subjects:
Primary: 46A20 , 60G40 , 91G20

Keywords: cheapest dominating European option , Duality , embedded American option , free boundary problem , Optimal stopping , representable American option

Rights: Copyright © 2022 Institute of Mathematical Statistics

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Vol.32 • No. 2 • April 2022
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