{"id":"https://openalex.org/W1977153352","doi":"https://doi.org/10.1137/s0036139902401550","title":"Singular Perturbations in Option Pricing","display_name":"Singular Perturbations in Option Pricing","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1977153352","doi":"https://doi.org/10.1137/s0036139902401550","mag":"1977153352"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139902401550","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139902401550","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied 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/A5051801244","display_name":"Jean\u2010Pierre Fouque","orcid":"https://orcid.org/0000-0001-8786-5645"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. P. Fouque","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102985833","display_name":"George Papanicolaou","orcid":"https://orcid.org/0000-0003-1507-956X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. Papanicolaou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039402165","display_name":"Ronnie Sircar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. Sircar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5076372723","display_name":"Knut S\u00f8lna","orcid":"https://orcid.org/0000-0002-8508-8288"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. Solna","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.7109,"has_fulltext":false,"cited_by_count":196,"citation_normalized_percentile":{"value":0.97130102,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"63","issue":"5","first_page":"1648","last_page":"1665"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9998000264167786,"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":0.9998000264167786,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9865999817848206,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9714000225067139,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-volatility","display_name":"Stochastic volatility","score":0.6382405161857605},{"id":"https://openalex.org/keywords/volatility","display_name":"Volatility (finance)","score":0.6151593923568726},{"id":"https://openalex.org/keywords/implied-volatility","display_name":"Implied volatility","score":0.6102482080459595},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.6000361442565918},{"id":"https://openalex.org/keywords/stochastic-game","display_name":"Stochastic game","score":0.5823490619659424},{"id":"https://openalex.org/keywords/local-volatility","display_name":"Local volatility","score":0.5737898945808411},{"id":"https://openalex.org/keywords/black\u2013scholes-model","display_name":"Black\u2013Scholes model","score":0.5479812026023865},{"id":"https://openalex.org/keywords/volatility-smile","display_name":"Volatility smile","score":0.5334326028823853},{"id":"https://openalex.org/keywords/valuation-of-options","display_name":"Valuation of options","score":0.515528678894043},{"id":"https://openalex.org/keywords/sabr-volatility-model","display_name":"SABR volatility model","score":0.47731050848960876},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4719725549221039},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.4704788327217102},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.44103696942329407},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.41230738162994385},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4109949767589569},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15374934673309326}],"concepts":[{"id":"https://openalex.org/C85393063","wikidata":"https://www.wikidata.org/wiki/Q596307","display_name":"Stochastic volatility","level":3,"score":0.6382405161857605},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.6151593923568726},{"id":"https://openalex.org/C24189920","wikidata":"https://www.wikidata.org/wiki/Q1660345","display_name":"Implied volatility","level":3,"score":0.6102482080459595},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6000361442565918},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.5823490619659424},{"id":"https://openalex.org/C2779834249","wikidata":"https://www.wikidata.org/wiki/Q6664586","display_name":"Local volatility","level":4,"score":0.5737898945808411},{"id":"https://openalex.org/C163128081","wikidata":"https://www.wikidata.org/wiki/Q1338307","display_name":"Black\u2013Scholes model","level":3,"score":0.5479812026023865},{"id":"https://openalex.org/C13290067","wikidata":"https://www.wikidata.org/wiki/Q915788","display_name":"Volatility smile","level":3,"score":0.5334326028823853},{"id":"https://openalex.org/C194483076","wikidata":"https://www.wikidata.org/wiki/Q380382","display_name":"Valuation of options","level":2,"score":0.515528678894043},{"id":"https://openalex.org/C187625094","wikidata":"https://www.wikidata.org/wiki/Q7388452","display_name":"SABR volatility model","level":4,"score":0.47731050848960876},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4719725549221039},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.4704788327217102},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.44103696942329407},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.41230738162994385},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4109949767589569},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15374934673309326},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s0036139902401550","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139902401550","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.15.2116","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.2116","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.princeton.edu/%7Esircar/Public/ARTICLES/proof7.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.152.5762","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.152.5762","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.stanford.edu/~papanico/pubftp/proof4.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.6.7219","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.7219","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.uci.edu/~ksolna/research/proof3.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.7.2911","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.2911","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://math.Stanford.EDU/pub/papers/papanicolaou/proof4.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth","score":0.5699999928474426}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W982383590","https://openalex.org/W1514815886","https://openalex.org/W1992598907","https://openalex.org/W2047774784","https://openalex.org/W2098612888","https://openalex.org/W2101891840","https://openalex.org/W2148080284","https://openalex.org/W3121780766"],"related_works":["https://openalex.org/W2578663297","https://openalex.org/W2207440459","https://openalex.org/W2975994083","https://openalex.org/W2488981443","https://openalex.org/W2083229504","https://openalex.org/W2901884678","https://openalex.org/W3123864348","https://openalex.org/W3038290341","https://openalex.org/W4287726409","https://openalex.org/W2549845650"],"abstract_inverted_index":{"After":[0],"the":[1,12,27,46,85,94,99,110,124,147,150,159,166,173,183,188,195,199,214],"celebrated":[2],"Black--Scholes":[3,201],"formula":[4],"for":[5,14,164],"pricing":[6,191],"call":[7,162],"options":[8,163],"under":[9],"constant":[10,120],"volatility,":[11],"need":[13],"more":[15],"general":[16],"nonconstant":[17],"volatility":[18,42,47,100,114,121],"models":[19,43],"in":[20,44,60,62,84,108,115,187],"financial":[21],"mathematics":[22],"motivated":[23],"numerous":[24],"works":[25],"during":[26],"1980s":[28],"and":[29,98],"1990s.":[30],"In":[31],"particular,":[32],"a":[33,88,134],"lot":[34],"of":[35,87,90,112,126,128,140,149,161,190,198],"attention":[36],"has":[37],"been":[38],"paid":[39],"to":[40,119,133,144,154],"stochastic":[41],"which":[45,165,209],"is":[48,143,178,210,216],"randomly":[49],"fluctuating":[50],"driven":[51],"by":[52,203],"an":[53,170,205],"additional":[54],"Brownian":[55],"motion.":[56],"We":[57,157,193],"have":[58],"shown":[59],"[Derivatives":[61],"Financial":[63],"Markets":[64],"with":[65,146],"Stochastic":[66],"Volatility,":[67],"Cambridge":[68],"University":[69],"Press,":[70],"Cambridge,":[71],"UK,":[72],"2000;":[73],"Internat.":[74],"J.":[75],"Theoret.":[76],"Appl.":[77],"Finance,":[78],"13":[79],"(2000),":[80],"pp.":[81],"101--142]":[82],"that,":[83],"presence":[86],"separation":[89],"time":[91],"scales":[92],"between":[93],"main":[95],"observed":[96],"process":[97],"driving":[101],"process,":[102],"asymptotic":[103],"methods":[104],"are":[105,182],"very":[106],"efficient":[107],"capturing":[109],"effects":[111],"random":[113],"simple":[116],"robust":[117],"corrections":[118],"formulas.":[122],"From":[123],"point":[125],"view":[127],"PDEs,":[129],"this":[130,141],"method":[131],"corresponds":[132],"singular":[135],"perturbation":[136],"analysis.":[137],"The":[138],"aim":[139],"paper":[142],"deal":[145],"nonsmoothness":[148],"payoff":[151,167,207],"function":[152,168],"inherent":[153],"option":[155],"pricing.":[156],"present":[158],"case":[160,177],"forms":[169],"angle":[171],"at":[172],"strike":[174],"price.":[175],"This":[176],"important":[179],"since":[180],"these":[181],"typical":[184],"instruments":[185],"used":[186],"calibration":[189],"models.":[192],"establish":[194],"pointwise":[196],"accuracy":[197],"corrected":[200],"price":[202],"using":[204],"appropriate":[206],"regularization":[208],"removed":[211],"simultaneously":[212],"as":[213],"asymptotics":[215],"performed.":[217]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":15}],"updated_date":"2026-06-27T08:28:00.272161","created_date":"2025-10-10T00:00:00"}