Option pricing with physics-informed neutral networks (PINNS)

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dc.contributor.advisorRudd, Ralph
dc.contributor.authorZamxaka, Nichume
dc.date.accessioned2024-11-04T08:18:00Z
dc.date.available2024-11-04T08:18:00Z
dc.date.issued2024
dc.date.updated2024-07-09T13:20:36Z
dc.description.abstractWe 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.
dc.identifier.apacitationZamxaka, N. (2024). <i>Option pricing with physics-informed neutral networks (PINNS)</i>. (). ,Faculty of Commerce ,Department of Finance and Tax. Retrieved from http://hdl.handle.net/11427/40675en_ZA
dc.identifier.chicagocitationZamxaka, Nichume. <i>"Option pricing with physics-informed neutral networks (PINNS)."</i> ., ,Faculty of Commerce ,Department of Finance and Tax, 2024. http://hdl.handle.net/11427/40675en_ZA
dc.identifier.citationZamxaka, N. 2024. Option pricing with physics-informed neutral networks (PINNS). . ,Faculty of Commerce ,Department of Finance and Tax. http://hdl.handle.net/11427/40675en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Zamxaka, Nichume AB - 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. DA - 2024 DB - OpenUCT DP - University of Cape Town KW - Finance and Tax LK - https://open.uct.ac.za PY - 2024 T1 - Option pricing with physics-informed neutral networks (PINNS) TI - Option pricing with physics-informed neutral networks (PINNS) UR - http://hdl.handle.net/11427/40675 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/40675
dc.identifier.vancouvercitationZamxaka N. Option pricing with physics-informed neutral networks (PINNS). []. ,Faculty of Commerce ,Department of Finance and Tax, 2024 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/40675en_ZA
dc.language.rfc3066Eng
dc.publisher.departmentDepartment of Finance and Tax
dc.publisher.facultyFaculty of Commerce
dc.subjectphysics-informed neural networks
dc.subjectpartial differential equation
dc.subjectoption pricing
dc.subjectmesh-free
dc.subjectlocal volatility
dc.titleOption pricing with physics-informed neutral networks (PINNS)
dc.typeThesis / Dissertation
dc.type.qualificationlevelMasters
dc.type.qualificationlevelMPhil
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