A survey and implementation of some calibration algorithms for the SABR and Heston models

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dc.contributor.advisorBecker, Ronalden_ZA
dc.contributor.authorWebber, Carolineen_ZA
dc.date.accessioned2014-10-17T10:08:23Z
dc.date.available2014-10-17T10:08:23Z
dc.date.issued2014en_ZA
dc.descriptionIncludes bibliographical references.en_ZA
dc.description.abstractThis thesis surveys and implements some calibration methods for the SABR and Heston models. Hagan (2002) examined the effect of the SABR parameters on the skew in order to determine which parameters may be redundant. Hagan andWest (2005) found that by fixing one of the parameters in the SABR model, the remaining parameters were stable over time. We implement a SABR calibrator to confirm that the parameters are stable over time. We then examine the effects of the five Heston parameters on the skew in order to determine if any of the parameters are redundant. Calibrators where some parameters have been fixed and calibrators where no parameters have been fixed are implemented. The performance of these calibrators is then compared based on three criteria: the stability of the parameters over time, the fit of the solution and the computational efficiency of the calibrator. We find that the Heston parameters are more stable if the redundant parameters are fixed, the computation time is less and the fit is slightly worse. All implementations are done in the context of the South African market. The calibrators are programmed in Matlab and the code is included in the appendix.en_ZA
dc.identifier.apacitationWebber, C. (2014). <i>A survey and implementation of some calibration algorithms for the SABR and Heston models</i>. (Thesis). University of Cape Town ,Faculty of Commerce ,School of Economics. Retrieved from http://hdl.handle.net/11427/8518en_ZA
dc.identifier.chicagocitationWebber, Caroline. <i>"A survey and implementation of some calibration algorithms for the SABR and Heston models."</i> Thesis., University of Cape Town ,Faculty of Commerce ,School of Economics, 2014. http://hdl.handle.net/11427/8518en_ZA
dc.identifier.citationWebber, C. 2014. A survey and implementation of some calibration algorithms for the SABR and Heston models. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Webber, Caroline AB - This thesis surveys and implements some calibration methods for the SABR and Heston models. Hagan (2002) examined the effect of the SABR parameters on the skew in order to determine which parameters may be redundant. Hagan andWest (2005) found that by fixing one of the parameters in the SABR model, the remaining parameters were stable over time. We implement a SABR calibrator to confirm that the parameters are stable over time. We then examine the effects of the five Heston parameters on the skew in order to determine if any of the parameters are redundant. Calibrators where some parameters have been fixed and calibrators where no parameters have been fixed are implemented. The performance of these calibrators is then compared based on three criteria: the stability of the parameters over time, the fit of the solution and the computational efficiency of the calibrator. We find that the Heston parameters are more stable if the redundant parameters are fixed, the computation time is less and the fit is slightly worse. All implementations are done in the context of the South African market. The calibrators are programmed in Matlab and the code is included in the appendix. DA - 2014 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2014 T1 - A survey and implementation of some calibration algorithms for the SABR and Heston models TI - A survey and implementation of some calibration algorithms for the SABR and Heston models UR - http://hdl.handle.net/11427/8518 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/8518
dc.identifier.vancouvercitationWebber C. A survey and implementation of some calibration algorithms for the SABR and Heston models. [Thesis]. University of Cape Town ,Faculty of Commerce ,School of Economics, 2014 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/8518en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentSchool of Economicsen_ZA
dc.publisher.facultyFaculty of Commerceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.titleA survey and implementation of some calibration algorithms for the SABR and Heston modelsen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMPhilen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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