Application of Effective Markovian Projection to SABR and Heston Models

dc.contributor.advisorOuwehand, Peter
dc.contributor.advisorMc Walter Thomas
dc.contributor.authorBagraim, Jacques
dc.date.accessioned2024-03-28T09:31:23Z
dc.date.available2024-03-28T09:31:23Z
dc.date.issued2023
dc.date.updated2024-03-28T09:17:53Z
dc.description.abstractModel flexibility is often at odds with tractable pricing, and models with tractable pricing often lack flexibility. This poses an issue when calibrating a model to market data where tractability and flexibility are both required. We investigate an approach that allows one model to be projected onto another, potentially allowing for a flexible model to be represented by a tractable one. Here, Effective Markovian Projection is used to obtain equivalent Heston model parameters from a range of SABR models with different skew parameters using two distinct point-matching algorithms. The implied parameters are used to price European claims under a variety of schemes in order to outline the efficacy in this context. We see that this technique is accurate when the underlying probability densities of both models match closely, i.e., when the SABR skew parameter approaches unity, as is seen by comparing prices of claims using Classic Markovian Projection where the underlying SABR processes share the same density. PDE and perturbation SABR prices match closely while Heston characteristic function prices become unstable at lower skew parameters and far in-the-money and out-the-money values of the strike. Lastly, a potential improvement to this application involving error-correction terms is proposed for further application.
dc.identifier.apacitationBagraim, J. (2023). <i>Application of Effective Markovian Projection to SABR and Heston Models</i>. (). ,Faculty of Commerce ,Department of Finance and Tax. Retrieved from http://hdl.handle.net/11427/39263en_ZA
dc.identifier.chicagocitationBagraim, Jacques. <i>"Application of Effective Markovian Projection to SABR and Heston Models."</i> ., ,Faculty of Commerce ,Department of Finance and Tax, 2023. http://hdl.handle.net/11427/39263en_ZA
dc.identifier.citationBagraim, J. 2023. Application of Effective Markovian Projection to SABR and Heston Models. . ,Faculty of Commerce ,Department of Finance and Tax. http://hdl.handle.net/11427/39263en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Bagraim, Jacques AB - Model flexibility is often at odds with tractable pricing, and models with tractable pricing often lack flexibility. This poses an issue when calibrating a model to market data where tractability and flexibility are both required. We investigate an approach that allows one model to be projected onto another, potentially allowing for a flexible model to be represented by a tractable one. Here, Effective Markovian Projection is used to obtain equivalent Heston model parameters from a range of SABR models with different skew parameters using two distinct point-matching algorithms. The implied parameters are used to price European claims under a variety of schemes in order to outline the efficacy in this context. We see that this technique is accurate when the underlying probability densities of both models match closely, i.e., when the SABR skew parameter approaches unity, as is seen by comparing prices of claims using Classic Markovian Projection where the underlying SABR processes share the same density. PDE and perturbation SABR prices match closely while Heston characteristic function prices become unstable at lower skew parameters and far in-the-money and out-the-money values of the strike. Lastly, a potential improvement to this application involving error-correction terms is proposed for further application. DA - 2023 DB - OpenUCT DP - University of Cape Town KW - Mathematical Finance LK - https://open.uct.ac.za PY - 2023 T1 - ETD: Application of Effective Markovian Projection to SABR and Heston Models TI - ETD: Application of Effective Markovian Projection to SABR and Heston Models UR - http://hdl.handle.net/11427/39263 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/39263
dc.identifier.vancouvercitationBagraim J. Application of Effective Markovian Projection to SABR and Heston Models. []. ,Faculty of Commerce ,Department of Finance and Tax, 2023 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/39263en_ZA
dc.language.rfc3066eng
dc.publisher.departmentDepartment of Finance and Tax
dc.publisher.facultyFaculty of Commerce
dc.subjectMathematical Finance
dc.titleApplication of Effective Markovian Projection to SABR and Heston Models
dc.typeThesis / Dissertation
dc.type.qualificationlevelMasters
dc.type.qualificationlevelMPhil
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