The robust pricing–hedging duality for American options in discrete time financial markets
We investigate the pricing–hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, for example, a family of European options, only statically. In the first part of the paper, we consider an abstract setting, which includes the class...
| Main Authors: | , , , |
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| Format: | Journal article |
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Wiley
2018
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| _version_ | 1826260893173809152 |
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| author | Aksamit, A Deng, S Obłój, J Tan, X |
| author_facet | Aksamit, A Deng, S Obłój, J Tan, X |
| author_sort | Aksamit, A |
| collection | OXFORD |
| description | We investigate the pricing–hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, for example, a family of European options, only statically. In the first part of the paper, we consider an abstract setting, which includes the classical case with a fixed reference probability measure as well as the robust framework with a nondominated family of probability measures. Our first insight is that, by considering an enlargement of the space, we can see American options as European options and recover the pricing–hedging duality, which may fail in the original formulation. This can be seen as a weak formulation of the original problem. Our second insight is that a duality gap arises from the lack of dynamic consistency, and hence that a different enlargement, which reintroduces dynamic consistency is sufficient to recover the pricing–hedging duality: It is enough to consider fictitious extensions of the market in which all the assets are traded dynamically. In the second part of the paper, we study two important examples of the robust framework: the setup of Bouchard and Nutz and the martingale optimal transport setup of Beiglböck, Henry‐Labordère, and Penkner, and show that our general results apply in both cases and enable us to obtain the pricing–hedging duality for American options. |
| first_indexed | 2024-03-06T19:12:57Z |
| format | Journal article |
| id | oxford-uuid:17604994-2bf3-4390-b51a-0b7b67648b34 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:12:57Z |
| publishDate | 2018 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:17604994-2bf3-4390-b51a-0b7b67648b342022-03-26T10:36:55ZThe robust pricing–hedging duality for American options in discrete time financial marketsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:17604994-2bf3-4390-b51a-0b7b67648b34Symplectic Elements at OxfordWiley2018Aksamit, ADeng, SObłój, JTan, XWe investigate the pricing–hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, for example, a family of European options, only statically. In the first part of the paper, we consider an abstract setting, which includes the classical case with a fixed reference probability measure as well as the robust framework with a nondominated family of probability measures. Our first insight is that, by considering an enlargement of the space, we can see American options as European options and recover the pricing–hedging duality, which may fail in the original formulation. This can be seen as a weak formulation of the original problem. Our second insight is that a duality gap arises from the lack of dynamic consistency, and hence that a different enlargement, which reintroduces dynamic consistency is sufficient to recover the pricing–hedging duality: It is enough to consider fictitious extensions of the market in which all the assets are traded dynamically. In the second part of the paper, we study two important examples of the robust framework: the setup of Bouchard and Nutz and the martingale optimal transport setup of Beiglböck, Henry‐Labordère, and Penkner, and show that our general results apply in both cases and enable us to obtain the pricing–hedging duality for American options. |
| spellingShingle | Aksamit, A Deng, S Obłój, J Tan, X The robust pricing–hedging duality for American options in discrete time financial markets |
| title | The robust pricing–hedging duality for American options in discrete time financial markets |
| title_full | The robust pricing–hedging duality for American options in discrete time financial markets |
| title_fullStr | The robust pricing–hedging duality for American options in discrete time financial markets |
| title_full_unstemmed | The robust pricing–hedging duality for American options in discrete time financial markets |
| title_short | The robust pricing–hedging duality for American options in discrete time financial markets |
| title_sort | robust pricing hedging duality for american options in discrete time financial markets |
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