Robust pricing and hedging of options on multiple assets and its numerics
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multimarginal martingale optimal transport problem. We propose two numerical methods to solve such problems: using discretization an...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2021
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| _version_ | 1797051425159643136 |
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| author | Eckstein, S Guo, G Lim, T Obłój, J |
| author_facet | Eckstein, S Guo, G Lim, T Obłój, J |
| author_sort | Eckstein, S |
| collection | OXFORD |
| description | We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multimarginal martingale optimal transport problem. We propose two numerical methods to solve such problems: using discretization and linear programming applied to the primal side and using penalization and deep neural networks optimization applied to the dual side. We prove convergence for our methods and compare their numerical performance. We show how adding further information about call option prices at additional maturities can be incorporated and narrows down the no-arbitrage pricing bounds. Finally, we obtain structural results for the case of the payoff given by a weighted sum of covariances between the assets. |
| first_indexed | 2024-03-06T18:19:23Z |
| format | Journal article |
| id | oxford-uuid:05c3c181-bfdb-4231-9d28-e7ccde100e5e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:19:23Z |
| publishDate | 2021 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:05c3c181-bfdb-4231-9d28-e7ccde100e5e2022-03-26T08:58:47ZRobust pricing and hedging of options on multiple assets and its numericsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:05c3c181-bfdb-4231-9d28-e7ccde100e5eEnglishSymplectic ElementsSociety for Industrial and Applied Mathematics 2021Eckstein, SGuo, GLim, TObłój, JWe consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multimarginal martingale optimal transport problem. We propose two numerical methods to solve such problems: using discretization and linear programming applied to the primal side and using penalization and deep neural networks optimization applied to the dual side. We prove convergence for our methods and compare their numerical performance. We show how adding further information about call option prices at additional maturities can be incorporated and narrows down the no-arbitrage pricing bounds. Finally, we obtain structural results for the case of the payoff given by a weighted sum of covariances between the assets. |
| spellingShingle | Eckstein, S Guo, G Lim, T Obłój, J Robust pricing and hedging of options on multiple assets and its numerics |
| title | Robust pricing and hedging of options on multiple assets and its numerics |
| title_full | Robust pricing and hedging of options on multiple assets and its numerics |
| title_fullStr | Robust pricing and hedging of options on multiple assets and its numerics |
| title_full_unstemmed | Robust pricing and hedging of options on multiple assets and its numerics |
| title_short | Robust pricing and hedging of options on multiple assets and its numerics |
| title_sort | robust pricing and hedging of options on multiple assets and its numerics |
| work_keys_str_mv | AT ecksteins robustpricingandhedgingofoptionsonmultipleassetsanditsnumerics AT guog robustpricingandhedgingofoptionsonmultipleassetsanditsnumerics AT limt robustpricingandhedgingofoptionsonmultipleassetsanditsnumerics AT obłojj robustpricingandhedgingofoptionsonmultipleassetsanditsnumerics |