Concurrence Between the Displaced Libor Market and Hull-White Models

Simple item page
dc.contributor.advisorMcWalter, Thomas
dc.contributor.authorThantsha, Kgothatso
dc.date.accessioned2022-03-22T08:48:58Z
dc.date.available2022-03-22T08:48:58Z
dc.date.issued2021
dc.date.updated2022-03-17T12:57:48Z
dc.description.abstractThe concurrence between the displaced lognormal forward-Libor model (DLFM), Gaussian Heath-Jarrow-Morton (GHJM) model and Hull-White (HW) model is explored. We briefly present the theory underpinning these models, specifically focusing on single factors. A useful volatility relation result adapted from Andersen and Piterbarg (2010) is derived. It relates the instantaneous volatility functions of the GHJM model and the DLFM model. The volatility relation allows us to state a specific GHJM model and derive a corresponding DLFM model that it is concurrent with. We take the Hull-White model and derive its corresponding GHJM model, the volatility of the GHJM model is then fed into the volatility relation in order to derive the corresponding DLFM model. This was sufficient mathematical proof of the concurrence, but numerical confirmation is also essential. The HW, GHJM and DLFM models were implemented, with applications to pricing European swaptions. Numerical results show that swaption prices are consistent across the three models. This provides good numerical evidence to support the concurrence between the DLFM and HW models.
dc.identifier.apacitationThantsha, K. (2021). <i>Concurrence Between the Displaced Libor Market and Hull-White Models</i>. (). ,Faculty of Commerce ,Department of Finance and Tax. Retrieved from http://hdl.handle.net/11427/36181en_ZA
dc.identifier.chicagocitationThantsha, Kgothatso. <i>"Concurrence Between the Displaced Libor Market and Hull-White Models."</i> ., ,Faculty of Commerce ,Department of Finance and Tax, 2021. http://hdl.handle.net/11427/36181en_ZA
dc.identifier.citationThantsha, K. 2021. Concurrence Between the Displaced Libor Market and Hull-White Models. . ,Faculty of Commerce ,Department of Finance and Tax. http://hdl.handle.net/11427/36181en_ZA
dc.identifier.ris TY - Master Thesis AU - Thantsha, Kgothatso AB - The concurrence between the displaced lognormal forward-Libor model (DLFM), Gaussian Heath-Jarrow-Morton (GHJM) model and Hull-White (HW) model is explored. We briefly present the theory underpinning these models, specifically focusing on single factors. A useful volatility relation result adapted from Andersen and Piterbarg (2010) is derived. It relates the instantaneous volatility functions of the GHJM model and the DLFM model. The volatility relation allows us to state a specific GHJM model and derive a corresponding DLFM model that it is concurrent with. We take the Hull-White model and derive its corresponding GHJM model, the volatility of the GHJM model is then fed into the volatility relation in order to derive the corresponding DLFM model. This was sufficient mathematical proof of the concurrence, but numerical confirmation is also essential. The HW, GHJM and DLFM models were implemented, with applications to pricing European swaptions. Numerical results show that swaption prices are consistent across the three models. This provides good numerical evidence to support the concurrence between the DLFM and HW models. DA - 2021_ DB - OpenUCT DP - University of Cape Town KW - Mathematical Finance LK - https://open.uct.ac.za PY - 2021 T1 - Concurrence Between the Displaced Libor Market and Hull-White Models TI - Concurrence Between the Displaced Libor Market and Hull-White Models UR - http://hdl.handle.net/11427/36181 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/36181
dc.identifier.vancouvercitationThantsha K. Concurrence Between the Displaced Libor Market and Hull-White Models. []. ,Faculty of Commerce ,Department of Finance and Tax, 2021 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/36181en_ZA
dc.language.rfc3066eng
dc.publisher.departmentDepartment of Finance and Tax
dc.publisher.facultyFaculty of Commerce
dc.subjectMathematical Finance
dc.titleConcurrence Between the Displaced Libor Market and Hull-White Models
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationlevelMPhil
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
thesis_com_2021_thantsha kgothatso.pdf
Size:
1.18 MB
Format:
Adobe Portable Document Format
Description:
Download
License bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
license.txt
Size:
0 B
Format:
Item-specific license agreed upon to submission
Description:
Download
Collections
Masters