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Kalman Filtering and the Estimation of Multi-factor Affine Term Structure Models
When optimising the likelihood function one often encounters various stationary points and sometimes discontinuities in the parameter space (Gupta and Mehra, 1974). This is certainly true for a majority of multi-factor affine term structure models. Practitioners often recover different parameter opt...
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| Format: | Thesis |
| Language: | English |
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African Institute of Financial Markets and Risk Management
2019
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| _version_ | 1867614157028720640 |
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| access_status_str | Open Access |
| author | Tokwe,Thabo |
| author2 | Ouwehand, Peter |
| author_browse | Ouwehand, Peter Tokwe,Thabo |
| author_facet | Ouwehand, Peter Tokwe,Thabo |
| author_sort | Tokwe,Thabo |
| collection | Thesis |
| description | When optimising the likelihood function one often encounters various stationary points and sometimes discontinuities in the parameter space (Gupta and Mehra, 1974). This is certainly true for a majority of multi-factor affine term structure models. Practitioners often recover different parameter optimisations depending on the initial parameters. If these parameters result in different option prices, the implications would be severe. This paper examines these implications through numerical experiments on the three-factor Vasicek and Arbitrage-free Nelson-Siegel (AFNS) models. The numerical experiments involve Kalman filtering as well as likelihood optimisation for parameter estimation. It was found that the parameter sets lead to the same short rate process and thus the same model. Moreover, likelihood optimisation in the AFNS does not result in different parameter sets irrespective of the starting point. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/29465 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:47:34.514Z |
| 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 | African Institute of Financial Markets and Risk Management |
| publisherStr | African Institute of Financial Markets and Risk Management |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/29465 Kalman Filtering and the Estimation of Multi-factor Affine Term Structure Models Tokwe,Thabo Ouwehand, Peter Mathematical Finance When optimising the likelihood function one often encounters various stationary points and sometimes discontinuities in the parameter space (Gupta and Mehra, 1974). This is certainly true for a majority of multi-factor affine term structure models. Practitioners often recover different parameter optimisations depending on the initial parameters. If these parameters result in different option prices, the implications would be severe. This paper examines these implications through numerical experiments on the three-factor Vasicek and Arbitrage-free Nelson-Siegel (AFNS) models. The numerical experiments involve Kalman filtering as well as likelihood optimisation for parameter estimation. It was found that the parameter sets lead to the same short rate process and thus the same model. Moreover, likelihood optimisation in the AFNS does not result in different parameter sets irrespective of the starting point. 2019-02-11T13:09:24Z 2019-02-11T13:09:24Z 2018 2019-02-11T11:50:30Z Master Thesis Masters MPhil http://hdl.handle.net/11427/29465 eng application/pdf African Institute of Financial Markets and Risk Management Faculty of Commerce University of Cape Town |
| spellingShingle | Mathematical Finance Tokwe,Thabo Kalman Filtering and the Estimation of Multi-factor Affine Term Structure Models |
| thesis_degree_str | Master's |
| title | Kalman Filtering and the Estimation of Multi-factor Affine Term Structure Models |
| title_full | Kalman Filtering and the Estimation of Multi-factor Affine Term Structure Models |
| title_fullStr | Kalman Filtering and the Estimation of Multi-factor Affine Term Structure Models |
| title_full_unstemmed | Kalman Filtering and the Estimation of Multi-factor Affine Term Structure Models |
| title_short | Kalman Filtering and the Estimation of Multi-factor Affine Term Structure Models |
| title_sort | kalman filtering and the estimation of multi factor affine term structure models |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/29465 |
| work_keys_str_mv | AT tokwethabo kalmanfilteringandtheestimationofmultifactoraffinetermstructuremodels |