{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/32556"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/32556","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Local Stochastic Volatility—The Hyp-Hyp Model","abstract":"Volatility modelling is used predominantly in order to explain the volatility smile observed in the market. Stochastic volatility models are mainly used to capture the curvature of a volatility smile while local volatility models generally model the skew. Jackel and Kahl ¨ (2008) present a hyperbolic-local hyperbolic-stochastic volatility (Hyp-Hyp) model which aims to improve upon existing local and stochastic volatility models such as the stochastic alpha, beta, rho (SABR) and constant elasticity of variance (CEV) models. The advantageous features of the Hyp-Hyp model are corroborated by implementing the model. Jackel and Kahl ¨ (2008) investigate the accuracy of a scaled analytical approximation for implied volatility, based on approximations presented by Watanabe (1987) and Fouque et al. (2000), for the Hyp-Hyp model. They use the approximation to derive an expression for the delta of an option. This dissertation analyses the Hyp-Hyp model, as well as the approximation, by deriving expressions for other sensitivities and by investigating the effect of the Hyp-Hyp model parameters on the volatility smile. The accuracy of the analytical approximation for functional forms other than those defined by the Hyp-Hyp model is explored. A derivation of the approximation is undertaken, presenting corrections to the expressions introduced by Kahl (2007) and used by Jackel and Kahl ¨ (2008).","abstract_html":"Volatility modelling is used predominantly in order to explain the volatility smile observed in the market. Stochastic volatility models are mainly used to capture the curvature of a volatility smile while local volatility models generally model the skew. Jackel and Kahl ¨ (2008) present a hyperbolic-local hyperbolic-stochastic volatility (Hyp-Hyp) model which aims to improve upon existing local and stochastic volatility models such as the stochastic alpha, beta, rho (SABR) and constant elasticity of variance (CEV) models. The advantageous features of the Hyp-Hyp model are corroborated by implementing the model. Jackel and Kahl ¨ (2008) investigate the accuracy of a scaled analytical approximation for implied volatility, based on approximations presented by Watanabe (1987) and Fouque et al. (2000), for the Hyp-Hyp model. They use the approximation to derive an expression for the delta of an option. This dissertation analyses the Hyp-Hyp model, as well as the approximation, by deriving expressions for other sensitivities and by investigating the effect of the Hyp-Hyp model parameters on the volatility smile. The accuracy of the analytical approximation for functional forms other than those defined by the Hyp-Hyp model is explored. A derivation of the approximation is undertaken, presenting corrections to the expressions introduced by Kahl (2007) and used by Jackel and Kahl ¨ (2008).","abstract_has_math":false,"creators":["Cowen, Nicholas"],"institution":"African Institute of Financial Markets and Risk Management","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["McWalter, Thomas","Kienitz, Jorg"],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020","date_published":"2020","updated_at":"2026-07-22T22:23:07Z","subjects":["Mathematical Finance"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/32556","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["McWalter, Thomas","Kienitz, Jorg"]},{"key":"dc:creator","label":"Author","values":["Cowen, Nicholas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2021-01-19T12:01:24Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2021-01-19T12:01:24Z"]},{"key":"dc:date.issued","label":"Date","values":["2020"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["African Institute of Financial Markets and Risk Management"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters","MPhil"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematical Finance"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/32556"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Volatility modelling is used predominantly in order to explain the volatility smile observed in the market. Stochastic volatility models are mainly used to capture the curvature of a volatility smile while local volatility models generally model the skew. Jackel and Kahl ¨ (2008) present a hyperbolic-local hyperbolic-stochastic volatility (Hyp-Hyp) model which aims to improve upon existing local and stochastic volatility models such as the stochastic alpha, beta, rho (SABR) and constant elasticity of variance (CEV) models. The advantageous features of the Hyp-Hyp model are corroborated by implementing the model. Jackel and Kahl ¨ (2008) investigate the accuracy of a scaled analytical approximation for implied volatility, based on approximations presented by Watanabe (1987) and Fouque et al. (2000), for the Hyp-Hyp model. They use the approximation to derive an expression for the delta of an option. This dissertation analyses the Hyp-Hyp model, as well as the approximation, by deriving expressions for other sensitivities and by investigating the effect of the Hyp-Hyp model parameters on the volatility smile. The accuracy of the analytical approximation for functional forms other than those defined by the Hyp-Hyp model is explored. A derivation of the approximation is undertaken, presenting corrections to the expressions introduced by Kahl (2007) and used by Jackel and Kahl ¨ (2008)."]},{"key":"dc:title","label":"Title","values":["Local Stochastic Volatility—The Hyp-Hyp Model"]}]}],"canonical_facts":{"dc:contributor.advisor":["McWalter, Thomas","Kienitz, Jorg"],"dc:creator":["Cowen, Nicholas"],"dc:date.accessioned":["2021-01-19T12:01:24Z"],"dc:date.available":["2021-01-19T12:01:24Z"],"dc:date.issued":["2020"],"dc:description.abstract":["Volatility modelling is used predominantly in order to explain the volatility smile observed in the market. Stochastic volatility models are mainly used to capture the curvature of a volatility smile while local volatility models generally model the skew. Jackel and Kahl ¨ (2008) present a hyperbolic-local hyperbolic-stochastic volatility (Hyp-Hyp) model which aims to improve upon existing local and stochastic volatility models such as the stochastic alpha, beta, rho (SABR) and constant elasticity of variance (CEV) models. The advantageous features of the Hyp-Hyp model are corroborated by implementing the model. Jackel and Kahl ¨ (2008) investigate the accuracy of a scaled analytical approximation for implied volatility, based on approximations presented by Watanabe (1987) and Fouque et al. (2000), for the Hyp-Hyp model. They use the approximation to derive an expression for the delta of an option. This dissertation analyses the Hyp-Hyp model, as well as the approximation, by deriving expressions for other sensitivities and by investigating the effect of the Hyp-Hyp model parameters on the volatility smile. The accuracy of the analytical approximation for functional forms other than those defined by the Hyp-Hyp model is explored. A derivation of the approximation is undertaken, presenting corrections to the expressions introduced by Kahl (2007) and used by Jackel and Kahl ¨ (2008)."],"dc:identifier.uri":["http://hdl.handle.net/11427/32556"],"dc:publisher.department":["African Institute of Financial Markets and Risk Management"],"dc:subject":["Mathematical Finance"],"dc:title":["Local Stochastic Volatility—The Hyp-Hyp Model"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters","MPhil"]},"updated_at":"2026-07-22T22:23:07Z"}