{"id":"https://openalex.org/W2434830265","doi":"https://doi.org/10.1080/03610918.2016.1175624","title":"Fitting Generalized Hyperbolic processes - New insights for generating initial values","display_name":"Fitting Generalized Hyperbolic processes - New insights for generating initial values","publication_year":2016,"publication_date":"2016-06-14","ids":{"openalex":"https://openalex.org/W2434830265","doi":"https://doi.org/10.1080/03610918.2016.1175624","mag":"2434830265"},"language":"en","primary_location":{"id":"doi:10.1080/03610918.2016.1175624","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2016.1175624","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-427215","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"A. W. Rathgeber","orcid":null},"institutions":[{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]},{"id":"https://openalex.org/I2801696985","display_name":"France Business School","ror":"https://ror.org/0287ptp38","country_code":"FR","type":"education","lineage":["https://openalex.org/I2801696985"]},{"id":"https://openalex.org/I4387155791","display_name":"Centre Europ\u00e9en de Recherche en Economie Financi\u00e8re et Gestion des Entreprises","ror":"https://ror.org/0106d5c37","country_code":null,"type":"facility","lineage":["https://openalex.org/I4387155791","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4400600934","display_name":"ICN Business School","ror":"https://ror.org/02f3ymk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I4400600934"]}],"countries":["DE","FR"],"is_corresponding":true,"raw_author_name":"A. W. Rathgeber","raw_affiliation_strings":["Institute for Materials Resource Management, University of Augsburg, Augsburg, Germany","ICN Business School (P\u00f4le lorrain de gestion - 13 Rue Michel Ney - 54000 Nancy - France)","CEREFIGE - Centre Europ\u00e9en de Recherche en Economie Financi\u00e8re et Gestion des Entreprises (UL, Maison de la Recherche, 23-25 rue Baron Louis, 54000 NANCY  - France)"],"affiliations":[{"raw_affiliation_string":"Institute for Materials Resource Management, University of Augsburg, Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]},{"raw_affiliation_string":"ICN Business School (P\u00f4le lorrain de gestion - 13 Rue Michel Ney - 54000 Nancy - France)","institution_ids":["https://openalex.org/I2801696985","https://openalex.org/I4400600934"]},{"raw_affiliation_string":"CEREFIGE - Centre Europ\u00e9en de Recherche en Economie Financi\u00e8re et Gestion des Entreprises (UL, Maison de la Recherche, 23-25 rue Baron Louis, 54000 NANCY  - France)","institution_ids":["https://openalex.org/I4387155791"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068083241","display_name":"Johannes Stadler","orcid":null},"institutions":[{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"J. Stadler","raw_affiliation_strings":["Institute for Materials Resource Management, University of Augsburg, Augsburg, Germany","Universit\u00e4t Augsburg [Augsburg] (Universit\u00e4tsstra\u00dfe 2, 86159 Augsburg - Germany)"],"affiliations":[{"raw_affiliation_string":"Institute for Materials Resource Management, University of Augsburg, Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]},{"raw_affiliation_string":"Universit\u00e4t Augsburg [Augsburg] (Universit\u00e4tsstra\u00dfe 2, 86159 Augsburg - Germany)","institution_ids":["https://openalex.org/I179225836"]}]},{"author_position":"last","author":{"id":null,"display_name":"S. St\u00f6ckl","orcid":null},"institutions":[{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]},{"id":"https://openalex.org/I4400600934","display_name":"ICN Business School","ror":"https://ror.org/02f3ymk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I4400600934"]}],"countries":["DE","FR"],"is_corresponding":false,"raw_author_name":"S. St\u00f6ckl","raw_affiliation_strings":["ICN Business School Nancy-Metz (Grande \u00e9cole) - CEREFIGE, METZ Technopole, France","Universit\u00e4t Augsburg [Augsburg] (Universit\u00e4tsstra\u00dfe 2, 86159 Augsburg - Germany)"],"affiliations":[{"raw_affiliation_string":"ICN Business School Nancy-Metz (Grande \u00e9cole) - CEREFIGE, METZ Technopole, France","institution_ids":["https://openalex.org/I4400600934"]},{"raw_affiliation_string":"Universit\u00e4t Augsburg [Augsburg] (Universit\u00e4tsstra\u00dfe 2, 86159 Augsburg - Germany)","institution_ids":["https://openalex.org/I179225836"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I179225836","https://openalex.org/I2801696985","https://openalex.org/I4387155791","https://openalex.org/I4400600934"],"apc_list":null,"apc_paid":null,"fwci":0.4703,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72421863,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"46","issue":"7","first_page":"5752","last_page":"5762"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9991000294685364,"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":0.9991000294685364,"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":0.988099992275238,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9610999822616577,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6401594877243042},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6136517524719238},{"id":"https://openalex.org/keywords/variance-gamma-distribution","display_name":"Variance-gamma distribution","score":0.5651789903640747},{"id":"https://openalex.org/keywords/bessel-function","display_name":"Bessel function","score":0.5572227835655212},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5299264788627625},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.527600109577179},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.5154200792312622},{"id":"https://openalex.org/keywords/inverse-gaussian-distribution","display_name":"Inverse Gaussian distribution","score":0.48967936635017395},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.48796314001083374},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4584566652774811},{"id":"https://openalex.org/keywords/normal-inverse-gaussian-distribution","display_name":"Normal-inverse Gaussian distribution","score":0.44984763860702515},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.4479392170906067},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4264904856681824},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.41939061880111694},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.40908384323120117},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39805129170417786},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.330992192029953},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3263125419616699},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20909127593040466},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"Asymptotic distribution","score":0.1850702166557312},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18292003870010376},{"id":"https://openalex.org/keywords/gaussian-random-field","display_name":"Gaussian random field","score":0.10097190737724304}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6401594877243042},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6136517524719238},{"id":"https://openalex.org/C30084815","wikidata":"https://www.wikidata.org/wiki/Q4390268","display_name":"Variance-gamma distribution","level":4,"score":0.5651789903640747},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.5572227835655212},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5299264788627625},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.527600109577179},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.5154200792312622},{"id":"https://openalex.org/C132878287","wikidata":"https://www.wikidata.org/wiki/Q1671727","display_name":"Inverse Gaussian distribution","level":3,"score":0.48967936635017395},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.48796314001083374},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4584566652774811},{"id":"https://openalex.org/C202021718","wikidata":"https://www.wikidata.org/wiki/Q7051759","display_name":"Normal-inverse Gaussian distribution","level":5,"score":0.44984763860702515},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.4479392170906067},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4264904856681824},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.41939061880111694},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.40908384323120117},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39805129170417786},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.330992192029953},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3263125419616699},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20909127593040466},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.1850702166557312},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18292003870010376},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.10097190737724304},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/03610918.2016.1175624","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2016.1175624","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01768898v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01768898","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":"Communications in Statistics - Simulation and Computation, 2017, 46 (7), pp.5752-5762. ⟨10.1080/03610918.2016.1175624⟩","raw_type":"Journal articles"},{"id":"pmh:oai:RePEc:hal:journl:hal-01768898","is_oa":false,"landing_page_url":null,"pdf_url":null,"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,"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:uni-augsburg.opus-bayern.de:42721","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-427215","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:uni-augsburg.opus-bayern.de:42721","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-427215","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1486748438","https://openalex.org/W1978211602","https://openalex.org/W1980519218","https://openalex.org/W1988615517","https://openalex.org/W1994858552","https://openalex.org/W2002530172","https://openalex.org/W2042326448","https://openalex.org/W2065807881","https://openalex.org/W2100190417","https://openalex.org/W2107291507","https://openalex.org/W2123446302","https://openalex.org/W2129199257","https://openalex.org/W2148688139","https://openalex.org/W2174253870","https://openalex.org/W2801179766","https://openalex.org/W3141915193"],"related_works":["https://openalex.org/W2008489469","https://openalex.org/W3216151428","https://openalex.org/W2341897833","https://openalex.org/W2123446302","https://openalex.org/W1977620257","https://openalex.org/W4255942042","https://openalex.org/W2355998038","https://openalex.org/W4212923888","https://openalex.org/W2022725103","https://openalex.org/W2902821395"],"abstract_inverted_index":{"The":[0,136],"fitting":[1,24],"of":[2,9,23,33,42,76,100,125,131],"L\u00e9vy":[3],"processes":[4],"is":[5,143],"an":[6,83,144],"important":[7],"field":[8],"interest":[10],"in":[11],"both":[12],"option":[13],"pricing":[14],"and":[15,107,146,155],"risk":[16],"management.":[17],"In":[18],"literature,":[19],"a":[20,48,91,104,108,112],"large":[21],"number":[22],"methods":[25],"requiring":[26],"adequate":[27],"initial":[28,52],"values":[29,53],"at":[30],"the":[31,34,55,60,68,74,77,96,101,115,123,129,132],"start":[32],"optimization":[35],"procedure":[36],"exists.":[37],"A":[38],"so-called":[39],"simplified":[40],"method":[41],"moments":[43],"(SMoM)":[44],"generates":[45],"by":[46,89],"assuming":[47],"symmetric":[49,109],"distribution":[50,110],"these":[51],"for":[54,95,114,149],"Variance":[56],"Gamma":[57],"process,":[58],"whereby":[59],"idea":[61],"behind":[62],"can":[63],"be":[64],"easily":[65],"transferred":[66],"to":[67],"Normal":[69],"Inverse":[70],"Gaussian":[71],"process.":[72],"However,":[73],"characteristics":[75],"Generalized":[78,116,151],"Hyperbolic":[79,117,152],"process":[80,153],"prevent":[81],"such":[82],"easy":[84],"adaption.":[85],"Therefore,":[86],"we":[87],"provide":[88],"applying":[90],"Taylor":[92],"series":[93],"approximation":[94],"modified":[97],"Bessel":[98],"function":[99],"third":[102],"kind,":[103],"Tschirnhaus":[105],"transformation":[106],"assumption,":[111],"SMOM":[113],"distribution.":[118],"Our":[119],"simulation":[120],"study":[121],"compares":[122],"results":[124,130,137],"our":[126,140],"SMoM":[127],"with":[128],"maximum":[133],"likelihood":[134],"estimation.":[135],"show":[138],"that":[139],"proposed":[141],"approach":[142],"appropriate":[145],"useful":[147],"way":[148],"estimating":[150],"parameters":[154],"significantly":[156],"reduces":[157],"estimation":[158],"time.":[159]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2016-06-24T00:00:00"}