{"id":"https://openalex.org/W7214717466","doi":"https://doi.org/10.48550/arxiv.2609.32238","title":"Exact Trade-Level Attribution of FRTB-IMA Capital","display_name":"Exact Trade-Level Attribution of FRTB-IMA Capital","publication_year":2026,"publication_date":"2026-09-26","ids":{"openalex":"https://openalex.org/W7214717466","doi":"https://doi.org/10.48550/arxiv.2609.32238"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.32238","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32238","pdf_url":"https://arxiv.org/pdf/2609.32238","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.32238","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147337357","display_name":"Yuhe Sui","orcid":"https://orcid.org/0009-0002-7456-0804","observed_orcids":["https://orcid.org/0009-0002-7456-0804"]},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Sui, Yuhe","raw_affiliation_strings":["Quantitative Research Society , Singapore Nanyang Technological University , Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Quantitative Research Society , Singapore Nanyang Technological University , Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5147337357"],"corresponding_institution_ids":["https://openalex.org/I172675005"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.28049999475479126,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.28049999475479126,"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/T10127","display_name":"Banking stability, regulation, efficiency","score":0.2312999963760376,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.20509999990463257,"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/market-risk-capital","display_name":"market risk capital","score":0.6959999799728394},{"id":"https://openalex.org/keywords/conditional-value-at-risk","display_name":"conditional value at risk","score":0.7739999890327454},{"id":"https://openalex.org/keywords/default-risk","display_name":"default risk","score":0.5910000205039978},{"id":"https://openalex.org/keywords/computational-graphs","display_name":"computational graphs","score":0.5799999833106995},{"id":"https://openalex.org/keywords/reverse-mode-automatic-differentiation","display_name":"reverse-mode differentiation","score":0.7419999837875366},{"id":"https://openalex.org/keywords/linear-programming","display_name":"linear programming","score":0.6520000100135803},{"id":"https://openalex.org/keywords/capital-planning","display_name":"capital planning","score":0.40299999713897705}],"concepts":[{"id":"https://openalex.org/C40410261","wikidata":"https://www.wikidata.org/wiki/Q16908579","display_name":"Marginal product of capital","level":5,"score":0.637499988079071},{"id":"https://openalex.org/C83646750","wikidata":"https://www.wikidata.org/wiki/Q193893","display_name":"Capital (architecture)","level":2,"score":0.6355999708175659},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.5412999987602234},{"id":"https://openalex.org/C9127897","wikidata":"https://www.wikidata.org/wiki/Q990550","display_name":"Physical capital","level":3,"score":0.48829999566078186},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.48170000314712524},{"id":"https://openalex.org/C57495647","wikidata":"https://www.wikidata.org/wiki/Q295385","display_name":"Economic capital","level":3,"score":0.45739999413490295},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.40470001101493835},{"id":"https://openalex.org/C138142054","wikidata":"https://www.wikidata.org/wiki/Q5035692","display_name":"Capital allocation line","level":3,"score":0.3944000005722046},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.3718999922275543},{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.3709999918937683},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.33799999952316284},{"id":"https://openalex.org/C44750222","wikidata":"https://www.wikidata.org/wiki/Q1897397","display_name":"Financial capital","level":3,"score":0.3375000059604645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33250001072883606},{"id":"https://openalex.org/C560292","wikidata":"https://www.wikidata.org/wiki/Q1113011","display_name":"Fixed capital","level":5,"score":0.3314000070095062},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C58202505","wikidata":"https://www.wikidata.org/wiki/Q5035700","display_name":"Capital formation","level":4,"score":0.3276999890804291},{"id":"https://openalex.org/C138551086","wikidata":"https://www.wikidata.org/wiki/Q842271","display_name":"Marginal utility","level":2,"score":0.31929999589920044},{"id":"https://openalex.org/C2864544","wikidata":"https://www.wikidata.org/wiki/Q2914988","display_name":"Capital requirement","level":3,"score":0.31520000100135803},{"id":"https://openalex.org/C202063016","wikidata":"https://www.wikidata.org/wiki/Q634028","display_name":"Marginal product","level":3,"score":0.3100000023841858},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.30000001192092896},{"id":"https://openalex.org/C74734477","wikidata":"https://www.wikidata.org/wiki/Q1479274","display_name":"Cost of capital","level":3,"score":0.27869999408721924},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C2992893776","wikidata":"https://www.wikidata.org/wiki/Q955421","display_name":"Capital equipment","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.32238","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32238","pdf_url":"https://arxiv.org/pdf/2609.32238","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.32238","doi":"https://doi.org/10.48550/arxiv.2609.32238","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.32238","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":"pmh:oai:arXiv.org:2609.32238","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32238","pdf_url":"https://arxiv.org/pdf/2609.32238","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214717466.pdf","grobid_xml":"https://content.openalex.org/works/W7214717466.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W637898570","https://openalex.org/W1647779468","https://openalex.org/W1966791450","https://openalex.org/W2047081575","https://openalex.org/W2126122556","https://openalex.org/W2132527237","https://openalex.org/W2146612430","https://openalex.org/W2487898712","https://openalex.org/W2548213636","https://openalex.org/W2784785742","https://openalex.org/W3015575765","https://openalex.org/W3124407081","https://openalex.org/W3158910908","https://openalex.org/W4411535575","https://openalex.org/W4412085024","https://openalex.org/W4416034134","https://openalex.org/W4416288093"],"related_works":["https://openalex.org/W2784785742","https://openalex.org/W6906320597","https://openalex.org/W3152248595","https://openalex.org/W6991209663","https://openalex.org/W4386888700","https://openalex.org/W4417196177","https://openalex.org/W4391133359","https://openalex.org/W4233081311","https://openalex.org/W4400994116","https://openalex.org/W4280514706"],"abstract_inverted_index":{"The":[0,91],"internal-models":[1],"approach":[2],"of":[3,7,19,78,219,232],"the":[4,8,16,126,139,154,166,202,209,229],"Fundamental":[5],"Review":[6],"Trading":[9],"Book":[10],"(FRTB-IMA)":[11],"determines":[12],"market-risk":[13],"capital":[14,41,54,80,131,144,181,233],"at":[15,122,158,195],"aggregate":[17],"level":[18],"a":[20,75,96,103,173],"bank's":[21],"approved":[22],"trading":[23],"desks,":[24],"but":[25],"it":[26,49,161],"does":[27],"not":[28,172,205],"say":[29],"how":[30],"that":[31,65,86],"charge":[32],"should":[33],"be":[34],"attributed":[35],"to":[36,52,81,88,143,146,165,183,235,246],"individual":[37],"trades.":[38],"Risk":[39],"managers,":[40],"planners":[42],"and":[43,48,62,68,124,145,152,169,243],"validators":[44],"often":[45],"need":[46],"one,":[47],"is":[50,93,162,204,239],"hard":[51],"obtain:":[53],"passes":[55],"through":[56,110],"expected-shortfall,":[57],"stress-scaling,":[58],"non-modellable,":[59],"default-risk,":[60],"history":[61],"standardised-approach":[63],"layers":[64],"are":[66],"nonsmooth":[67],"depend":[69],"on":[70],"past":[71,236],"positions.":[72],"We":[73],"present":[74],"formula-complete":[76],"attribution":[77],"FRTB-IMA":[79],"(observation":[82],"date,":[83],"trade)":[84],"positions":[85],"reconciles":[87],"computed":[89],"capital.":[90],"calculation":[92,168],"written":[94],"as":[95],"computational":[97],"graph;":[98],"after":[99],"one":[100,130,220],"forward":[101],"evaluation,":[102],"single":[104],"reverse":[105],"pass":[106],"propagates":[107],"allocation":[108,157],"vectors":[109],"every":[111],"node":[112],"by":[113,191,214],"local":[114],"Euler":[115,155],"rules":[116],"(expected-shortfall":[117],"dual":[118],"weights,":[119],"active-branch":[120],"weights":[121],"floors":[123],"maxima,":[125],"default-quantile":[127],"scenario),":[128],"avoiding":[129],"re-evaluation":[132],"per":[133],"trade.":[134],"Under":[135],"stated":[136],"homogeneity":[137],"assumptions":[138],"ledger":[140],"provably":[141],"sums":[142],"any":[147],"desk":[148],"or":[149],"product":[150],"grouping,":[151],"equals":[153],"(gradient)":[156],"smooth":[159,196,224],"points;":[160],"exact":[163,193,215],"relative":[164,249],"implemented":[167],"this":[170],"rule,":[171],"regulatorily":[174],"prescribed":[175],"attribution.":[176],"Its":[177],"past-date":[178],"entries":[179],"capture":[180],"allocated":[182,234],"earlier":[184],"observation":[185,237],"dates,":[186],"which":[187],"today's-book":[188],"sensitivities":[189],"miss":[190],"an":[192],"identity":[194],"points.":[197],"At":[198],"regulatory":[199],"ties,":[200],"where":[201],"marginal":[203,211],"unique,":[206],"we":[207],"report":[208],"realisable":[210],"vertices,":[212],"identified":[213],"linear-programming":[216],"tests,":[217],"instead":[218],"selection.":[221],"On":[222],"14":[223],"96-trade":[225],"synthetic":[226],"benchmark":[227],"books,":[228],"median":[230],"share":[231],"dates":[238],"61%":[240],"(range":[241],"21%-99%),":[242],"ledgers":[244],"reconcile":[245],"within":[247],"5.6e-16":[248],"error.":[250]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-09-30T00:00:00"}