Calibrating Term Structure Models to an Initial Yield Curve
| dc.contributor.advisor | Backwell, Alex | |
| dc.contributor.author | Sylvester, Matthew | |
| dc.date.accessioned | 2021-03-01T15:34:32Z | |
| dc.date.available | 2021-03-01T15:34:32Z | |
| dc.date.issued | 2020 | |
| dc.date.updated | 2021-03-01T14:25:19Z | |
| dc.description.abstract | 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 | |
| dc.identifier.apacitation | Sylvester, M. (2020). <i>Calibrating Term Structure Models to an Initial Yield Curve</i>. (). ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management. Retrieved from http://hdl.handle.net/11427/33027 | en_ZA |
| dc.identifier.chicagocitation | Sylvester, Matthew. <i>"Calibrating Term Structure Models to an Initial Yield Curve."</i> ., ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management, 2020. http://hdl.handle.net/11427/33027 | en_ZA |
| dc.identifier.citation | Sylvester, M. 2020. Calibrating Term Structure Models to an Initial Yield Curve. . ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management. http://hdl.handle.net/11427/33027 | en_ZA |
| dc.identifier.ris | TY - Master Thesis AU - Sylvester, Matthew AB - 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 DA - 2020_ DB - OpenUCT DP - University of Cape Town KW - Mathematical Finance LK - https://open.uct.ac.za PY - 2020 T1 - Calibrating Term Structure Models to an Initial Yield Curve TI - Calibrating Term Structure Models to an Initial Yield Curve UR - http://hdl.handle.net/11427/33027 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/33027 | |
| dc.identifier.vancouvercitation | Sylvester M. Calibrating Term Structure Models to an Initial Yield Curve. []. ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management, 2020 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/33027 | en_ZA |
| dc.language.rfc3066 | eng | |
| dc.publisher.department | African Institute of Financial Markets and Risk Management | |
| dc.publisher.faculty | Faculty of Commerce | |
| dc.subject | Mathematical Finance | |
| dc.title | Calibrating Term Structure Models to an Initial Yield Curve | |
| dc.type | Master Thesis | |
| dc.type.qualificationlevel | Masters | |
| dc.type.qualificationlevel | MPhil |