Lie Analysis for Partial Differential Equations in Finance

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dc.contributor.advisorFredericks, Ebrahim
dc.contributor.advisorCanhanga , Betuel
dc.contributor.authorNhangumbe, Clarinda Vitorino
dc.date.accessioned2020-05-06T12:57:35Z
dc.date.available2020-05-06T12:57:35Z
dc.date.issued2019
dc.date.updated2020-05-06T01:36:19Z
dc.description.abstractWeather derivatives are financial tools used to manage the risks related to changes in the weather and are priced considering weather variables such as rainfall, temperature, humidity and wind as the underlying asset. Some recent researches suggest to model the amount of rainfall by considering the mean reverting processes. As an example, the Ornstein Uhlenbeck process was proposed by Allen [3] to model yearly rainfall and by Unami et al. [52] to model the irregularity of rainfall intensity as well as duration of dry spells. By using the Feynman-Kac theorem and the rainfall indexes we derive the partial differential equations (PDEs) that governs the price of an European option. We apply the Lie analysis theory to solve the PDEs, we provide the group classification and use it to find the invariant analytical solutions, particularly the ones compatible with the terminal conditions.
dc.identifier.apacitationNhangumbe, C. V. (2019). <i>Lie Analysis for Partial Differential Equations in Finance</i>. (). ,Faculty of Science ,Department of Maths and Applied Maths. Retrieved from en_ZA
dc.identifier.chicagocitationNhangumbe, Clarinda Vitorino. <i>"Lie Analysis for Partial Differential Equations in Finance."</i> ., ,Faculty of Science ,Department of Maths and Applied Maths, 2019. en_ZA
dc.identifier.citationNhangumbe, C.V. 2019. Lie Analysis for Partial Differential Equations in Finance. . ,Faculty of Science ,Department of Maths and Applied Maths. en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Nhangumbe, Clarinda Vitorino AB - Weather derivatives are financial tools used to manage the risks related to changes in the weather and are priced considering weather variables such as rainfall, temperature, humidity and wind as the underlying asset. Some recent researches suggest to model the amount of rainfall by considering the mean reverting processes. As an example, the Ornstein Uhlenbeck process was proposed by Allen [3] to model yearly rainfall and by Unami et al. [52] to model the irregularity of rainfall intensity as well as duration of dry spells. By using the Feynman-Kac theorem and the rainfall indexes we derive the partial differential equations (PDEs) that governs the price of an European option. We apply the Lie analysis theory to solve the PDEs, we provide the group classification and use it to find the invariant analytical solutions, particularly the ones compatible with the terminal conditions. DA - 2019 DB - OpenUCT DP - University of Cape Town KW - Lie symmetry analysis KW - Ornstein-Uhlenbeck process KW - Partial differential equations KW - Rainfall index KW - Weather derivatives LK - https://open.uct.ac.za PY - 2019 T1 - Lie Analysis for Partial Differential Equations in Finance TI - Lie Analysis for Partial Differential Equations in Finance UR - ER - en_ZA
dc.identifier.urihttps://hdl.handle.net/11427/31817
dc.identifier.vancouvercitationNhangumbe CV. Lie Analysis for Partial Differential Equations in Finance. []. ,Faculty of Science ,Department of Maths and Applied Maths, 2019 [cited yyyy month dd]. Available from: en_ZA
dc.language.rfc3066eng
dc.publisher.departmentDepartment of Maths and Applied Maths
dc.publisher.facultyFaculty of Science
dc.subjectLie symmetry analysis
dc.subjectOrnstein-Uhlenbeck process
dc.subjectPartial differential equations
dc.subjectRainfall index
dc.subjectWeather derivatives
dc.titleLie Analysis for Partial Differential Equations in Finance
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMSc
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