{"id":"https://openalex.org/W3157822449","doi":"https://doi.org/10.1016/j.amc.2022.127446","title":"Sparse grid method for highly efficient computation of exposures for xVA","display_name":"Sparse grid method for highly efficient computation of exposures for xVA","publication_year":2022,"publication_date":"2022-08-10","ids":{"openalex":"https://openalex.org/W3157822449","doi":"https://doi.org/10.1016/j.amc.2022.127446","mag":"3157822449"},"language":"en","primary_location":{"id":"doi:10.1016/j.amc.2022.127446","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.amc.2022.127446","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.amc.2022.127446","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046181858","display_name":"Lech A. Grzelak","orcid":"https://orcid.org/0000-0003-2329-5254"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]},{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Lech A. Grzelak","raw_affiliation_strings":["Financial Engineering, Rabobank, Utrecht, the Netherlands","Mathematical Institute, Utrecht University, Utrecht, the Netherlands","(Delft University of Technology)"],"affiliations":[{"raw_affiliation_string":"Financial Engineering, Rabobank, Utrecht, the Netherlands","institution_ids":[]},{"raw_affiliation_string":"Mathematical Institute, Utrecht University, Utrecht, the Netherlands","institution_ids":["https://openalex.org/I193662353"]},{"raw_affiliation_string":"(Delft University of Technology)","institution_ids":["https://openalex.org/I98358874"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046181858"],"corresponding_institution_ids":["https://openalex.org/I193662353","https://openalex.org/I98358874"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":{"value":3550,"currency":"USD","value_usd":3550},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00368979,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"434","issue":null,"first_page":"127446","last_page":"127446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9968000054359436,"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"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9962000250816345,"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/sparse-grid","display_name":"Sparse grid","score":0.7763506174087524},{"id":"https://openalex.org/keywords/portfolio","display_name":"Portfolio","score":0.714066207408905},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7016352415084839},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5680088996887207},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5484857559204102},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5458917021751404},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.5430779457092285},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.5071070194244385},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.4796057939529419},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.4695257246494293},{"id":"https://openalex.org/keywords/risk-management","display_name":"Risk management","score":0.44550126791000366},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43820828199386597},{"id":"https://openalex.org/keywords/portfolio-optimization","display_name":"Portfolio optimization","score":0.42995989322662354},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.32825222611427307},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23320737481117249},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18664026260375977},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.14053770899772644},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.13726288080215454},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.10833537578582764},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10606205463409424}],"concepts":[{"id":"https://openalex.org/C156439662","wikidata":"https://www.wikidata.org/wiki/Q7573793","display_name":"Sparse grid","level":2,"score":0.7763506174087524},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.714066207408905},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7016352415084839},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5680088996887207},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5484857559204102},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5458917021751404},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.5430779457092285},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.5071070194244385},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.4796057939529419},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.4695257246494293},{"id":"https://openalex.org/C32896092","wikidata":"https://www.wikidata.org/wiki/Q189447","display_name":"Risk management","level":2,"score":0.44550126791000366},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43820828199386597},{"id":"https://openalex.org/C202655437","wikidata":"https://www.wikidata.org/wiki/Q7231728","display_name":"Portfolio optimization","level":3,"score":0.42995989322662354},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.32825222611427307},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23320737481117249},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18664026260375977},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.14053770899772644},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.13726288080215454},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.10833537578582764},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10606205463409424},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1016/j.amc.2022.127446","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.amc.2022.127446","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2104.14319","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.14319","pdf_url":"https://arxiv.org/pdf/2104.14319","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:3157822449","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2104.14319.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:RePEc:arx:papers:2104.14319","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:RePEc:eee:apmaco:v:434:y:2022:i:c:s0096300322005203","is_oa":false,"landing_page_url":"http://www.sciencedirect.com/science/article/pii/S0096300322005203","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":"article"},{"id":"pmh:oai:dspace.library.uu.nl:1874/426899","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/426899","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:dspace.library.uu.nl:1874/429784","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/429784","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2104.14319","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2104.14319","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1016/j.amc.2022.127446","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.amc.2022.127446","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W240907682","https://openalex.org/W1542118577","https://openalex.org/W1841486359","https://openalex.org/W1971099220","https://openalex.org/W2033022456","https://openalex.org/W2142863015","https://openalex.org/W2143591652","https://openalex.org/W2618142242","https://openalex.org/W2794337809","https://openalex.org/W2804354687","https://openalex.org/W3005371110","https://openalex.org/W3045736336","https://openalex.org/W3085015010","https://openalex.org/W3123185727","https://openalex.org/W3123515469","https://openalex.org/W3123528665","https://openalex.org/W3124606840","https://openalex.org/W3125480909","https://openalex.org/W3154362755","https://openalex.org/W3164764925","https://openalex.org/W3165882213","https://openalex.org/W4234209951","https://openalex.org/W6642746754","https://openalex.org/W6658715121","https://openalex.org/W6728701595","https://openalex.org/W6738643775","https://openalex.org/W6751902685","https://openalex.org/W6772478501","https://openalex.org/W6789505175"],"related_works":["https://openalex.org/W3167804879","https://openalex.org/W2434553776","https://openalex.org/W2290619576","https://openalex.org/W2265721031","https://openalex.org/W1555207426","https://openalex.org/W1935041359","https://openalex.org/W2171879406","https://openalex.org/W115841351","https://openalex.org/W2594545404","https://openalex.org/W2045513909","https://openalex.org/W3124018520","https://openalex.org/W2767853049","https://openalex.org/W1875886693","https://openalex.org/W3125822593","https://openalex.org/W101554702","https://openalex.org/W1844358724","https://openalex.org/W1595928107","https://openalex.org/W2465012345","https://openalex.org/W3123585497","https://openalex.org/W3153409316"],"abstract_inverted_index":{"Every":[0],"\u201cx\u201d-adjustment":[1],"in":[2,111,150],"the":[3,12,37,40,45,61,69,86,112,147,151,160,163,172],"so-called":[4],"xVA":[5],"financial":[6,28],"risk":[7,81,122],"management":[8],"framework":[9],"relies":[10],"on":[11,159],"computation":[13],"of":[14,18,24,39,47,50,63,71,85,114,179],"exposures.":[15,64],"Considering":[16],"thousands":[17],"Monte":[19],"Carlo":[20],"paths":[21],"and":[22,134,144,162,170,183],"tens":[23],"simulation":[25,49,62],"steps,":[26],"a":[27,108,139],"portfolio":[29,72,115,133,141,152],"needs":[30],"to":[31,67,131],"be":[32,128],"evaluated":[33],"numerous":[34],"times":[35],"during":[36],"lifetime":[38],"underlying":[41],"assets.":[42],"This":[43],"is":[44],"bottleneck":[46],"every":[48],"xVA.":[51],"In":[52],"this":[53],"article,":[54],"we":[55],"explore":[56],"numerical":[57],"techniques":[58],"for":[59,75,107,138],"improving":[60],"We":[65,166],"aim":[66],"decimate":[68],"number":[70,113],"evaluations,":[73,116],"particularly":[74],"large":[76],"portfolios":[77,177],"involving":[78],"multiple,":[79],"correlated":[80],"factors.":[82,123],"The":[83,124],"usage":[84],"Stochastic":[87],"Collocation":[88],"(SC)":[89],"method":[90,173],"Grzelak":[91],"et":[92,100],"al.":[93,101],"(2019)[,":[94],"together":[95],"with":[96,120,174],"Smolyak\u2019s":[97],"(1963),":[98],"Judd":[99],"(2014)":[102],"sparse":[103],"grid":[104],"extension,":[105],"allows":[106],"significant":[109],"reduction":[110,149],"even":[117],"when":[118],"dealing":[119],"many":[121],"proposed":[125],"model":[126],"can":[127],"easily":[129],"applied":[130],"any":[132],"size.We":[135],"report":[136],"that":[137],"realistic":[140,175],"comprising":[142],"linear":[143],"non-linear":[145],"derivatives,":[146],"expected":[148],"evaluations":[153],"may":[154],"exceed":[155],"6000":[156],"times,":[157],"depending":[158],"dimensionality":[161],"required":[164],"accuracy.":[165],"give":[167],"illustrative":[168],"examples":[169],"examine":[171],"multi-currency":[176],"consisting":[178],"interest":[180],"rate":[181],"swaps":[182],"swaptions.":[184]},"counts_by_year":[],"updated_date":"2026-04-04T08:04:53.788161","created_date":"2025-10-10T00:00:00"}
