{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/106406"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/106406","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Machine learning for pricing European basket options","abstract":"In this thesis, we show how to deploy machine learning techniques such as Gaussian process regression to approximate the European basket option prices. For the underlying asset of European basket option, we assume it follows multivariate Black \\&\\ Scholes model, and we can derive the PDE for the option price. In order to deal with the curse of dimensionality, we assume that the basket consists of several comonotonic groups, in each comonotonic group, the stock prices are driven by a single random source. Then we can derive an approximation for the price of European basket option. Next, we introduce the finite difference scheme to price the European basket option for given parameters such as risk-free interest rates, maturities and so on. However, for approximating the European basket option for different risk-free interest rates, maturities and strikes, using finite difference scheme to get corresponding approximations costs much time. Hence, in order to save time for approximating the European basket option for different risk-free interest rates, maturities and strikes, we deploy Gaussian process regression to fit the training set produced by finite difference scheme and after comparing the results, we can conclude that the errors are often well within reasonable limits and hence very acceptable from a practical point of view and the Gaussian process regression truly save much time.","abstract_html":"In this thesis, we show how to deploy machine learning techniques such as Gaussian process regression to approximate the European basket option prices. For the underlying asset of European basket option, we assume it follows multivariate Black \\&\\ Scholes model, and we can derive the PDE for the option price. In order to deal with the curse of dimensionality, we assume that the basket consists of several comonotonic groups, in each comonotonic group, the stock prices are driven by a single random source. Then we can derive an approximation for the price of European basket option. Next, we introduce the finite difference scheme to price the European basket option for given parameters such as risk-free interest rates, maturities and so on. However, for approximating the European basket option for different risk-free interest rates, maturities and strikes, using finite difference scheme to get corresponding approximations costs much time. Hence, in order to save time for approximating the European basket option for different risk-free interest rates, maturities and strikes, we deploy Gaussian process regression to fit the training set produced by finite difference scheme and after comparing the results, we can conclude that the errors are often well within reasonable limits and hence very acceptable from a practical point of view and the Gaussian process regression truly save much time.","abstract_has_math":false,"creators":["Ling, Biwen"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Actuarial Science","degree_department":null,"school":null,"contributors":["Linders, Daniel","Chong, Alfred"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-03-02T22:18:21Z","date_published":"2020-03-02T22:18:21Z","updated_at":"2026-07-22T22:24:47Z","subjects":["partial dependence structure, gaussian process regression"],"languages":["en"],"rights":["Copyright 2019 Biwen Ling"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/106406","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Linders, Daniel","Chong, Alfred"]},{"key":"dc:creator","label":"Author","values":["Ling, Biwen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-03-02T22:18:21Z","2022-03-03T10:15:16Z","2019-12-13","2019-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Actuarial Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["partial dependence structure, gaussian process regression"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 Biwen Ling"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/106406"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis, we show how to deploy machine learning techniques such as Gaussian process regression to approximate the European basket option prices. For the underlying asset of European basket option, we assume it follows multivariate Black \\&\\ Scholes model, and we can derive the PDE for the option price. In order to deal with the curse of dimensionality, we assume that the basket consists of several comonotonic groups, in each comonotonic group, the stock prices are driven by a single random source. Then we can derive an approximation for the price of European basket option. Next, we introduce the finite difference scheme to price the European basket option for given parameters such as risk-free interest rates, maturities and so on. However, for approximating the European basket option for different risk-free interest rates, maturities and strikes, using finite difference scheme to get corresponding approximations costs much time. Hence, in order to save time for approximating the European basket option for different risk-free interest rates, maturities and strikes, we deploy Gaussian process regression to fit the training set produced by finite difference scheme and after comparing the results, we can conclude that the errors are often well within reasonable limits and hence very acceptable from a practical point of view and the Gaussian process regression truly save much time.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2021-12-01","The student, Biwen Ling, accepted the attached license on 2019-12-13 at 06:40.","The student, Biwen Ling, submitted this Thesis for approval on 2019-12-13 at 06:57.","This Thesis was approved for publication on 2019-12-13 at 13:17.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14824 on 2020-02-28 at 17:24:34","Made available in DSpace on 2020-03-02T22:18:21Z (GMT). No. of bitstreams: 2 LING-THESIS-2019.pdf: 469193 bytes, checksum: c19a92ab5968c64d0d767678d2b9ea74 (MD5) LICENSE.txt: 4207 bytes, checksum: 1962b08879d0c40953202c035daa6228 (MD5) Previous issue date: 2019-12-13","Embargo set by: Seth Robbins for item 113949 Lift date: 2022-03-02T22:18:25Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","U of I Only Restriction Lifted for Item 113949 on 2022-03-03T10:15:16Z."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Machine learning for pricing European basket options"]}]}],"canonical_facts":{"dc:contributor":["Linders, Daniel","Chong, Alfred"],"dc:creator":["Ling, Biwen"],"dc:date":["2020-03-02T22:18:21Z","2022-03-03T10:15:16Z","2019-12-13","2019-12"],"dc:description":["In this thesis, we show how to deploy machine learning techniques such as Gaussian process regression to approximate the European basket option prices. For the underlying asset of European basket option, we assume it follows multivariate Black \\&\\ Scholes model, and we can derive the PDE for the option price. In order to deal with the curse of dimensionality, we assume that the basket consists of several comonotonic groups, in each comonotonic group, the stock prices are driven by a single random source. Then we can derive an approximation for the price of European basket option. Next, we introduce the finite difference scheme to price the European basket option for given parameters such as risk-free interest rates, maturities and so on. However, for approximating the European basket option for different risk-free interest rates, maturities and strikes, using finite difference scheme to get corresponding approximations costs much time. Hence, in order to save time for approximating the European basket option for different risk-free interest rates, maturities and strikes, we deploy Gaussian process regression to fit the training set produced by finite difference scheme and after comparing the results, we can conclude that the errors are often well within reasonable limits and hence very acceptable from a practical point of view and the Gaussian process regression truly save much time.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2021-12-01","The student, Biwen Ling, accepted the attached license on 2019-12-13 at 06:40.","The student, Biwen Ling, submitted this Thesis for approval on 2019-12-13 at 06:57.","This Thesis was approved for publication on 2019-12-13 at 13:17.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14824 on 2020-02-28 at 17:24:34","Made available in DSpace on 2020-03-02T22:18:21Z (GMT). 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