{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/27105"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/27105","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Functional quantization-based stratified sampling","abstract":"Functional quantization-based stratified sampling is a method for variance reduction proposed by Corlay and Pagès (2015). This method requires the ability to both create functional quantizers and to sample Brownian paths from the strata defined by the quantizers. We show that product quantizers are a suitable approximation of an optimal quantizer for the formation of functional quantizers. The notion of functional stratification is then extended to options written on multiple stocks and American options priced using the Longstaff-Schwartz method. To illustrate the gains in performance we focus on geometric brownian motion (GBM), constant elasticity of variance (CEV) and constant elasticity of variance with stochastic volatility (CEV-SV) models. The pricing algorithm is used to price knock-in, knockout, autocall, call on the max and path dependent call on the max options.","abstract_html":"Functional quantization-based stratified sampling is a method for variance reduction proposed by Corlay and Pagès (2015). This method requires the ability to both create functional quantizers and to sample Brownian paths from the strata defined by the quantizers. We show that product quantizers are a suitable approximation of an optimal quantizer for the formation of functional quantizers. The notion of functional stratification is then extended to options written on multiple stocks and American options priced using the Longstaff-Schwartz method. To illustrate the gains in performance we focus on geometric brownian motion (GBM), constant elasticity of variance (CEV) and constant elasticity of variance with stochastic volatility (CEV-SV) models. The pricing algorithm is used to price knock-in, knockout, autocall, call on the max and path dependent call on the max options.","abstract_has_math":false,"creators":["Platts, Alexander"],"institution":"Division of Actuarial Science","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["McWalter, Thomas"],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-22T22:23:27Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/27105","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["McWalter, Thomas"]},{"key":"dc:creator","label":"Author","values":["Platts, Alexander"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-01-30T10:26:29Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-01-30T10:26:29Z"]},{"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/11427/27105"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Functional quantization-based stratified sampling is a method for variance reduction proposed by Corlay and Pagès (2015). This method requires the ability to both create functional quantizers and to sample Brownian paths from the strata defined by the quantizers. We show that product quantizers are a suitable approximation of an optimal quantizer for the formation of functional quantizers. The notion of functional stratification is then extended to options written on multiple stocks and American options priced using the Longstaff-Schwartz method. To illustrate the gains in performance we focus on geometric brownian motion (GBM), constant elasticity of variance (CEV) and constant elasticity of variance with stochastic volatility (CEV-SV) models. The pricing algorithm is used to price knock-in, knockout, autocall, call on the max and path dependent call on the max options."]},{"key":"dc:title","label":"Title","values":["Functional quantization-based stratified sampling"]}]}],"canonical_facts":{"dc:contributor.advisor":["McWalter, Thomas"],"dc:creator":["Platts, Alexander"],"dc:date.accessioned":["2018-01-30T10:26:29Z"],"dc:date.available":["2018-01-30T10:26:29Z"],"dc:date.issued":["2017"],"dc:description.abstract":["Functional quantization-based stratified sampling is a method for variance reduction proposed by Corlay and Pagès (2015). This method requires the ability to both create functional quantizers and to sample Brownian paths from the strata defined by the quantizers. We show that product quantizers are a suitable approximation of an optimal quantizer for the formation of functional quantizers. The notion of functional stratification is then extended to options written on multiple stocks and American options priced using the Longstaff-Schwartz method. To illustrate the gains in performance we focus on geometric brownian motion (GBM), constant elasticity of variance (CEV) and constant elasticity of variance with stochastic volatility (CEV-SV) models. The pricing algorithm is used to price knock-in, knockout, autocall, call on the max and path dependent call on the max options."],"dc:identifier.uri":["http://hdl.handle.net/11427/27105"],"dc:language.iso":["eng"],"dc:publisher.department":["Division of Actuarial Science"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Functional quantization-based stratified sampling"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MPhil"]},"updated_at":"2026-07-22T22:23:27Z"}