{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/8520"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/8520","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Two dimensional COS method for pricing early-exercise and discrete barrier options under the Heston Model","abstract":"We focus on the pricing of Bermudan and barrier options under the dynamics of the Heston stochastic volatility model. The two-dimensional nature of the Heston model makes the pricing of these options problematic, as the risk-neutral expectations need to be calculated at each exercise/observation date along a continuum of the two state spaces. We examine the 2D-COS method, which makes use of Fourier-cosine expansions in each of the two dimensions in order to approximate the integrals. Using the fast Fourier transform, we are able to efficiently calculate the cosine series coefficients at each exercise/observation date. A construction of this method is provided and we conduct numerical experiments to evaluate its speed and accuracy.","abstract_html":"We focus on the pricing of Bermudan and barrier options under the dynamics of the Heston stochastic volatility model. The two-dimensional nature of the Heston model makes the pricing of these options problematic, as the risk-neutral expectations need to be calculated at each exercise/observation date along a continuum of the two state spaces. We examine the 2D-COS method, which makes use of Fourier-cosine expansions in each of the two dimensions in order to approximate the integrals. Using the fast Fourier transform, we are able to efficiently calculate the cosine series coefficients at each exercise/observation date. A construction of this method is provided and we conduct numerical experiments to evaluate its speed and accuracy.","abstract_has_math":false,"creators":["Moir, Richard"],"institution":"Division of Actuarial Science","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Becker, Ronald"],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014","date_published":"2014","updated_at":"2026-07-22T22:23:22Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/8520","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Becker, Ronald"]},{"key":"dc:creator","label":"Author","values":["Moir, Richard"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-10-17T10:09:45Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-10-17T10:09:45Z"]},{"key":"dc:date.issued","label":"Date","values":["2014"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Division of Actuarial Science"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MPhil"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/8520"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Includes bibliographical references."]},{"key":"dc:description.abstract","label":"Abstract","values":["We focus on the pricing of Bermudan and barrier options under the dynamics of the Heston stochastic volatility model. The two-dimensional nature of the Heston model makes the pricing of these options problematic, as the risk-neutral expectations need to be calculated at each exercise/observation date along a continuum of the two state spaces. We examine the 2D-COS method, which makes use of Fourier-cosine expansions in each of the two dimensions in order to approximate the integrals. Using the fast Fourier transform, we are able to efficiently calculate the cosine series coefficients at each exercise/observation date. A construction of this method is provided and we conduct numerical experiments to evaluate its speed and accuracy."]},{"key":"dc:title","label":"Title","values":["Two dimensional COS method for pricing early-exercise and discrete barrier options under the Heston Model"]}]}],"canonical_facts":{"dc:contributor.advisor":["Becker, Ronald"],"dc:creator":["Moir, Richard"],"dc:date.accessioned":["2014-10-17T10:09:45Z"],"dc:date.available":["2014-10-17T10:09:45Z"],"dc:date.issued":["2014"],"dc:description":["Includes bibliographical references."],"dc:description.abstract":["We focus on the pricing of Bermudan and barrier options under the dynamics of the Heston stochastic volatility model. The two-dimensional nature of the Heston model makes the pricing of these options problematic, as the risk-neutral expectations need to be calculated at each exercise/observation date along a continuum of the two state spaces. We examine the 2D-COS method, which makes use of Fourier-cosine expansions in each of the two dimensions in order to approximate the integrals. Using the fast Fourier transform, we are able to efficiently calculate the cosine series coefficients at each exercise/observation date. A construction of this method is provided and we conduct numerical experiments to evaluate its speed and accuracy."],"dc:identifier.uri":["http://hdl.handle.net/11427/8520"],"dc:language.iso":["eng"],"dc:publisher.department":["Division of Actuarial Science"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Two dimensional COS method for pricing early-exercise and discrete barrier options under the Heston Model"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MPhil"]},"updated_at":"2026-07-22T22:23:22Z"}