Implementation of Bivariate Unspanned Stochastic Volatility Models
dc.contributor.advisor | Backwell, Alex | |
dc.contributor.author | Cullinan, Cian | |
dc.date.accessioned | 2019-02-04T12:23:46Z | |
dc.date.available | 2019-02-04T12:23:46Z | |
dc.date.issued | 2018 | |
dc.date.updated | 2019-02-01T08:51:41Z | |
dc.description.abstract | 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 | |
dc.identifier.apacitation | Cullinan, 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/11427/29266 | en_ZA |
dc.identifier.chicagocitation | Cullinan, 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/11427/29266 | en_ZA |
dc.identifier.citation | Cullinan, 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.uri | http://hdl.handle.net/11427/29266 | |
dc.identifier.vancouvercitation | Cullinan 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/11427/29266 | en_ZA |
dc.language.iso | eng | |
dc.publisher.department | Department of Mathematics and Applied Mathematics | |
dc.publisher.faculty | Faculty of Science | |
dc.publisher.institution | University of Cape Town | |
dc.subject.other | mathematical finance | |
dc.title | Implementation of Bivariate Unspanned Stochastic Volatility Models | |
dc.type | Master Thesis | |
dc.type.qualificationlevel | Masters | |
dc.type.qualificationname | MPhil |