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Efficient numerical methods for the valuation of American barrier options
[Thesis has an accompanying disc.] The barrier option is the most popular exotic option traded today. Because such options have a discontinuous payoff pattern, their accurate valuation is a particular challenge. Most popular in the OTC market, a lack of a liquid secondary market in these products ha...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2024
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| _version_ | 1867613171089408000 |
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| access_status_str | Open Access |
| author | Dlamini, Mkhululi |
| author_browse | Dlamini, Mkhululi |
| author_facet | Dlamini, Mkhululi |
| author_sort | Dlamini, Mkhululi |
| collection | Thesis |
| description | [Thesis has an accompanying disc.] The barrier option is the most popular exotic option traded today. Because such options have a discontinuous payoff pattern, their accurate valuation is a particular challenge. Most popular in the OTC market, a lack of a liquid secondary market in these products has meant that very often, an early exercise feature is added to the contract. This makes it of particular interest to study efficient numerical methods for the valuation of American barrier options . This thesis considers three methods that have been developed to price such options; the Ritchken Trinomial Method <RTM), the Finite Difference Method <FDM> and the Finite Element Method <FEM>. First an account is given of the barrier option pricing problem accompanied by a description of the behavior of barrier option price and delta curves. Then the theory and implementation of each method is described in turn. Finally a detailed computational analysis is given where the three methods are compared in pricing and hedging applications, with concluding remarks on the performance results. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/40094 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:53.390Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| 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:11427/40094 Efficient numerical methods for the valuation of American barrier options Dlamini, Mkhululi Mathematics and Applied Mathematics [Thesis has an accompanying disc.] The barrier option is the most popular exotic option traded today. Because such options have a discontinuous payoff pattern, their accurate valuation is a particular challenge. Most popular in the OTC market, a lack of a liquid secondary market in these products has meant that very often, an early exercise feature is added to the contract. This makes it of particular interest to study efficient numerical methods for the valuation of American barrier options . This thesis considers three methods that have been developed to price such options; the Ritchken Trinomial Method <RTM), the Finite Difference Method <FDM> and the Finite Element Method <FEM>. First an account is given of the barrier option pricing problem accompanied by a description of the behavior of barrier option price and delta curves. Then the theory and implementation of each method is described in turn. Finally a detailed computational analysis is given where the three methods are compared in pricing and hedging applications, with concluding remarks on the performance results. 2024-07-02T09:15:19Z 2024-07-02T09:15:19Z 2002 2024-07-01T13:22:30Z Thesis / Dissertation Masters MSc http://hdl.handle.net/11427/40094 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Mathematics and Applied Mathematics Dlamini, Mkhululi Efficient numerical methods for the valuation of American barrier options |
| thesis_degree_str | Master's |
| title | Efficient numerical methods for the valuation of American barrier options |
| title_full | Efficient numerical methods for the valuation of American barrier options |
| title_fullStr | Efficient numerical methods for the valuation of American barrier options |
| title_full_unstemmed | Efficient numerical methods for the valuation of American barrier options |
| title_short | Efficient numerical methods for the valuation of American barrier options |
| title_sort | efficient numerical methods for the valuation of american barrier options |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/40094 |
| work_keys_str_mv | AT dlaminimkhululi efficientnumericalmethodsforthevaluationofamericanbarrieroptions |