{"id":"https://openalex.org/W1649019767","doi":"https://doi.org/10.1137/140981216","title":"Reduced Basis Methods for Pricing Options with the Black--Scholes and Heston Models","display_name":"Reduced Basis Methods for Pricing Options with the Black--Scholes and Heston Models","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1649019767","doi":"https://doi.org/10.1137/140981216","mag":"1649019767"},"language":"en","primary_location":{"id":"doi:10.1137/140981216","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140981216","pdf_url":null,"source":{"id":"https://openalex.org/S75627377","display_name":"SIAM Journal on Financial Mathematics","issn_l":"1945-497X","issn":["1945-497X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Financial Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007562442","display_name":"Olena Burkovska","orcid":"https://orcid.org/0000-0001-6310-1130"},"institutions":[{"id":"https://openalex.org/I4210166048","display_name":"Gesellschaft Fur Mathematik Und Datenverarbeitung","ror":"https://ror.org/02g6d4t03","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210166048"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"O. Burkovska","raw_affiliation_strings":["LNM - Lehrstuhl fuer Numerische Mathematik (Fakultaet fuer Mathematik, Lehrstuhl fuer Numerische Mathematik Boltzmannstrasse 3, 85748 Garching bei Muenchen - Germany)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LNM - Lehrstuhl fuer Numerische Mathematik (Fakultaet fuer Mathematik, Lehrstuhl fuer Numerische Mathematik Boltzmannstrasse 3, 85748 Garching bei Muenchen - Germany)","institution_ids":["https://openalex.org/I4210166048"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073837806","display_name":"Bernard Haasdonk","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. Haasdonk","raw_affiliation_strings":["IANS - Institut f\u00fcr Angewandte Analysis und Numerische Simulation [Stuttgart] (Pfaffenwaldring 57 70569 Stuttgart Deutschland - Germany)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IANS - Institut f\u00fcr Angewandte Analysis und Numerische Simulation [Stuttgart] (Pfaffenwaldring 57 70569 Stuttgart Deutschland - Germany)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053245247","display_name":"Julien Salomon","orcid":"https://orcid.org/0000-0001-8707-6371"},"institutions":[{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J. Salomon","raw_affiliation_strings":["CEREMADE - CEntre de REcherches en MAth\u00e9matiques de la DEcision (Place du Mar\u00e9chal de Lattre de Tassigny 75775 - Paris Cedex 16 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CEREMADE - CEntre de REcherches en MAth\u00e9matiques de la DEcision (Place du Mar\u00e9chal de Lattre de Tassigny 75775 - Paris Cedex 16 - France)","institution_ids":["https://openalex.org/I171048554"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018841476","display_name":"Barbara Wohlmuth","orcid":"https://orcid.org/0000-0001-6908-6015"},"institutions":[{"id":"https://openalex.org/I4210166048","display_name":"Gesellschaft Fur Mathematik Und Datenverarbeitung","ror":"https://ror.org/02g6d4t03","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210166048"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"B. Wohlmuth","raw_affiliation_strings":["LNM - Lehrstuhl fuer Numerische Mathematik (Fakultaet fuer Mathematik, Lehrstuhl fuer Numerische Mathematik Boltzmannstrasse 3, 85748 Garching bei Muenchen - Germany)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LNM - Lehrstuhl fuer Numerische Mathematik (Fakultaet fuer Mathematik, Lehrstuhl fuer Numerische Mathematik Boltzmannstrasse 3, 85748 Garching bei Muenchen - Germany)","institution_ids":["https://openalex.org/I4210166048"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.4604,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.94196187,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"6","issue":"1","first_page":"685","last_page":"712"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9707000255584717,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9616000056266785,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6239187717437744},{"id":"https://openalex.org/keywords/black\u2013scholes-model","display_name":"Black\u2013Scholes model","score":0.6093221306800842},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5699807405471802},{"id":"https://openalex.org/keywords/valuation-of-options","display_name":"Valuation of options","score":0.5476866364479065},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.537676990032196},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5353569984436035},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5309849381446838},{"id":"https://openalex.org/keywords/heston-model","display_name":"Heston model","score":0.5073923468589783},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.49158939719200134},{"id":"https://openalex.org/keywords/monte-carlo-methods-for-option-pricing","display_name":"Monte Carlo methods for option pricing","score":0.47812309861183167},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.4501004219055176},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4302331507205963},{"id":"https://openalex.org/keywords/stochastic-volatility","display_name":"Stochastic volatility","score":0.39348289370536804},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.22947081923484802},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.16892024874687195}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6239187717437744},{"id":"https://openalex.org/C163128081","wikidata":"https://www.wikidata.org/wiki/Q1338307","display_name":"Black\u2013Scholes model","level":3,"score":0.6093221306800842},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5699807405471802},{"id":"https://openalex.org/C194483076","wikidata":"https://www.wikidata.org/wiki/Q380382","display_name":"Valuation of options","level":2,"score":0.5476866364479065},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.537676990032196},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5353569984436035},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5309849381446838},{"id":"https://openalex.org/C93045229","wikidata":"https://www.wikidata.org/wiki/Q5746554","display_name":"Heston model","level":5,"score":0.5073923468589783},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.49158939719200134},{"id":"https://openalex.org/C101710237","wikidata":"https://www.wikidata.org/wiki/Q6904701","display_name":"Monte Carlo methods for option pricing","level":3,"score":0.47812309861183167},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.4501004219055176},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4302331507205963},{"id":"https://openalex.org/C85393063","wikidata":"https://www.wikidata.org/wiki/Q596307","display_name":"Stochastic volatility","level":3,"score":0.39348289370536804},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.22947081923484802},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.16892024874687195},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.0},{"id":"https://openalex.org/C187625094","wikidata":"https://www.wikidata.org/wiki/Q7388452","display_name":"SABR volatility model","level":4,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140981216","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140981216","pdf_url":null,"source":{"id":"https://openalex.org/S75627377","display_name":"SIAM Journal on Financial Mathematics","issn_l":"1945-497X","issn":["1945-497X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Financial Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01097423v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01097423","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Financial Mathematics, 2015, 6 (1), pp.685-712. ⟨10.1137/140981216⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7200000286102295,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G523492319","display_name":null,"funder_award_id":"EXC 310","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6039471144","display_name":null,"funder_award_id":"EXC 310/1","funder_id":"https://openalex.org/F4320325850","funder_display_name":"Universit\u00e4t Stuttgart"},{"id":"https://openalex.org/G630505497","display_name":null,"funder_award_id":"IGDK1754","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6468402549","display_name":null,"funder_award_id":"EXC 310/1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320310414","display_name":"Baden-W\u00fcrttemberg Stiftung","ror":"https://ror.org/031h5fa94"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320325850","display_name":"Universit\u00e4t Stuttgart","ror":"https://ror.org/04vnq7t77"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W109754632","https://openalex.org/W195653134","https://openalex.org/W592911714","https://openalex.org/W1496270222","https://openalex.org/W1516681311","https://openalex.org/W1520204308","https://openalex.org/W1547373495","https://openalex.org/W1604311391","https://openalex.org/W1688631392","https://openalex.org/W1887186184","https://openalex.org/W1902027874","https://openalex.org/W1909146625","https://openalex.org/W1969483425","https://openalex.org/W1984977185","https://openalex.org/W2001169279","https://openalex.org/W2003360807","https://openalex.org/W2026365342","https://openalex.org/W2050222014","https://openalex.org/W2051583875","https://openalex.org/W2064978316","https://openalex.org/W2077407187","https://openalex.org/W2077791698","https://openalex.org/W2085335060","https://openalex.org/W2085739550","https://openalex.org/W2094712886","https://openalex.org/W2104225554","https://openalex.org/W2110917150","https://openalex.org/W2122080931","https://openalex.org/W2137275615","https://openalex.org/W2138583506","https://openalex.org/W2151591383","https://openalex.org/W2163282685","https://openalex.org/W2242435127","https://openalex.org/W2251813065","https://openalex.org/W2314187005","https://openalex.org/W2427541736","https://openalex.org/W2444177550","https://openalex.org/W2479942139","https://openalex.org/W2487202609","https://openalex.org/W2964080327","https://openalex.org/W2985272081","https://openalex.org/W3123609652","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3183442954","https://openalex.org/W2056825716","https://openalex.org/W2088436879","https://openalex.org/W2640518324","https://openalex.org/W1988744059","https://openalex.org/W2062418210","https://openalex.org/W4311889558","https://openalex.org/W2483316594","https://openalex.org/W3172188645","https://openalex.org/W2559726123"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,27,77,112],"present":[4],"a":[5,34,42,60,88],"reduced":[6,44,74,84],"basis":[7,45],"method":[8,58],"for":[9,47,66,105],"pricing":[10,109],"European":[11],"and":[12,19,63,72,86,100,116],"American":[13],"options":[14],"based":[15],"on":[16],"the":[17,29,57,67,70,79,83,97,106,114,119],"Black--Scholes":[18],"Heston":[20],"models.":[21,110],"To":[22],"tackle":[23],"each":[24],"model":[25],"numerically,":[26],"formulate":[28],"problem":[30],"in":[31,56],"terms":[32],"of":[33,50,69,82,102,118],"time-dependent":[35],"variational":[36],"equality":[37],"or":[38],"inequality.":[39],"We":[40],"apply":[41],"suitable":[43],"approach":[46,104],"both":[48],"types":[49],"options.":[51],"The":[52],"characteristic":[53],"ingredients":[54],"used":[55],"are":[59,94],"combined":[61],"POD-Greedy":[62],"Angle-Greedy":[64],"procedure":[65],"construction":[68],"primal":[71],"dual":[73],"spaces.":[75],"Analytically,":[76],"prove":[78],"reproduction":[80],"property":[81],"scheme":[85],"derive":[87],"posteriori":[89],"error":[90,120],"estimators.":[91,121],"Numerical":[92],"examples":[93],"provided,":[95],"illustrating":[96],"approximation":[98],"quality":[99],"convergence":[101],"our":[103],"different":[107],"option":[108],"Also,":[111],"investigate":[113],"reliability":[115],"effectivity":[117]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}