{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/40094"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/40094","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Efficient numerical methods for the valuation of American barrier options","abstract":"[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.","abstract_html":"[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 &lt;RTM), the Finite Difference Method &lt;FDM&gt; and the Finite Element Method &lt;FEM&gt;. 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.","abstract_has_math":false,"creators":["Dlamini, Mkhululi"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2002,"date_issued":"2002","date_published":"2002","updated_at":"2026-07-22T22:22:41Z","subjects":["Mathematics and Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/40094","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Dlamini, Mkhululi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-07-02T09:15:19Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-07-02T09:15:19Z"]},{"key":"dc:date.issued","label":"Date","values":["2002"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:type","label":"Dc Type","values":["Thesis / Dissertation"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters","MSc"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics and Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/40094"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["[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."]},{"key":"dc:title","label":"Title","values":["Efficient numerical methods for the valuation of American barrier options"]}]}],"canonical_facts":{"dc:creator":["Dlamini, Mkhululi"],"dc:date.accessioned":["2024-07-02T09:15:19Z"],"dc:date.available":["2024-07-02T09:15:19Z"],"dc:date.issued":["2002"],"dc:description.abstract":["[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."],"dc:identifier.uri":["http://hdl.handle.net/11427/40094"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:subject":["Mathematics and Applied Mathematics"],"dc:title":["Efficient numerical methods for the valuation of American barrier options"],"dc:type":["Thesis / Dissertation"],"dc:type.qualificationlevel":["Masters","MSc"]},"updated_at":"2026-07-22T22:22:41Z"}