Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model

dc.contributor.advisorMcWalter, Thomas
dc.contributor.advisorKienitz, Joerg
dc.contributor.authorVan Gysen, Richard John
dc.date.accessioned2020-02-25T12:00:49Z
dc.date.available2020-02-25T12:00:49Z
dc.date.issued2019
dc.date.updated2020-02-25T08:34:58Z
dc.description.abstractIn 2009, Trolle and Schwartz (2008) produced an instantaneous forward interest rate model with several stylised facts such as stochastic volatility. They derived pricing formulae in order to price bonds and bond options, which can be altered to price interest rate options such as caplets, caps and swaptions. These formulae involve implementing numerical methods for solving an ordinary differential equation (ODE). Schumann (2016) confirmed the accuracy of the pricing formulae in the Trolle and Schwartz (2008) model using Monte-Carlo simulation. Both authors used a numerical ODE solver to estimate the ODE. In this dissertation, a closed-form solution for this ODE is presented. Two solutions were found. However, these solutions rely on a simplification of the instantaneous volatility function originally proposed in the Trolle and Schwartz (2008) model. This case happens to be the stochastic volatility version of the Hull and White (1990) model. The two solutions are compared to an ODE solver for one stochastic volatility term and then extended to three stochastic volatility terms.
dc.identifier.apacitationVan Gysen, R. J. (2019). <i>Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model</i>. (). ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management. Retrieved from http://hdl.handle.net/11427/31328en_ZA
dc.identifier.chicagocitationVan Gysen, Richard John. <i>"Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model."</i> ., ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management, 2019. http://hdl.handle.net/11427/31328en_ZA
dc.identifier.citationVan Gysen, R. 2019. Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Van Gysen, Richard John AB - In 2009, Trolle and Schwartz (2008) produced an instantaneous forward interest rate model with several stylised facts such as stochastic volatility. They derived pricing formulae in order to price bonds and bond options, which can be altered to price interest rate options such as caplets, caps and swaptions. These formulae involve implementing numerical methods for solving an ordinary differential equation (ODE). Schumann (2016) confirmed the accuracy of the pricing formulae in the Trolle and Schwartz (2008) model using Monte-Carlo simulation. Both authors used a numerical ODE solver to estimate the ODE. In this dissertation, a closed-form solution for this ODE is presented. Two solutions were found. However, these solutions rely on a simplification of the instantaneous volatility function originally proposed in the Trolle and Schwartz (2008) model. This case happens to be the stochastic volatility version of the Hull and White (1990) model. The two solutions are compared to an ODE solver for one stochastic volatility term and then extended to three stochastic volatility terms. DA - 2019 DB - OpenUCT DP - University of Cape Town KW - Mathematical Finance LK - https://open.uct.ac.za PY - 2019 T1 - Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model TI - Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model UR - http://hdl.handle.net/11427/31328 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/31328
dc.identifier.vancouvercitationVan Gysen RJ. Analytical Solution of the Characteristic Function in the Trolle-Schwartz Model. []. ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management, 2019 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/31328en_ZA
dc.language.rfc3066eng
dc.publisher.departmentAfrican Institute of Financial Markets and Risk Management
dc.publisher.facultyFaculty of Commerce
dc.subjectMathematical Finance
dc.titleAnalytical Solution of the Characteristic Function in the Trolle-Schwartz Model
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMPhil
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