{"id":"https://openalex.org/W4416405237","doi":"https://doi.org/10.48550/arxiv.2507.19003","title":"A diffusion-based generative model for financial time series via geometric Brownian motion","display_name":"A diffusion-based generative model for financial time series via geometric Brownian motion","publication_year":2025,"publication_date":"2025-07-25","ids":{"openalex":"https://openalex.org/W4416405237","doi":"https://doi.org/10.48550/arxiv.2507.19003"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2507.19003","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.19003","pdf_url":"https://arxiv.org/pdf/2507.19003","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2507.19003","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003099897","display_name":"Gihun Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kim, Gihun","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055325039","display_name":"Sun\u2010Yong Choi","orcid":"https://orcid.org/0000-0001-7234-7183"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Choi, Sun-Yong","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028468023","display_name":"Yeoneung Kim","orcid":"https://orcid.org/0000-0001-6293-3939"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Yeoneung","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003099897"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.23669999837875366,"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"}},"topics":[{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.23669999837875366,"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"}},{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.13330000638961792,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11326","display_name":"Stock Market Forecasting Methods","score":0.08250000327825546,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stylized-fact","display_name":"Stylized fact","score":0.6417999863624573},{"id":"https://openalex.org/keywords/geometric-brownian-motion","display_name":"Geometric Brownian motion","score":0.6018999814987183},{"id":"https://openalex.org/keywords/heteroscedasticity","display_name":"Heteroscedasticity","score":0.5637000203132629},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.4535999894142151},{"id":"https://openalex.org/keywords/diffusion-process","display_name":"Diffusion process","score":0.4291999936103821},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.4196999967098236},{"id":"https://openalex.org/keywords/stochastic-volatility","display_name":"Stochastic volatility","score":0.41780000925064087},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.41040000319480896},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.4049000144004822},{"id":"https://openalex.org/keywords/volatility","display_name":"Volatility (finance)","score":0.38659998774528503}],"concepts":[{"id":"https://openalex.org/C38935604","wikidata":"https://www.wikidata.org/wiki/Q4330363","display_name":"Stylized fact","level":2,"score":0.6417999863624573},{"id":"https://openalex.org/C101615488","wikidata":"https://www.wikidata.org/wiki/Q1503307","display_name":"Geometric Brownian motion","level":4,"score":0.6018999814987183},{"id":"https://openalex.org/C101104100","wikidata":"https://www.wikidata.org/wiki/Q1063540","display_name":"Heteroscedasticity","level":2,"score":0.5637000203132629},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4657999873161316},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.4535999894142151},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.439300000667572},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.4291999936103821},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.4196999967098236},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41940000653266907},{"id":"https://openalex.org/C85393063","wikidata":"https://www.wikidata.org/wiki/Q596307","display_name":"Stochastic volatility","level":3,"score":0.41780000925064087},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.41040000319480896},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.4049000144004822},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.38659998774528503},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.364300012588501},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.36250001192092896},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.36010000109672546},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.3407000005245209},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.334199994802475},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.33320000767707825},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3199000060558319},{"id":"https://openalex.org/C23922673","wikidata":"https://www.wikidata.org/wiki/Q180752","display_name":"Autoregressive conditional heteroskedasticity","level":3,"score":0.305400013923645},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C2779664328","wikidata":"https://www.wikidata.org/wiki/Q6311158","display_name":"Jump diffusion","level":3,"score":0.29989999532699585},{"id":"https://openalex.org/C93373587","wikidata":"https://www.wikidata.org/wiki/Q335632","display_name":"Mathematical finance","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28690001368522644},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C204036174","wikidata":"https://www.wikidata.org/wiki/Q909380","display_name":"Stock (firearms)","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.27489998936653137},{"id":"https://openalex.org/C2778705799","wikidata":"https://www.wikidata.org/wiki/Q2823610","display_name":"Financial asset","level":2,"score":0.2736999988555908},{"id":"https://openalex.org/C2780550144","wikidata":"https://www.wikidata.org/wiki/Q1156976","display_name":"Excursion","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2646999955177307},{"id":"https://openalex.org/C2779309563","wikidata":"https://www.wikidata.org/wiki/Q649206","display_name":"Order book","level":3,"score":0.26030001044273376},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.251800000667572},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.25}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2507.19003","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.19003","pdf_url":"https://arxiv.org/pdf/2507.19003","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2507.19003","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.19003","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2507.19003","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.19003","pdf_url":"https://arxiv.org/pdf/2507.19003","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,77,101],"novel":[3],"diffusion-based":[4],"generative":[5,88,92],"framework":[6],"for":[7],"financial":[8,57],"time":[9,50,58],"series":[10],"that":[11,32,70,120],"incorporates":[12],"geometric":[13],"Brownian":[14],"motion":[15],"(GBM),":[16],"the":[17,20,24,53,63,71,84,106,133],"foundation":[18],"of":[19],"Black--Scholes":[21],"theory,":[22],"into":[23],"forward":[25],"noising":[26],"process.":[27],"Unlike":[28],"standard":[29],"score-based":[30,87],"models":[31],"treat":[33],"price":[34],"trajectories":[35],"as":[36],"generic":[37],"numerical":[38],"sequences,":[39],"our":[40,121],"method":[41],"injects":[42],"noise":[43],"proportionally":[44],"to":[45,76],"asset":[46],"prices":[47],"at":[48],"each":[49],"step,":[51],"reflecting":[52],"heteroskedasticity":[54],"observed":[55],"in":[56,86],"series.":[59],"By":[60],"accurately":[61],"balancing":[62],"drift":[64],"and":[65,132],"diffusion":[66,140],"terms,":[67],"we":[68],"show":[69],"resulting":[72],"log-price":[73],"process":[74,93],"reduces":[75],"variance-exploding":[78],"stochastic":[79],"differential":[80],"equation,":[81],"aligning":[82],"with":[83],"formulation":[85],"models.":[89,141],"The":[90],"reverse-time":[91],"is":[94],"trained":[95],"via":[96],"denoising":[97],"score":[98],"matching":[99],"using":[100],"Transformer-based":[102],"architecture":[103],"adapted":[104],"from":[105],"Conditional":[107],"Score-based":[108],"Diffusion":[109],"Imputation":[110],"(CSDI)":[111],"framework.":[112],"Empirical":[113],"evaluations":[114],"on":[115],"historical":[116],"stock":[117],"data":[118],"demonstrate":[119],"model":[122],"reproduces":[123],"key":[124],"stylized":[125],"facts":[126],"heavy-tailed":[127],"return":[128],"distributions,":[129],"volatility":[130],"clustering,":[131],"leverage":[134],"effect":[135],"more":[136],"realistically":[137],"than":[138],"conventional":[139]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}