Implementation of Bivariate Unspanned Stochastic Volatility Models

dc.contributor.advisorBackwell, Alex
dc.contributor.authorCullinan, Cian
dc.date.accessioned2019-02-04T12:23:46Z
dc.date.available2019-02-04T12:23:46Z
dc.date.issued2018
dc.date.updated2019-02-01T08:51:41Z
dc.description.abstractUnspanned stochastic volatility term structure models have gained popularity in the literature. This dissertation focuses on the challenges of implementing the simplest case – bivariate unspanned stochastic volatility models, where there is one state variable controlling the term structure, and one scaling the volatility. Specifically, we consider the Log-Affine Double Quadratic (1,1) model of Backwell (2017). In the class of affine term structure models, state variables are virtually always spanned and can therefore be inferred from bond yields. When fitting unspanned models, it is necessary to include option data, which adds further challenges. Because there are no analytical solutions in the LADQ (1,1) model, we show how options can be priced using an Alternating Direction Implicit finite difference scheme. We then implement an Unscented Kalman filter — a non-linear extension of the Kalman filter, which is a popular method for inferring state variable values — to recover the latent state variables from market observable data
dc.identifier.apacitationCullinan, C. (2018). <i>Implementation of Bivariate Unspanned Stochastic Volatility Models</i>. (). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/29266en_ZA
dc.identifier.chicagocitationCullinan, Cian. <i>"Implementation of Bivariate Unspanned Stochastic Volatility Models."</i> ., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2018. http://hdl.handle.net/11427/29266en_ZA
dc.identifier.citationCullinan, C. 2018. Implementation of Bivariate Unspanned Stochastic Volatility Models. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Cullinan, Cian AB - Unspanned stochastic volatility term structure models have gained popularity in the literature. This dissertation focuses on the challenges of implementing the simplest case – bivariate unspanned stochastic volatility models, where there is one state variable controlling the term structure, and one scaling the volatility. Specifically, we consider the Log-Affine Double Quadratic (1,1) model of Backwell (2017). In the class of affine term structure models, state variables are virtually always spanned and can therefore be inferred from bond yields. When fitting unspanned models, it is necessary to include option data, which adds further challenges. Because there are no analytical solutions in the LADQ (1,1) model, we show how options can be priced using an Alternating Direction Implicit finite difference scheme. We then implement an Unscented Kalman filter — a non-linear extension of the Kalman filter, which is a popular method for inferring state variable values — to recover the latent state variables from market observable data DA - 2018 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2018 T1 - Implementation of Bivariate Unspanned Stochastic Volatility Models TI - Implementation of Bivariate Unspanned Stochastic Volatility Models UR - http://hdl.handle.net/11427/29266 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/29266
dc.identifier.vancouvercitationCullinan C. Implementation of Bivariate Unspanned Stochastic Volatility Models. []. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2018 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/29266en_ZA
dc.language.isoeng
dc.publisher.departmentDepartment of Mathematics and Applied Mathematics
dc.publisher.facultyFaculty of Science
dc.publisher.institutionUniversity of Cape Town
dc.subject.othermathematical finance
dc.titleImplementation of Bivariate Unspanned Stochastic Volatility Models
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMPhil
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