{"id":"https://openalex.org/W4389820573","doi":"https://doi.org/10.1111/mafi.70064","title":"Convergence of Heavy\u2010Tailed Hawkes Processes and the Microstructure of Rough Volatility","display_name":"Convergence of Heavy\u2010Tailed Hawkes Processes and the Microstructure of Rough Volatility","publication_year":2026,"publication_date":"2026-11-01","ids":{"openalex":"https://openalex.org/W4389820573","doi":"https://doi.org/10.1111/mafi.70064"},"language":"en","primary_location":{"id":"doi:10.1111/mafi.70064","doi":"https://doi.org/10.1111/mafi.70064","is_oa":true,"landing_page_url":"https://doi.org/10.1111/mafi.70064","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/mafi.70064","source":{"id":"https://openalex.org/S133335107","display_name":"Mathematical Finance","issn_l":"0960-1627","issn":["0960-1627","1467-9965"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","fnege-2","jufo-2","ki-jl-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Finance","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/mafi.70064","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029654636","display_name":"Ulrich Horst","orcid":"https://orcid.org/0000-0001-9000-0220","observed_orcids":["https://orcid.org/0000-0001-9000-0220"]},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Ulrich Horst","raw_affiliation_strings":["Department of Mathematics, School of Business and Economics Humboldt\u2010Universit\u00e4t zu Berlin  Berlin Germany"],"raw_orcid":"https://orcid.org/0000-0001-9000-0220","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Business and Economics Humboldt\u2010Universit\u00e4t zu Berlin  Berlin Germany","institution_ids":["https://openalex.org/I39343248"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101592590","display_name":"Wei Xu","orcid":"https://orcid.org/0000-0002-9370-8846","observed_orcids":["https://orcid.org/0000-0002-9370-8846"]},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Xu","raw_affiliation_strings":["School of Mathematics and Statistics Beijing Institute of Technology  Beijing China"],"raw_orcid":"https://orcid.org/0000-0002-9370-8846","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics Beijing Institute of Technology  Beijing China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":null,"display_name":"Rouyi Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rouyi Zhang","raw_affiliation_strings":["Department of Mathematics Humboldt\u2010Universit\u00e4t zu Berlin  Berlin China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Humboldt\u2010Universit\u00e4t zu Berlin  Berlin China","institution_ids":["https://openalex.org/I39343248"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029654636"],"corresponding_institution_ids":["https://openalex.org/I39343248"],"apc_list":{"value":3840,"currency":"USD","value_usd":3840},"apc_paid":{"value":3840,"currency":"USD","value_usd":3840},"fwci":4.4052,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.88684697,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":92,"max":97},"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9984999895095825,"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":0.9984999895095825,"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":0.0006000000284984708,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hawkes-process","display_name":"Hawkes process","score":0.8450000286102295},{"id":"https://openalex.org/keywords/power-law-kernel","display_name":"power-law kernel","score":0.8659999966621399},{"id":"https://openalex.org/keywords/rough-volatility","display_name":"rough volatility","score":0.7670000195503235},{"id":"https://openalex.org/keywords/rough-heston-model","display_name":"rough Heston model","score":0.9769999980926514},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"weak convergence","score":0.8040000200271606},{"id":"https://openalex.org/keywords/scaling-limits","display_name":"scaling limits","score":0.8550000190734863},{"id":"https://openalex.org/keywords/market-microstructure","display_name":"market microstructure","score":0.621999979019165},{"id":"https://openalex.org/keywords/volatility-process","display_name":"volatility process","score":0.5410000085830688},{"id":"https://openalex.org/keywords/tightness","display_name":"tightness","score":0.7179999947547913},{"id":"https://openalex.org/keywords/cadlag-processes","display_name":"c\u00e0dl\u00e0g processes","score":0.871999979019165},{"id":"https://openalex.org/keywords/high-frequency-data","display_name":"high-frequency data","score":0.3499999940395355}],"concepts":[{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.7153763771057129},{"id":"https://openalex.org/C85393063","wikidata":"https://www.wikidata.org/wiki/Q596307","display_name":"Stochastic volatility","level":3,"score":0.5365825295448303},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.526710569858551},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.518694281578064},{"id":"https://openalex.org/C93045229","wikidata":"https://www.wikidata.org/wiki/Q5746554","display_name":"Heston model","level":5,"score":0.5033826231956482},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4998645782470703},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46064144372940063},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.40061700344085693},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3879801630973816},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38320213556289673},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15948283672332764},{"id":"https://openalex.org/C187625094","wikidata":"https://www.wikidata.org/wiki/Q7388452","display_name":"SABR volatility model","level":4,"score":0.1493048071861267},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11324241757392883},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1111/mafi.70064","doi":"https://doi.org/10.1111/mafi.70064","is_oa":true,"landing_page_url":"https://doi.org/10.1111/mafi.70064","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/mafi.70064","source":{"id":"https://openalex.org/S133335107","display_name":"Mathematical Finance","issn_l":"0960-1627","issn":["0960-1627","1467-9965"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","fnege-2","jufo-2","ki-jl-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Finance","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:arx:papers:2312.08784","doi":null,"is_oa":false,"landing_page_url":"http://arxiv.org/pdf/2312.08784","pdf_url":"http://arxiv.org/pdf/2312.08784","source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"preprint"},{"id":"pmh:oai:arXiv.org:2312.08784","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.08784","pdf_url":"https://arxiv.org/pdf/2312.08784","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2312.08784","doi":"https://doi.org/10.48550/arxiv.2312.08784","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2312.08784","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1111/mafi.70064","doi":"https://doi.org/10.1111/mafi.70064","is_oa":true,"landing_page_url":"https://doi.org/10.1111/mafi.70064","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/mafi.70064","source":{"id":"https://openalex.org/S133335107","display_name":"Mathematical Finance","issn_l":"0960-1627","issn":["0960-1627","1467-9965"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","fnege-2","jufo-2","ki-jl-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Finance","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389820573.pdf","grobid_xml":"https://content.openalex.org/works/W4389820573.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2282116991","https://openalex.org/W2014601298","https://openalex.org/W7128733098","https://openalex.org/W2621243364","https://openalex.org/W2831763736","https://openalex.org/W4415241226","https://openalex.org/W7202155241","https://openalex.org/W2311961928","https://openalex.org/W7160399065","https://openalex.org/W2610071188"],"abstract_inverted_index":{"ABSTRACT":[0],"We":[1],"establish":[2,88,107],"the":[3,7,51,78,89,92,108,115],"weak":[4],"convergence":[5,62,79],"of":[6,9,80,91,94,110],"intensity":[8],"a":[10,23,27,42,57,103],"nearly\u2010unstable":[11],"Hawkes":[12,43],"process":[13,44,53],"with":[14,45],"heavy\u2010tailed":[15],"kernel.":[16,47],"Our":[17,61],"result":[18,63],"is":[19,64,86,99],"used":[20],"to":[21,33,41,56,87,106],"derive":[22],"scaling":[24],"limit":[25],"for":[26,120],"financial":[28],"market":[29],"model":[30],"where":[31],"orders":[32],"buy":[34],"or":[35,77],"sell":[36],"an":[37],"asset":[38],"arrive":[39],"according":[40],"power\u2010law":[46],"After":[48],"suitable":[49],"rescaling":[50],"price\u2010volatility":[52],"converges":[54],"weakly":[55],"rough":[58],"Heston":[59],"model.":[60],"stronger":[65],"than":[66],"previously":[67],"established":[68],"ones":[69],"that":[70],"have":[71],"either":[72],"focused":[73],"on":[74,114],"light\u2010tailed":[75],"kernels":[76],"integrated":[81],"volatility":[82,96],"process.":[83],"The":[84],"key":[85],"tightness":[90,118],"family":[93],"rescaled":[95],"processes.":[97,122],"This":[98],"achieved":[100],"by":[101],"introducing":[102],"new":[104],"method":[105],"\u2010tightness":[109],"c\u00e0dl\u00e0g":[111],"processes":[112],"based":[113],"classical":[116],"Kolmogorov\u2010Chentsov":[117],"criterion":[119],"continuous":[121]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2023-12-16T00:00:00"}
