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Estimation of Shadow-Rate Term Structure Models Near the Zero-Lower Bound
Though it is customary to use standard Gaussian term structure models for term structure modelling, this becomes theoretically implausible in cases when nominal interest rates are near zero: Gaussian models can have arbitrarily large negative rates, whereas arbitrage considerations dictate that rate...
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| Format: | Thesis |
| Language: | English |
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Division of Actuarial Science
2020
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| _version_ | 1867613958670647296 |
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| access_status_str | Open Access |
| author | Esmail, Shabbirhussein |
| author2 | Ouwehand, Peter |
| author_browse | Esmail, Shabbirhussein Ouwehand, Peter |
| author_facet | Ouwehand, Peter Esmail, Shabbirhussein |
| author_sort | Esmail, Shabbirhussein |
| collection | Thesis |
| description | Though it is customary to use standard Gaussian term structure models for term structure modelling, this becomes theoretically implausible in cases when nominal interest rates are near zero: Gaussian models can have arbitrarily large negative rates, whereas arbitrage considerations dictate that rates should remain positive (or very slightly negative at most). Black (1995) suggests that interest rates include an optionality which restricts them to non-negative values. This introduces a non-linearity at the zero-lower bound that makes these so-called shadow-rate models a computational challenge. This dissertation analyses the shadow-rate approximations suggested by Krippner (2013) and Priebsch (2013) for the Vasicek and ˇ arbitrage-free Nelson-Siegel (AFNS) models. We also investigate and compare the accuracy of the iterated extended Kalman filter (IEKF) with that of the unscented Kalman filter (UKF). We find that Krippner’s approach approximates interest rates within reasonable bounds for both the 1-factor Vasicek and AFNS models. Prieb- ˇ sch’s first-cumulant method is more accurate than Krippner’s method for a 1-factor Vasicek model, while Priebsch’s second-cumulant method is deemed impractical ˇ because of the computational time it takes. In a multi-factor AFNS model, only Krippner’s framework is feasible. Moreover, the IEKF outperforms the UKF in terms of filtering with no significant difference in run-time. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/31152 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:44:25.346Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2020 |
| publishDateRange | 2020 |
| publishDateSort | 2020 |
| publisher | Division of Actuarial Science |
| publisherStr | Division of Actuarial Science |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/31152 Estimation of Shadow-Rate Term Structure Models Near the Zero-Lower Bound Esmail, Shabbirhussein Ouwehand, Peter actuarial science Though it is customary to use standard Gaussian term structure models for term structure modelling, this becomes theoretically implausible in cases when nominal interest rates are near zero: Gaussian models can have arbitrarily large negative rates, whereas arbitrage considerations dictate that rates should remain positive (or very slightly negative at most). Black (1995) suggests that interest rates include an optionality which restricts them to non-negative values. This introduces a non-linearity at the zero-lower bound that makes these so-called shadow-rate models a computational challenge. This dissertation analyses the shadow-rate approximations suggested by Krippner (2013) and Priebsch (2013) for the Vasicek and ˇ arbitrage-free Nelson-Siegel (AFNS) models. We also investigate and compare the accuracy of the iterated extended Kalman filter (IEKF) with that of the unscented Kalman filter (UKF). We find that Krippner’s approach approximates interest rates within reasonable bounds for both the 1-factor Vasicek and AFNS models. Prieb- ˇ sch’s first-cumulant method is more accurate than Krippner’s method for a 1-factor Vasicek model, while Priebsch’s second-cumulant method is deemed impractical ˇ because of the computational time it takes. In a multi-factor AFNS model, only Krippner’s framework is feasible. Moreover, the IEKF outperforms the UKF in terms of filtering with no significant difference in run-time. 2020-02-18T09:22:08Z 2020-02-18T09:22:08Z 2019 2020-02-18T08:09:47Z Master Thesis Masters MPhil http://hdl.handle.net/11427/31152 eng application/pdf Division of Actuarial Science Faculty of Commerce |
| spellingShingle | actuarial science Esmail, Shabbirhussein Estimation of Shadow-Rate Term Structure Models Near the Zero-Lower Bound |
| thesis_degree_str | Master's |
| title | Estimation of Shadow-Rate Term Structure Models Near the Zero-Lower Bound |
| title_full | Estimation of Shadow-Rate Term Structure Models Near the Zero-Lower Bound |
| title_fullStr | Estimation of Shadow-Rate Term Structure Models Near the Zero-Lower Bound |
| title_full_unstemmed | Estimation of Shadow-Rate Term Structure Models Near the Zero-Lower Bound |
| title_short | Estimation of Shadow-Rate Term Structure Models Near the Zero-Lower Bound |
| title_sort | estimation of shadow rate term structure models near the zero lower bound |
| topic | actuarial science |
| url | http://hdl.handle.net/11427/31152 |
| work_keys_str_mv | AT esmailshabbirhussein estimationofshadowratetermstructuremodelsnearthezerolowerbound |