{"id":"https://openalex.org/W4382242593","doi":"https://doi.org/10.1007/s11075-023-01563-4","title":"Parameter estimation for time-fractional Black-Scholes equation with S &amp;P 500 index option","display_name":"Parameter estimation for time-fractional Black-Scholes equation with S &amp;P 500 index option","publication_year":2023,"publication_date":"2023-06-27","ids":{"openalex":"https://openalex.org/W4382242593","doi":"https://doi.org/10.1007/s11075-023-01563-4"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-023-01563-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-023-01563-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-023-01563-4.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11075-023-01563-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012462515","display_name":"Xingyu An","orcid":null},"institutions":[{"id":"https://openalex.org/I160993911","display_name":"Queensland University of Technology","ror":"https://ror.org/03pnv4752","country_code":"AU","type":"education","lineage":["https://openalex.org/I160993911"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Xingyu An","raw_affiliation_strings":["School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia","institution_ids":["https://openalex.org/I160993911"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101920263","display_name":"Qingxia Wang","orcid":"https://orcid.org/0000-0003-0626-1538"},"institutions":[{"id":"https://openalex.org/I160993911","display_name":"Queensland University of Technology","ror":"https://ror.org/03pnv4752","country_code":"AU","type":"education","lineage":["https://openalex.org/I160993911"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Qingxia Wang","raw_affiliation_strings":["School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia","institution_ids":["https://openalex.org/I160993911"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073778062","display_name":"Fawang Liu","orcid":"https://orcid.org/0000-0003-1034-2349"},"institutions":[{"id":"https://openalex.org/I160993911","display_name":"Queensland University of Technology","ror":"https://ror.org/03pnv4752","country_code":"AU","type":"education","lineage":["https://openalex.org/I160993911"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Fawang Liu","raw_affiliation_strings":["School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia"],"raw_orcid":"https://orcid.org/0000-0003-1034-2349","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia","institution_ids":["https://openalex.org/I160993911"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061268303","display_name":"Vo Anh","orcid":"https://orcid.org/0000-0003-2463-2099"},"institutions":[{"id":"https://openalex.org/I57093077","display_name":"Swinburne University of Technology","ror":"https://ror.org/031rekg67","country_code":"AU","type":"education","lineage":["https://openalex.org/I57093077"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Vo V. Anh","raw_affiliation_strings":["Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne, Australia","institution_ids":["https://openalex.org/I57093077"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007130769","display_name":"Ian Turner","orcid":"https://orcid.org/0000-0003-2794-3968"},"institutions":[{"id":"https://openalex.org/I160993911","display_name":"Queensland University of Technology","ror":"https://ror.org/03pnv4752","country_code":"AU","type":"education","lineage":["https://openalex.org/I160993911"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Ian W. Turner","raw_affiliation_strings":["School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia","institution_ids":["https://openalex.org/I160993911"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5012462515"],"corresponding_institution_ids":["https://openalex.org/I160993911"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":3.3231,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.92372716,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"95","issue":"1","first_page":"1","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9987000226974487,"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":0.9987000226974487,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10047","display_name":"Financial Markets and Investment Strategies","score":0.9724000096321106,"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/algorithm","display_name":"Algorithm","score":0.6048653721809387},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48411428928375244},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3380984663963318}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6048653721809387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48411428928375244},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3380984663963318}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-023-01563-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-023-01563-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-023-01563-4.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11075-023-01563-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-023-01563-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-023-01563-4.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.41999998688697815}],"awards":[{"id":"https://openalex.org/G1408897352","display_name":null,"funder_award_id":"12120101001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3378525746","display_name":null,"funder_award_id":"201907510005","funder_id":"https://openalex.org/F4320326186","funder_display_name":"China National Textile and Apparel Council"},{"id":"https://openalex.org/G6925223386","display_name":null,"funder_award_id":"DP190101889","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G7923246479","display_name":null,"funder_award_id":"DP180103858 and DP190101889","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G882678982","display_name":null,"funder_award_id":"12120101001","funder_id":"https://openalex.org/F4320322163","funder_display_name":"Natural Science Foundation of Hebei Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322163","display_name":"Natural Science Foundation of Hebei Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"},{"id":"https://openalex.org/F4320326186","display_name":"China National Textile and Apparel Council","ror":null},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4382242593.pdf"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W1562837474","https://openalex.org/W1902909323","https://openalex.org/W1969312973","https://openalex.org/W1972754929","https://openalex.org/W1983618156","https://openalex.org/W2001602513","https://openalex.org/W2006884639","https://openalex.org/W2010925068","https://openalex.org/W2012698396","https://openalex.org/W2016680653","https://openalex.org/W2022685032","https://openalex.org/W2039076597","https://openalex.org/W2041015802","https://openalex.org/W2062266804","https://openalex.org/W2065232540","https://openalex.org/W2105973145","https://openalex.org/W2118371342","https://openalex.org/W2133672408","https://openalex.org/W2143004014","https://openalex.org/W2143623732","https://openalex.org/W2148080284","https://openalex.org/W2157834649","https://openalex.org/W2164822588","https://openalex.org/W2171074980","https://openalex.org/W2293176873","https://openalex.org/W2315653911","https://openalex.org/W2511264644","https://openalex.org/W2513457959","https://openalex.org/W2578293889","https://openalex.org/W2623729930","https://openalex.org/W2779454589","https://openalex.org/W2781766156","https://openalex.org/W2893426469","https://openalex.org/W2914183047","https://openalex.org/W2976709899","https://openalex.org/W2978166210","https://openalex.org/W2988207590","https://openalex.org/W2995887867","https://openalex.org/W3005491224","https://openalex.org/W3032001790","https://openalex.org/W3119129124","https://openalex.org/W4231057775","https://openalex.org/W4231591459","https://openalex.org/W4242694222","https://openalex.org/W4283658368"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"aims":[3],"to":[4,75,99],"estimate":[5],"the":[6,9,17,23,28,35,60,77,82,101,120,125,142,145,152,163,169,173,200,213,221,249,253],"parameters":[7],"of":[8,27,81,119,128,154,167,206],"time-fractional":[10],"Black-Scholes":[11],"(TFBS)":[12],"partial":[13],"differential":[14],"equation":[15],"with":[16,45,212],"Caputo":[18],"fractional":[19,102],"derivative":[20],"by":[21,40],"using":[22],"real":[24,208],"option":[25,209],"prices":[26],"S":[29],"&amp;P":[30],"500":[31],"index":[32],"options.":[33],"First,":[34],"numerical":[36],"solution":[37],"is":[38,203],"obtained":[39],"developing":[41],"a":[42,88,191],"high-order":[43],"scheme":[44],"order":[46,74,103],"(":[47],"$$3-\\alpha":[48],"$$":[49,105,114,130,156,182,235,242],"<mml:math":[50,106,115,131,157,183,236,243],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[51,107,116,132,158,184,237,244],"<mml:mrow>":[52],"<mml:mn>3</mml:mn>":[53],"<mml:mo>-</mml:mo>":[54],"<mml:mi>\u03b1</mml:mi>":[55,108,133,159,185,238],"</mml:mrow>":[56],"</mml:math>":[57,109,118,134,160,186,239,246],")":[58],"for":[59,195,217,265],"time":[61],"discretisation.":[62],"Some":[63],"theoretical":[64],"analyses":[65],"such":[66,140],"as":[67,141,190],"stability":[68],"and":[69,79,94,110,123,144,161,172,199,228,240,252],"convergence":[70],"are":[71],"presented":[72],"in":[73,256],"verify":[76],"efficiency":[78],"accuracy":[80],"proposed":[83],"scheme.":[84],"Secondly,":[85],"we":[86,226],"employ":[87],"modified":[89],"hybrid":[90],"Nelder-Mead":[91],"simplex":[92],"search":[93],"particle":[95],"swarm":[96],"optimization":[97],"(MH-NMSS-PSO)":[98],"identify":[100],"$$\\alpha":[104,129,155,181,234],"implied":[111],"volatility":[112],"$$\\sigma":[113,241],"<mml:mi>\u03c3</mml:mi>":[117,245],"TFBS":[121,170,201,250],"equation,":[122],"explore":[124],"financial":[126,148,197],"meanings":[127],"under":[135],"extreme":[136],"stock":[137],"market":[138,192],"conditions":[139],"Covid-19":[143],"2008":[146],"global":[147],"crisis.":[149],"We":[150],"analyse":[151],"values":[153],"compare":[162],"mean":[164],"squared":[165],"errors":[166],"both":[168,248],"model":[171,202,251,255],"BS":[174,214,254],"model.":[175],"Our":[176],"empirical":[177],"results":[178],"show":[179],"that":[180],"may":[187],"be":[188,261],"regarded":[189],"fluctuation":[193],"indicator":[194],"classifying":[196],"environments,":[198],"more":[204],"capable":[205],"fitting":[207],"data":[210],"compared":[211],"model,":[215],"especially":[216],"put":[218],"options":[219],"during":[220],"economic":[222],"downturn.":[223],"In":[224],"addition,":[225],"find":[227],"discuss":[229],"an":[230,262],"interesting":[231],"relation":[232],"between":[233],"from":[247],"three":[257],"expressions,":[258],"which":[259],"could":[260],"open":[263],"problem":[264],"further":[266],"research.":[267]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
