Approximations to the Lévy LIBOR Model

Simple item page
dc.contributor.advisorBecker, Ronalden_ZA
dc.contributor.advisorMataramvura, Sureen_ZA
dc.contributor.authorAl-Hassan, Hassanaen_ZA
dc.date.accessioned2016-09-30T11:41:15Z
dc.date.available2016-09-30T11:41:15Z
dc.date.issued2014en_ZA
dc.description.abstractIn this thesis, we study the LIBOR Market Model and the Lévy-LIBOR. We first look at the construction of LIBOR Market Model (LMM) and address the major problems associated with specifically the drift component of LMM. Due to the complexity of the drift for LMM, the Monte Carlo method seems to be the ideal tool to use. However, the Monte Carlo method is time consuming and therefore an expensive tool to use. To improve on the process we look beyond the dynamics of the lognormal distribution, where Brownian motion (the only Lévy process with continuous paths), is the driving process and apply other Lévy processes with jumps as the driving process in the dynamics of LIBOR. The resulting process is called Lévy LIBOR Model constructed in the framework of Eberlein and Özkan (2005). The Lévy LIBOR model is a very flexible and a general process to use but has a complicated drift part in the terminal measure. The complicated drift term has random terms in the drift part as a result of change of measure. We employ Picard approximation and cumulant expansions in the resulting drift component to make the processes tractable in the framework of Papapantoleon and Skovmand (2010).en_ZA
dc.identifier.apacitationAl-Hassan, H. (2014). <i>Approximations to the Lévy LIBOR Model</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/22029en_ZA
dc.identifier.chicagocitationAl-Hassan, Hassana. <i>"Approximations to the Lévy LIBOR Model."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2014. http://hdl.handle.net/11427/22029en_ZA
dc.identifier.citationAl-Hassan, H. 2014. Approximations to the Lévy LIBOR Model. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Al-Hassan, Hassana AB - In this thesis, we study the LIBOR Market Model and the Lévy-LIBOR. We first look at the construction of LIBOR Market Model (LMM) and address the major problems associated with specifically the drift component of LMM. Due to the complexity of the drift for LMM, the Monte Carlo method seems to be the ideal tool to use. However, the Monte Carlo method is time consuming and therefore an expensive tool to use. To improve on the process we look beyond the dynamics of the lognormal distribution, where Brownian motion (the only Lévy process with continuous paths), is the driving process and apply other Lévy processes with jumps as the driving process in the dynamics of LIBOR. The resulting process is called Lévy LIBOR Model constructed in the framework of Eberlein and Özkan (2005). The Lévy LIBOR model is a very flexible and a general process to use but has a complicated drift part in the terminal measure. The complicated drift term has random terms in the drift part as a result of change of measure. We employ Picard approximation and cumulant expansions in the resulting drift component to make the processes tractable in the framework of Papapantoleon and Skovmand (2010). DA - 2014 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2014 T1 - Approximations to the Lévy LIBOR Model TI - Approximations to the Lévy LIBOR Model UR - http://hdl.handle.net/11427/22029 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/22029
dc.identifier.vancouvercitationAl-Hassan H. Approximations to the Lévy LIBOR Model. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2014 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/22029en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematics and Applied Mathematicsen_ZA
dc.titleApproximations to the Lévy LIBOR Modelen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
thesis_sci_2014_al_hassan_hassana.pdf
Size:
1.41 MB
Format:
Adobe Portable Document Format
Description:
Download
Collections
Masters