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Option pricing with physics-informed neutral networks (PINNS)
We investigate the application of physics-informed neural networks (PINNs) to option pricing. PINNs are neural networks that are trained to numerically solve partial differential equations (PDEs) by obeying the dynamics induced by the PDE as well as the initial/terminal conditions of the PDE. They a...
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| Format: | Thesis |
| Language: | Eng |
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Department of Finance and Tax
2024
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| _version_ | 1867613265232658432 |
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| access_status_str | Open Access |
| author | Zamxaka, Nichume |
| author2 | Rudd, Ralph |
| author_browse | Rudd, Ralph Zamxaka, Nichume |
| author_facet | Rudd, Ralph Zamxaka, Nichume |
| author_sort | Zamxaka, Nichume |
| collection | Thesis |
| description | We investigate the application of physics-informed neural networks (PINNs) to option pricing. PINNs are neural networks that are trained to numerically solve partial differential equations (PDEs) by obeying the dynamics induced by the PDE as well as the initial/terminal conditions of the PDE. They are mesh-free to an extent and compute the derivatives of the PDE through backward-propagation. We construct a PINN toy example to solve the Black-Scholes-Merton PDE for a vanilla European option. The numerical solutions from the PINN are compared against the true analytical solution – the Black-Scholes-Merton equation. The problem is also extended by incorporating a local volatility model. Here, we derive the PDE of a vanilla European option under the constant elasticity of variance (CEV) model. We then construct and train a PINN to solve the PDE and compare it to the true analytical solution of a special case of the CEV model, the square-root process. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/40675 |
| institution | University of Cape Town (South Africa) |
| language | Eng |
| last_indexed | 2026-06-10T12:33:23.204Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | Department of Finance and Tax |
| publisherStr | Department of Finance and Tax |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/40675 Option pricing with physics-informed neutral networks (PINNS) Zamxaka, Nichume Rudd, Ralph physics-informed neural networks partial differential equation option pricing mesh-free local volatility We investigate the application of physics-informed neural networks (PINNs) to option pricing. PINNs are neural networks that are trained to numerically solve partial differential equations (PDEs) by obeying the dynamics induced by the PDE as well as the initial/terminal conditions of the PDE. They are mesh-free to an extent and compute the derivatives of the PDE through backward-propagation. We construct a PINN toy example to solve the Black-Scholes-Merton PDE for a vanilla European option. The numerical solutions from the PINN are compared against the true analytical solution – the Black-Scholes-Merton equation. The problem is also extended by incorporating a local volatility model. Here, we derive the PDE of a vanilla European option under the constant elasticity of variance (CEV) model. We then construct and train a PINN to solve the PDE and compare it to the true analytical solution of a special case of the CEV model, the square-root process. 2024-11-04T08:18:00Z 2024-11-04T08:18:00Z 2024 2024-07-09T13:20:36Z Thesis / Dissertation Masters MPhil http://hdl.handle.net/11427/40675 Eng application/pdf Department of Finance and Tax Faculty of Commerce |
| spellingShingle | physics-informed neural networks partial differential equation option pricing mesh-free local volatility Zamxaka, Nichume Option pricing with physics-informed neutral networks (PINNS) |
| thesis_degree_str | Master's |
| title | Option pricing with physics-informed neutral networks (PINNS) |
| title_full | Option pricing with physics-informed neutral networks (PINNS) |
| title_fullStr | Option pricing with physics-informed neutral networks (PINNS) |
| title_full_unstemmed | Option pricing with physics-informed neutral networks (PINNS) |
| title_short | Option pricing with physics-informed neutral networks (PINNS) |
| title_sort | option pricing with physics informed neutral networks pinns |
| topic | physics-informed neural networks partial differential equation option pricing mesh-free local volatility |
| url | http://hdl.handle.net/11427/40675 |
| work_keys_str_mv | AT zamxakanichume optionpricingwithphysicsinformedneutralnetworkspinns |