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Implementation of Bivariate Unspanned Stochastic Volatility Models
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...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2019
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| _version_ | 1867613162045440000 |
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| access_status_str | Open Access |
| author | Cullinan, Cian |
| author2 | Backwell, Alex |
| author_browse | Backwell, Alex Cullinan, Cian |
| author_facet | Backwell, Alex Cullinan, Cian |
| author_sort | Cullinan, Cian |
| collection | Thesis |
| description | 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 |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/29266 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:45.395Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2019 |
| publishDateRange | 2019 |
| publishDateSort | 2019 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/29266 Implementation of Bivariate Unspanned Stochastic Volatility Models Cullinan, Cian Backwell, Alex mathematical finance 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 2019-02-04T12:23:46Z 2019-02-04T12:23:46Z 2018 2019-02-01T08:51:41Z Master Thesis Masters MPhil http://hdl.handle.net/11427/29266 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | mathematical finance Cullinan, Cian Implementation of Bivariate Unspanned Stochastic Volatility Models |
| thesis_degree_str | Master's |
| title | Implementation of Bivariate Unspanned Stochastic Volatility Models |
| title_full | Implementation of Bivariate Unspanned Stochastic Volatility Models |
| title_fullStr | Implementation of Bivariate Unspanned Stochastic Volatility Models |
| title_full_unstemmed | Implementation of Bivariate Unspanned Stochastic Volatility Models |
| title_short | Implementation of Bivariate Unspanned Stochastic Volatility Models |
| title_sort | implementation of bivariate unspanned stochastic volatility models |
| topic | mathematical finance |
| url | http://hdl.handle.net/11427/29266 |
| work_keys_str_mv | AT cullinancian implementationofbivariateunspannedstochasticvolatilitymodels |