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Approximations to the Lévy LIBOR Model
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...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613206725263360 |
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| access_status_str | Open Access |
| author | Al-Hassan, Hassana |
| author2 | Becker, Ronald |
| author_browse | Al-Hassan, Hassana Becker, Ronald |
| author_facet | Becker, Ronald Al-Hassan, Hassana |
| author_sort | Al-Hassan, Hassana |
| collection | Thesis |
| description | 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). |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/22029 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:27.580Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/22029 Approximations to the Lévy LIBOR Model Al-Hassan, Hassana Becker, Ronald Mataramvura, Sure Mathematics and Applied Mathematics 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). 2016-09-30T11:41:15Z 2016-09-30T11:41:15Z 2014 Master Thesis Masters MSc http://hdl.handle.net/11427/22029 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics and Applied Mathematics Al-Hassan, Hassana Approximations to the Lévy LIBOR Model |
| thesis_degree_str | Master's |
| title | Approximations to the Lévy LIBOR Model |
| title_full | Approximations to the Lévy LIBOR Model |
| title_fullStr | Approximations to the Lévy LIBOR Model |
| title_full_unstemmed | Approximations to the Lévy LIBOR Model |
| title_short | Approximations to the Lévy LIBOR Model |
| title_sort | approximations to the levy libor model |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/22029 |
| work_keys_str_mv | AT alhassanhassana approximationstothelevylibormodel |