{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/27102"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/27102","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Modelling stochastic multi-curve basis","abstract":"As a consequence of the 2007 financial crisis, the market has shifted towards a multi-curve approach in modelling the prevailing interest rate environment. Currently, there is a reliance on the assumption of deterministic- or constant-basis spreads. This assumption is too simplistic to describe the modern multi-curve environment and serves as the motivation for this work. A stochastic-basis framework, presented by Mercurio and Xie (2012), with one- and two-factor OIS short-rate models is reviewed and implemented in order to analyse the effect of the inclusion of stochastic-basis in the pricing of interest rate derivatives. In order to preclude the existence of negative spreads in the model, a constraint on the spread model parameters is necessary. The inclusion of stochastic-basis results in a clear shift in the terminal distributions of FRA and swap rates. In spite of this, stochastic-basis is found to have a negligible effect on cap/floor and swaption prices for the admissible spread model parameters. To overcome challenges surrounding parameter estimation under the framework, a rudimentary calibration procedure is developed, where the spread model parameters are estimated from historical data; and the OIS rate model parameters are calibrated to a market swaption volatility surface.","abstract_html":"As a consequence of the 2007 financial crisis, the market has shifted towards a multi-curve approach in modelling the prevailing interest rate environment. Currently, there is a reliance on the assumption of deterministic- or constant-basis spreads. This assumption is too simplistic to describe the modern multi-curve environment and serves as the motivation for this work. A stochastic-basis framework, presented by Mercurio and Xie (2012), with one- and two-factor OIS short-rate models is reviewed and implemented in order to analyse the effect of the inclusion of stochastic-basis in the pricing of interest rate derivatives. In order to preclude the existence of negative spreads in the model, a constraint on the spread model parameters is necessary. The inclusion of stochastic-basis results in a clear shift in the terminal distributions of FRA and swap rates. In spite of this, stochastic-basis is found to have a negligible effect on cap/floor and swaption prices for the admissible spread model parameters. To overcome challenges surrounding parameter estimation under the framework, a rudimentary calibration procedure is developed, where the spread model parameters are estimated from historical data; and the OIS rate model parameters are calibrated to a market swaption volatility surface.","abstract_has_math":false,"creators":["Dalton, Rowan"],"institution":"Division of Actuarial Science","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Kienitz, Jörg","McWalter, Thomas"],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-22T22:23:46Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/27102","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Kienitz, Jörg","McWalter, Thomas"]},{"key":"dc:creator","label":"Author","values":["Dalton, Rowan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-01-30T10:26:26Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-01-30T10:26:26Z"]},{"key":"dc:date.issued","label":"Date","values":["2017"]},{"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/11427/27102"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["As a consequence of the 2007 financial crisis, the market has shifted towards a multi-curve approach in modelling the prevailing interest rate environment. Currently, there is a reliance on the assumption of deterministic- or constant-basis spreads. This assumption is too simplistic to describe the modern multi-curve environment and serves as the motivation for this work. A stochastic-basis framework, presented by Mercurio and Xie (2012), with one- and two-factor OIS short-rate models is reviewed and implemented in order to analyse the effect of the inclusion of stochastic-basis in the pricing of interest rate derivatives. In order to preclude the existence of negative spreads in the model, a constraint on the spread model parameters is necessary. The inclusion of stochastic-basis results in a clear shift in the terminal distributions of FRA and swap rates. In spite of this, stochastic-basis is found to have a negligible effect on cap/floor and swaption prices for the admissible spread model parameters. To overcome challenges surrounding parameter estimation under the framework, a rudimentary calibration procedure is developed, where the spread model parameters are estimated from historical data; and the OIS rate model parameters are calibrated to a market swaption volatility surface."]},{"key":"dc:title","label":"Title","values":["Modelling stochastic multi-curve basis"]}]}],"canonical_facts":{"dc:contributor.advisor":["Kienitz, Jörg","McWalter, Thomas"],"dc:creator":["Dalton, Rowan"],"dc:date.accessioned":["2018-01-30T10:26:26Z"],"dc:date.available":["2018-01-30T10:26:26Z"],"dc:date.issued":["2017"],"dc:description.abstract":["As a consequence of the 2007 financial crisis, the market has shifted towards a multi-curve approach in modelling the prevailing interest rate environment. Currently, there is a reliance on the assumption of deterministic- or constant-basis spreads. This assumption is too simplistic to describe the modern multi-curve environment and serves as the motivation for this work. A stochastic-basis framework, presented by Mercurio and Xie (2012), with one- and two-factor OIS short-rate models is reviewed and implemented in order to analyse the effect of the inclusion of stochastic-basis in the pricing of interest rate derivatives. In order to preclude the existence of negative spreads in the model, a constraint on the spread model parameters is necessary. The inclusion of stochastic-basis results in a clear shift in the terminal distributions of FRA and swap rates. In spite of this, stochastic-basis is found to have a negligible effect on cap/floor and swaption prices for the admissible spread model parameters. To overcome challenges surrounding parameter estimation under the framework, a rudimentary calibration procedure is developed, where the spread model parameters are estimated from historical data; and the OIS rate model parameters are calibrated to a market swaption volatility surface."],"dc:identifier.uri":["http://hdl.handle.net/11427/27102"],"dc:language.iso":["eng"],"dc:publisher.department":["Division of Actuarial Science"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Modelling stochastic multi-curve basis"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MPhil"]},"updated_at":"2026-07-22T22:23:46Z"}