{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/13156"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/13156","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Stochastic time-changed Lévy processes with their implementation","abstract":"We focus on the implementation details for Lévy processes and their extension to stochastic volatility models for pricing European vanilla options and exotic options. We calibrated five models to European options on the S&P500 and used the calibrated models to price a cliquet option using Monte Carlo simulation. We provide the algorithms required to value the options when using Lévy processes. We found that these models were able to closely reproduce the market option prices for many strikes and maturities. We also found that the models we studied produced different prices for the cliquet option even though all the models produced the same prices for vanilla options. This highlighted a feature of model uncertainty when valuing a cliquet option. Further research is required to develop tools to understand and manage this model uncertainty. We make a recommendation on how to proceed with this research by studying the cliquet option’s sensitivity to the model parameters.","abstract_html":"We focus on the implementation details for Lévy processes and their extension to stochastic volatility models for pricing European vanilla options and exotic options. We calibrated five models to European options on the S&P500 and used the calibrated models to price a cliquet option using Monte Carlo simulation. We provide the algorithms required to value the options when using Lévy processes. We found that these models were able to closely reproduce the market option prices for many strikes and maturities. We also found that the models we studied produced different prices for the cliquet option even though all the models produced the same prices for vanilla options. This highlighted a feature of model uncertainty when valuing a cliquet option. Further research is required to develop tools to understand and manage this model uncertainty. We make a recommendation on how to proceed with this research by studying the cliquet option’s sensitivity to the model parameters.","abstract_has_math":false,"creators":["Sihlobo, Odwa"],"institution":"Division of Actuarial Science","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Mataramvura, Sure"],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014","date_published":"2014","updated_at":"2026-07-22T22:23:36Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/13156","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Mataramvura, Sure"]},{"key":"dc:creator","label":"Author","values":["Sihlobo, Odwa"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-06-29T07:46:30Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-06-29T07:46:30Z"]},{"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/11427/13156"]}]},{"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 implementation details for Lévy processes and their extension to stochastic volatility models for pricing European vanilla options and exotic options. We calibrated five models to European options on the S&P500 and used the calibrated models to price a cliquet option using Monte Carlo simulation. We provide the algorithms required to value the options when using Lévy processes. We found that these models were able to closely reproduce the market option prices for many strikes and maturities. We also found that the models we studied produced different prices for the cliquet option even though all the models produced the same prices for vanilla options. This highlighted a feature of model uncertainty when valuing a cliquet option. Further research is required to develop tools to understand and manage this model uncertainty. We make a recommendation on how to proceed with this research by studying the cliquet option’s sensitivity to the model parameters."]},{"key":"dc:title","label":"Title","values":["Stochastic time-changed Lévy processes with their implementation"]}]}],"canonical_facts":{"dc:contributor.advisor":["Mataramvura, Sure"],"dc:creator":["Sihlobo, Odwa"],"dc:date.accessioned":["2015-06-29T07:46:30Z"],"dc:date.available":["2015-06-29T07:46:30Z"],"dc:date.issued":["2014"],"dc:description":["Includes bibliographical references."],"dc:description.abstract":["We focus on the implementation details for Lévy processes and their extension to stochastic volatility models for pricing European vanilla options and exotic options. We calibrated five models to European options on the S&P500 and used the calibrated models to price a cliquet option using Monte Carlo simulation. We provide the algorithms required to value the options when using Lévy processes. We found that these models were able to closely reproduce the market option prices for many strikes and maturities. We also found that the models we studied produced different prices for the cliquet option even though all the models produced the same prices for vanilla options. This highlighted a feature of model uncertainty when valuing a cliquet option. Further research is required to develop tools to understand and manage this model uncertainty. We make a recommendation on how to proceed with this research by studying the cliquet option’s sensitivity to the model parameters."],"dc:identifier.uri":["http://hdl.handle.net/11427/13156"],"dc:language.iso":["eng"],"dc:publisher.department":["Division of Actuarial Science"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Stochastic time-changed Lévy processes with their implementation"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MPhil"]},"updated_at":"2026-07-22T22:23:36Z"}