{"id":"https://openalex.org/W3193234940","doi":"https://doi.org/10.1137/21m1443546","title":"Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders","display_name":"Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders","publication_year":2023,"publication_date":"2023-10-11","ids":{"openalex":"https://openalex.org/W3193234940","doi":"https://doi.org/10.1137/21m1443546","mag":"3193234940"},"language":"en","primary_location":{"id":"doi:10.1137/21m1443546","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1443546","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/A5053793053","display_name":"Brian Ning","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Brian (Xin) Ning","raw_affiliation_strings":["Department of Statistical Sciences, University of Toronto, Toronto, M5G 1Z5, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistical Sciences, University of Toronto, Toronto, M5G 1Z5, ON, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016897782","display_name":"Sebastian Jaimungal","orcid":"https://orcid.org/0000-0002-0193-0993"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Sebastian Jaimungal","raw_affiliation_strings":["Department of Statistical Sciences, University of Toronto, Toronto, M5G 1Z5, ON, Canada"],"raw_orcid":"https://orcid.org/0000-0002-0193-0993","affiliations":[{"raw_affiliation_string":"Department of Statistical Sciences, University of Toronto, Toronto, M5G 1Z5, ON, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100706233","display_name":"Xiaorong Zhang","orcid":"https://orcid.org/0000-0002-2769-2532"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Xiaorong Zhang","raw_affiliation_strings":["Department of Statistical Sciences, University of Toronto, Toronto, M5G 1Z5, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistical Sciences, University of Toronto, Toronto, M5G 1Z5, ON, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013392570","display_name":"Maxime Bergeron","orcid":"https://orcid.org/0000-0003-3988-2170"},"institutions":[{"id":"https://openalex.org/I4210088367","display_name":"Systems Analytics (United States)","ror":"https://ror.org/005ksdp35","country_code":"US","type":"company","lineage":["https://openalex.org/I4210088367"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maxime Bergeron","raw_affiliation_strings":["Riskfuel Analytics, Toronto, M5C 1X6, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Riskfuel Analytics, Toronto, M5C 1X6, ON, Canada","institution_ids":["https://openalex.org/I4210088367"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.083,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.93890597,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"14","issue":"4","first_page":"1004","last_page":"1027"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9901000261306763,"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/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9732000231742859,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/arbitrage","display_name":"Arbitrage","score":0.6441726088523865},{"id":"https://openalex.org/keywords/stochastic-volatility","display_name":"Stochastic volatility","score":0.6181541681289673},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.6120327711105347},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6051816940307617},{"id":"https://openalex.org/keywords/generative-model","display_name":"Generative model","score":0.5361855626106262},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5075706243515015},{"id":"https://openalex.org/keywords/quadratic-variation","display_name":"Quadratic variation","score":0.49298617243766785},{"id":"https://openalex.org/keywords/volatility","display_name":"Volatility (finance)","score":0.46549496054649353},{"id":"https://openalex.org/keywords/boltzmann-machine","display_name":"Boltzmann machine","score":0.425098717212677},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.4207504391670227},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40642017126083374},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.35930711030960083},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31646764278411865},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28795334696769714},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.14063382148742676},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1230400800704956},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.10798633098602295},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.10704180598258972},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.07982799410820007}],"concepts":[{"id":"https://openalex.org/C160623529","wikidata":"https://www.wikidata.org/wiki/Q273088","display_name":"Arbitrage","level":2,"score":0.6441726088523865},{"id":"https://openalex.org/C85393063","wikidata":"https://www.wikidata.org/wiki/Q596307","display_name":"Stochastic volatility","level":3,"score":0.6181541681289673},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.6120327711105347},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6051816940307617},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.5361855626106262},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5075706243515015},{"id":"https://openalex.org/C90087638","wikidata":"https://www.wikidata.org/wiki/Q7268374","display_name":"Quadratic variation","level":3,"score":0.49298617243766785},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.46549496054649353},{"id":"https://openalex.org/C192576344","wikidata":"https://www.wikidata.org/wiki/Q194706","display_name":"Boltzmann machine","level":3,"score":0.425098717212677},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.4207504391670227},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40642017126083374},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.35930711030960083},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31646764278411865},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28795334696769714},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.14063382148742676},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1230400800704956},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.10798633098602295},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.10704180598258972},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.07982799410820007}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1443546","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1443546","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G48083957","display_name":null,"funder_award_id":"ALLRP 550308 - 20","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W194721474","https://openalex.org/W385466589","https://openalex.org/W1531532214","https://openalex.org/W1591798773","https://openalex.org/W2018952448","https://openalex.org/W2037506728","https://openalex.org/W2050888606","https://openalex.org/W2064978316","https://openalex.org/W2086234878","https://openalex.org/W2116569334","https://openalex.org/W2138540172","https://openalex.org/W2491851875","https://openalex.org/W2753738274","https://openalex.org/W2778939515","https://openalex.org/W2797602122","https://openalex.org/W2895907884","https://openalex.org/W2914215310","https://openalex.org/W2940793771","https://openalex.org/W2951004968","https://openalex.org/W2963323474","https://openalex.org/W3009519538","https://openalex.org/W3022439851","https://openalex.org/W3037971676","https://openalex.org/W3048247926","https://openalex.org/W3080232699","https://openalex.org/W3101650270","https://openalex.org/W3102239781","https://openalex.org/W3121972394","https://openalex.org/W3122402328","https://openalex.org/W3124397939","https://openalex.org/W3124960685","https://openalex.org/W3127467160","https://openalex.org/W3167120613","https://openalex.org/W3194974717","https://openalex.org/W3206550597","https://openalex.org/W4205112682","https://openalex.org/W4233762729"],"related_works":["https://openalex.org/W188472100","https://openalex.org/W2171145682","https://openalex.org/W4388063460","https://openalex.org/W1487804950","https://openalex.org/W4360831753","https://openalex.org/W2140585983","https://openalex.org/W3140456158","https://openalex.org/W3123747248","https://openalex.org/W3124385409","https://openalex.org/W2213614553"],"abstract_inverted_index":{".We":[0],"propose":[1],"a":[2,59,74,133],"hybrid":[3],"method":[4,128],"for":[5],"generating":[6],"arbitrage-free":[7],"implied":[8],"volatility":[9],"(IV)":[10],"surfaces":[11,49,78],"consistent":[12],"with":[13,22],"historical":[14,48],"data":[15,68,134],"by":[16,82,112],"combining":[17],"model-free":[18],"variational":[19],"autoencoders":[20],"(VAEs)":[21],"continuous":[23],"time":[24],"stochastic":[25],"differential":[26],"equation":[27],"(SDE)":[28],"driven":[29],"models.":[30],"We":[31,106],"focus":[32],"on":[33,61,69,88],"two":[34],"classes":[35],"of":[36,53,144],"SDE":[37,54,95],"models:":[38],"regime":[39],"switching":[40],"models":[41],"and":[42,98,116],"L\u00e9vy":[43],"additive":[44],"processes.":[45],"By":[46],"projecting":[47],"onto":[50],"the":[51,62,67,85,89,109,141],"space":[52],"model":[55,96,111],"parameters,":[56,97],"we":[57,71,124],"obtain":[58,94],"distribution":[60,87],"parameter":[63],"subspace":[64],"faithful":[65],"to":[66,93,103,137],"which":[70],"then":[72,80],"train":[73],"VAE.":[75],"Arbitrage-free":[76],"IV":[77,104],"are":[79],"generated":[81],"sampling":[83],"from":[84],"posterior":[86],"latent":[90],"space,":[91],"decoding":[92],"finally":[99],"mapping":[100],"those":[101],"parameters":[102],"surfaces.":[105],"further":[107],"refine":[108],"VAE":[110],"including":[113],"conditional":[114],"features":[115],"demonstrate":[117],"its":[118],"superior":[119],"generative":[120],"out-of-sample":[121],"performance.":[122],"Finally,":[123],"showcase":[125],"how":[126],"our":[127],"can":[129],"be":[130],"used":[131],"as":[132],"augmentation":[135],"tool":[136],"help":[138],"practitioners":[139],"manage":[140],"tail":[142],"risk":[143],"option":[145],"portfolios.Keywordsmachine":[146],"learningcomputational":[147],"financeimplied":[148],"volatilityvariational":[149],"autoencoderL\u00e9vy":[150],"processesMSC":[151],"codes91-0891G2068T07":[152]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
