Random neural networks for rough volatility
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910006794780672 |
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| author | Jacquier, Antoine Zuric, Zan |
| author_facet | Jacquier, Antoine Zuric, Zan |
| contents | We construct a deep learning-based numerical algorithm to solve path-dependent partial differential equations arising in the context of rough volatility. Our approach is based on interpreting the PDE as a solution to an BSDE, building upon recent insights by Bayer, Qiu and Yao, and on constructing a neural network of reservoir type as originally developed by Gonon, Grigoryeva, Ortega. The reservoir approach allows us to formulate the optimisation problem as a simple least-square regression for which we prove theoretical convergence properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_01035 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Random neural networks for rough volatility Jacquier, Antoine Zuric, Zan Pricing of Securities Probability 60G22, 35K10, 65C20, 68T07, 91G60 We construct a deep learning-based numerical algorithm to solve path-dependent partial differential equations arising in the context of rough volatility. Our approach is based on interpreting the PDE as a solution to an BSDE, building upon recent insights by Bayer, Qiu and Yao, and on constructing a neural network of reservoir type as originally developed by Gonon, Grigoryeva, Ortega. The reservoir approach allows us to formulate the optimisation problem as a simple least-square regression for which we prove theoretical convergence properties. |
| title | Random neural networks for rough volatility |
| topic | Pricing of Securities Probability 60G22, 35K10, 65C20, 68T07, 91G60 |
| url | https://arxiv.org/abs/2305.01035 |