Incompatibility of lognormal forward-Libor and Swap market models

 

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dc.contributor.advisor MacGregor, Ken en_ZA
dc.contributor.author Goschen, Wayne S en_ZA
dc.date.accessioned 2014-10-20T07:45:29Z
dc.date.available 2014-10-20T07:45:29Z
dc.date.issued 2005 en_ZA
dc.identifier.citation Goschen, W. 2005. Incompatibility of lognormal forward-Libor and Swap market models. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/8648
dc.description Includes bibliographical references (p. 156-160). en_ZA
dc.description.abstract The lognormal forward-Libor and Swap market models were formulated to price caps and swaptions. However, the prices computed by these two models, under equivalent measures, are reported to be unequal. This study investigates this incompatibility by computing the prices of caps and swaptions under both the forward Libor measure and the forward Swap measure, in both the Libor and Swap market models. This was done by building a computer program that implements the Monte Carlo versions of the models, using data from caps and swaptions traded in the South African market. It was found that the actual price of caps, using the same implied volatility, were simulated accurately in both the Libor and Swap market models under both the forward Libor measure and the forward Swap measure. On the other hand, although the actual swaption prices were also simulated accurately in both the Libor and Swap market models under both the forward Libor measure and the forward Swap measure, a different implied volatility was used for each model. Therefore, the swaption price computed by the Libor market model was inconsistent with the price generated by the Swap market model; the two models are indeed incompatible. In order to price interest rate derivatives consistently, either the Libor market model or the Swap market model must be chosen. Since the Libor market model priced consistently under the two forward measures, and the time taken to simulate a price in the Libor market model was much less than in the Swap market model, the practice in the market to use the Libor market model in favour of the Swap market model is justified. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Information Technology en_ZA
dc.title Incompatibility of lognormal forward-Libor and Swap market models en_ZA
dc.type Master Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Computer Science en_ZA
dc.type.qualificationlevel Masters
dc.type.qualificationname MSc en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Goschen, W. S. (2005). <i>Incompatibility of lognormal forward-Libor and Swap market models</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Computer Science. Retrieved from http://hdl.handle.net/11427/8648 en_ZA
dc.identifier.chicagocitation Goschen, Wayne S. <i>"Incompatibility of lognormal forward-Libor and Swap market models."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Computer Science, 2005. http://hdl.handle.net/11427/8648 en_ZA
dc.identifier.vancouvercitation Goschen WS. Incompatibility of lognormal forward-Libor and Swap market models. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Computer Science, 2005 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/8648 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Goschen, Wayne S AB - The lognormal forward-Libor and Swap market models were formulated to price caps and swaptions. However, the prices computed by these two models, under equivalent measures, are reported to be unequal. This study investigates this incompatibility by computing the prices of caps and swaptions under both the forward Libor measure and the forward Swap measure, in both the Libor and Swap market models. This was done by building a computer program that implements the Monte Carlo versions of the models, using data from caps and swaptions traded in the South African market. It was found that the actual price of caps, using the same implied volatility, were simulated accurately in both the Libor and Swap market models under both the forward Libor measure and the forward Swap measure. On the other hand, although the actual swaption prices were also simulated accurately in both the Libor and Swap market models under both the forward Libor measure and the forward Swap measure, a different implied volatility was used for each model. Therefore, the swaption price computed by the Libor market model was inconsistent with the price generated by the Swap market model; the two models are indeed incompatible. In order to price interest rate derivatives consistently, either the Libor market model or the Swap market model must be chosen. Since the Libor market model priced consistently under the two forward measures, and the time taken to simulate a price in the Libor market model was much less than in the Swap market model, the practice in the market to use the Libor market model in favour of the Swap market model is justified. DA - 2005 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2005 T1 - Incompatibility of lognormal forward-Libor and Swap market models TI - Incompatibility of lognormal forward-Libor and Swap market models UR - http://hdl.handle.net/11427/8648 ER - en_ZA


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