Numerical methods for weather derivatives pricing
| dc.contributor.advisor | Fredericks, Ebrahim | |
| dc.contributor.advisor | Canhanga, Betuel | |
| dc.contributor.author | Nhangumbe, Clarinda | |
| dc.date.accessioned | 2025-09-18T09:57:44Z | |
| dc.date.available | 2025-09-18T09:57:44Z | |
| dc.date.issued | 2025 | |
| dc.date.updated | 2025-09-18T09:48:55Z | |
| dc.description.abstract | Weather derivatives are financial products used to hedge non-catastrophic weather risks with a weather index as an underlying asset. Mispricing these contracts poses a significant risk due the nature of weather variable. On rainfall derivatives pricing, the rainfall process is considered to be a stochastic, consisting of two random variables: one representing frequency, which is a two state Markov Chain, and the other representing the rainfall amount. Generally, these variables are modelled separately. The frequency is modelled by the discrete models and the rain-fall amount by the continuous models. However, the debate on how to model the dynamics of rainfall amounts still open. The main objective of this thesis, is to price rainfall based derivatives using only monthly rainfall amount. The monthly rainfall amount are modeled by Ornstein-Uhlenbeck process. Then, applying the Feynman-Kac theorem we derive the partial differential equations that govern the price of an European derivative option. Since the partial deferential equation does not admit analytical solutions, we use the numerical methods to solve it. The explicit numerical methods that are special cases of finite-difference schemes and nonstandard finite difference combined with the operator splitting approaches, are proposed. The methods are effective on handling with convection dominant condition and preserve the positivity. The positivity and stability conditions are established and the numerical solutions are simulated. Furthermore, we propose the boundary conditions which have financial interpretation that are also compatible with the mathematical view points. | |
| dc.identifier.apacitation | Nhangumbe, C. (2025). <i>Numerical methods for weather derivatives pricing</i>. (). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/41853 | en_ZA |
| dc.identifier.chicagocitation | Nhangumbe, Clarinda. <i>"Numerical methods for weather derivatives pricing."</i> ., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2025. http://hdl.handle.net/11427/41853 | en_ZA |
| dc.identifier.citation | Nhangumbe, C. 2025. Numerical methods for weather derivatives pricing. . University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/41853 | en_ZA |
| dc.identifier.ris | TY - Thesis / Dissertation AU - Nhangumbe, Clarinda AB - Weather derivatives are financial products used to hedge non-catastrophic weather risks with a weather index as an underlying asset. Mispricing these contracts poses a significant risk due the nature of weather variable. On rainfall derivatives pricing, the rainfall process is considered to be a stochastic, consisting of two random variables: one representing frequency, which is a two state Markov Chain, and the other representing the rainfall amount. Generally, these variables are modelled separately. The frequency is modelled by the discrete models and the rain-fall amount by the continuous models. However, the debate on how to model the dynamics of rainfall amounts still open. The main objective of this thesis, is to price rainfall based derivatives using only monthly rainfall amount. The monthly rainfall amount are modeled by Ornstein-Uhlenbeck process. Then, applying the Feynman-Kac theorem we derive the partial differential equations that govern the price of an European derivative option. Since the partial deferential equation does not admit analytical solutions, we use the numerical methods to solve it. The explicit numerical methods that are special cases of finite-difference schemes and nonstandard finite difference combined with the operator splitting approaches, are proposed. The methods are effective on handling with convection dominant condition and preserve the positivity. The positivity and stability conditions are established and the numerical solutions are simulated. Furthermore, we propose the boundary conditions which have financial interpretation that are also compatible with the mathematical view points. DA - 2025 DB - OpenUCT DP - University of Cape Town KW - Finite differences KW - Nonstandard schemes KW - Operator splitting KW - Partial dif- ferential equation KW - Stochastic models KW - Weather derivatives LK - https://open.uct.ac.za PB - University of Cape Town PY - 2025 T1 - Numerical methods for weather derivatives pricing TI - Numerical methods for weather derivatives pricing UR - http://hdl.handle.net/11427/41853 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/41853 | |
| dc.identifier.vancouvercitation | Nhangumbe C. Numerical methods for weather derivatives pricing. []. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2025 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/41853 | en_ZA |
| dc.language.iso | en | |
| dc.language.rfc3066 | eng | |
| dc.publisher.department | Department of Mathematics and Applied Mathematics | |
| dc.publisher.faculty | Faculty of Science | |
| dc.publisher.institution | University of Cape Town | |
| dc.subject | Finite differences | |
| dc.subject | Nonstandard schemes | |
| dc.subject | Operator splitting | |
| dc.subject | Partial dif- ferential equation | |
| dc.subject | Stochastic models | |
| dc.subject | Weather derivatives | |
| dc.title | Numerical methods for weather derivatives pricing | |
| dc.type | Thesis / Dissertation | |
| dc.type.qualificationlevel | Doctoral | |
| dc.type.qualificationlevel | PhD |