A time-stepping deep gradient flow method for option pricing in (rough) diffusion models
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917975285563392 |
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| author | Papapantoleon, Antonis Rou, Jasper |
| author_facet | Papapantoleon, Antonis Rou, Jasper |
| contents | We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial differential equation is reformulated as an energy minimization problem, which is approximated in a time-stepping fashion by deep artificial neural networks. The proposed scheme respects the asymptotic behavior of option prices for large levels of moneyness, and adheres to a priori known bounds for option prices. The accuracy and efficiency of the proposed method is assessed in a series of numerical examples, with particular focus in the lifted Heston model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00746 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A time-stepping deep gradient flow method for option pricing in (rough) diffusion models Papapantoleon, Antonis Rou, Jasper Computational Finance Machine Learning Probability Mathematical Finance 91G20, 91G60, 68T07 We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial differential equation is reformulated as an energy minimization problem, which is approximated in a time-stepping fashion by deep artificial neural networks. The proposed scheme respects the asymptotic behavior of option prices for large levels of moneyness, and adheres to a priori known bounds for option prices. The accuracy and efficiency of the proposed method is assessed in a series of numerical examples, with particular focus in the lifted Heston model. |
| title | A time-stepping deep gradient flow method for option pricing in (rough) diffusion models |
| topic | Computational Finance Machine Learning Probability Mathematical Finance 91G20, 91G60, 68T07 |
| url | https://arxiv.org/abs/2403.00746 |