{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/40675"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/40675","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Option pricing with physics-informed neutral networks (PINNS)","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Zamxaka, Nichume"],"institution":"Department of Finance and Tax","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Rudd, Ralph"],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024","date_published":"2024","updated_at":"2026-07-22T22:23:10Z","subjects":["physics-informed neural networks","partial differential equation","option pricing","mesh-free","local volatility"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/40675","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Rudd, Ralph"]},{"key":"dc:creator","label":"Author","values":["Zamxaka, Nichume"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-11-04T08:18:00Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-11-04T08:18:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2024"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Finance and Tax"]},{"key":"dc:type","label":"Dc Type","values":["Thesis / Dissertation"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters","MPhil"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["physics-informed neural networks","partial differential equation","option pricing","mesh-free","local volatility"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/40675"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Option pricing with physics-informed neutral networks (PINNS)"]}]}],"canonical_facts":{"dc:contributor.advisor":["Rudd, Ralph"],"dc:creator":["Zamxaka, Nichume"],"dc:date.accessioned":["2024-11-04T08:18:00Z"],"dc:date.available":["2024-11-04T08:18:00Z"],"dc:date.issued":["2024"],"dc:description.abstract":["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."],"dc:identifier.uri":["http://hdl.handle.net/11427/40675"],"dc:publisher.department":["Department of Finance and Tax"],"dc:subject":["physics-informed neural networks","partial differential equation","option pricing","mesh-free","local volatility"],"dc:title":["Option pricing with physics-informed neutral networks (PINNS)"],"dc:type":["Thesis / Dissertation"],"dc:type.qualificationlevel":["Masters","MPhil"]},"updated_at":"2026-07-22T22:23:10Z"}