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Calibrating Term Structure Models to an Initial Yield Curve
The modelling of the short rate offers many advantages, with the models explored in this dissertation all offering closed-form, analytic formulae for bond prices and for options on bonds. Often, a vital primary condition is for a model to be calibrated to the initial term structure and to recover th...
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| Format: | Thesis |
| Language: | English |
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African Institute of Financial Markets and Risk Management
2021
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| _version_ | 1867613162185949184 |
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| access_status_str | Open Access |
| author | Sylvester, Matthew |
| author2 | Backwell, Alex |
| author_browse | Backwell, Alex Sylvester, Matthew |
| author_facet | Backwell, Alex Sylvester, Matthew |
| author_sort | Sylvester, Matthew |
| collection | Thesis |
| description | The modelling of the short rate offers many advantages, with the models explored in this dissertation all offering closed-form, analytic formulae for bond prices and for options on bonds. Often, a vital primary condition is for a model to be calibrated to the initial term structure and to recover the bond prices observed in the market – that is, to be calibrated to the initial yield curve. Under the two exogenous models explored in this dissertation, the Hull-White and the CIR++, the effect of increasing the volatility parameter of the SDE increases the mean of the short rate. Increasing volatility of an SDE is a common approach to stress testing a model, as such, the consequences of bumping volatility in a calibrated model is a vital concern. The Hull-White model and CIR++ model were calibrated to market data, with the former being able to match the observed cap prices, while the latter failed, displaying an upper bound on cap prices. Investigating this, under CIR++ model, bond option prices are shown to not be straightforward increasing functions of the volatility parameter. In fact, for high volatility, bond option prices display an upper limit before decreasing, thus providing a limit to the level of cap prices too. This dissertation points to the reason residing in the underlying CIR model from which the CIR++ is based on, and the manner in which the model is extended |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/33027 |
| 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 | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| 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:11427/33027 Calibrating Term Structure Models to an Initial Yield Curve Sylvester, Matthew Backwell, Alex Mathematical Finance The modelling of the short rate offers many advantages, with the models explored in this dissertation all offering closed-form, analytic formulae for bond prices and for options on bonds. Often, a vital primary condition is for a model to be calibrated to the initial term structure and to recover the bond prices observed in the market – that is, to be calibrated to the initial yield curve. Under the two exogenous models explored in this dissertation, the Hull-White and the CIR++, the effect of increasing the volatility parameter of the SDE increases the mean of the short rate. Increasing volatility of an SDE is a common approach to stress testing a model, as such, the consequences of bumping volatility in a calibrated model is a vital concern. The Hull-White model and CIR++ model were calibrated to market data, with the former being able to match the observed cap prices, while the latter failed, displaying an upper bound on cap prices. Investigating this, under CIR++ model, bond option prices are shown to not be straightforward increasing functions of the volatility parameter. In fact, for high volatility, bond option prices display an upper limit before decreasing, thus providing a limit to the level of cap prices too. This dissertation points to the reason residing in the underlying CIR model from which the CIR++ is based on, and the manner in which the model is extended 2021-03-01T15:34:32Z 2021-03-01T15:34:32Z 2020 2021-03-01T14:25:19Z Master Thesis Masters MPhil http://hdl.handle.net/11427/33027 eng application/pdf African Institute of Financial Markets and Risk Management Faculty of Commerce |
| spellingShingle | Mathematical Finance Sylvester, Matthew Calibrating Term Structure Models to an Initial Yield Curve |
| thesis_degree_str | Master's |
| title | Calibrating Term Structure Models to an Initial Yield Curve |
| title_full | Calibrating Term Structure Models to an Initial Yield Curve |
| title_fullStr | Calibrating Term Structure Models to an Initial Yield Curve |
| title_full_unstemmed | Calibrating Term Structure Models to an Initial Yield Curve |
| title_short | Calibrating Term Structure Models to an Initial Yield Curve |
| title_sort | calibrating term structure models to an initial yield curve |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/33027 |
| work_keys_str_mv | AT sylvestermatthew calibratingtermstructuremodelstoaninitialyieldcurve |