Calibrating the LIBOR market model to swaptions with an extension for illiquidity in South Africa

 

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dc.contributor.advisor Taylor, David en_ZA
dc.contributor.author Moodliyar, Leenesh en_ZA
dc.date.accessioned 2016-07-14T12:20:55Z
dc.date.available 2016-07-14T12:20:55Z
dc.date.issued 2016 en_ZA
dc.identifier.citation Moodliyar, L. 2016. Calibrating the LIBOR market model to swaptions with an extension for illiquidity in South Africa. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/20346
dc.description.abstract The popularity of the LIBOR Market Model (LMM) in interest rate modelling is a result of its consistency with market practice of pricing interest rate derivatives. In the context of a life insurance company, the LMM is calibrated to swaptions as they are actively traded for a wide variety of maturities and they serve as the natural hedge instruments for many of the long dated maturity products with embedded options. Before calibrating the model we extend the calibration process to address the issue of illiquidity in the South African swaption market. The swaption surface used in calibrating the model is generated with market implied quotes for the hedgeable component and thereafter using historical volatilities for the unhedgeable or illiquid component. Rebonato's 3 parameter correlation function proposed by Rebonato (2005) provides the best fit to historical data. We assume a general piecewise constant parameterisation for the instantaneous forward rate volatilities. These volatilities are then determined analytically using the Rectangular Cascade Calibration Algorithm from Brigo and Morini (2006). The calibration generates a stable volatility term structure with the instantaneous forward rate volatilities being positive and real. Through an extension of the calibration we are able to capture the benefits of a pure replication component and accommodate a large unhedgeable component in the price faced by life insurance companies in South Africa. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Mathematical Finance en_ZA
dc.title Calibrating the LIBOR market model to swaptions with an extension for illiquidity in South Africa 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 Commerce en_ZA
dc.publisher.department Division of Actuarial Science en_ZA
dc.type.qualificationlevel Masters
dc.type.qualificationname MPhil en_ZA
uct.type.filetype Text
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dc.identifier.apacitation Moodliyar, L. (2016). <i>Calibrating the LIBOR market model to swaptions with an extension for illiquidity in South Africa</i>. (Thesis). University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science. Retrieved from http://hdl.handle.net/11427/20346 en_ZA
dc.identifier.chicagocitation Moodliyar, Leenesh. <i>"Calibrating the LIBOR market model to swaptions with an extension for illiquidity in South Africa."</i> Thesis., University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2016. http://hdl.handle.net/11427/20346 en_ZA
dc.identifier.vancouvercitation Moodliyar L. Calibrating the LIBOR market model to swaptions with an extension for illiquidity in South Africa. [Thesis]. University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2016 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/20346 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Moodliyar, Leenesh AB - The popularity of the LIBOR Market Model (LMM) in interest rate modelling is a result of its consistency with market practice of pricing interest rate derivatives. In the context of a life insurance company, the LMM is calibrated to swaptions as they are actively traded for a wide variety of maturities and they serve as the natural hedge instruments for many of the long dated maturity products with embedded options. Before calibrating the model we extend the calibration process to address the issue of illiquidity in the South African swaption market. The swaption surface used in calibrating the model is generated with market implied quotes for the hedgeable component and thereafter using historical volatilities for the unhedgeable or illiquid component. Rebonato's 3 parameter correlation function proposed by Rebonato (2005) provides the best fit to historical data. We assume a general piecewise constant parameterisation for the instantaneous forward rate volatilities. These volatilities are then determined analytically using the Rectangular Cascade Calibration Algorithm from Brigo and Morini (2006). The calibration generates a stable volatility term structure with the instantaneous forward rate volatilities being positive and real. Through an extension of the calibration we are able to capture the benefits of a pure replication component and accommodate a large unhedgeable component in the price faced by life insurance companies in South Africa. DA - 2016 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2016 T1 - Calibrating the LIBOR market model to swaptions with an extension for illiquidity in South Africa TI - Calibrating the LIBOR market model to swaptions with an extension for illiquidity in South Africa UR - http://hdl.handle.net/11427/20346 ER - en_ZA


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