Recovering the local volatility in Black-Scholes model by numerical differentiation
In this article, a numerical method for recovering the local volatility in Black-Scholes model is proposed based on the Dupire formula in which the numerical derivatives are used. By Tikhonov regularization, a new numerical differentiation method in two-dimensional (2-D) case is presented. The conve...
Saved in:
| Published in | Applicable analysis Vol. 85; no. 6-7; pp. 681 - 692 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis Group
01.06.2006
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0003-6811 1563-504X |
| DOI | 10.1080/00036810500475025 |
Cover
| Abstract | In this article, a numerical method for recovering the local volatility in Black-Scholes model is proposed based on the Dupire formula in which the numerical derivatives are used. By Tikhonov regularization, a new numerical differentiation method in two-dimensional (2-D) case is presented. The convergent analysis and numerical examples are also given. It shows that our method is efficient and stable. |
|---|---|
| AbstractList | In this article, a numerical method for recovering the local volatility in Black-Scholes model is proposed based on the Dupire formula in which the numerical derivatives are used. By Tikhonov regularization, a new numerical differentiation method in two-dimensional (2-D) case is presented. The convergent analysis and numerical examples are also given. It shows that our method is efficient and stable. |
| Author | Yin, Binbin Ye, Yuzhang |
| Author_xml | – sequence: 1 givenname: Binbin surname: Yin fullname: Yin, Binbin email: 022018025@fudan.edu.cn, ybb_12@yahoo.com.cn organization: Institute of Mathematics , School of Mathematical Sciences , Fudan University – sequence: 2 givenname: Yuzhang surname: Ye fullname: Ye, Yuzhang organization: Institute of Mathematics , School of Mathematical Sciences , Fudan University |
| BookMark | eNqN0D1PJDEMBuAIcRILdz_guqnoBuxkPiUaQHxJSEgHxXVRNuNAIJNAkl3Yf3-zLBVI6CoXfh9b9i7b9sETY78RDhA6OAQA0XQINUDV1sDrLTbDuhFlDdXfbTZb98spgDtsN6VHAORd3czY7R_SYUnR-vsiP1DhglauWAansnU2rwrrixOn9FN5qx-Co1SMYSBXzFeFX4yTW8cHawxF8tlOKvif7IdRLtGvj7rH7s7P7k4vy-ubi6vT4-tS857nUgFhRa0B3fQt9vNOU68bUaNpTNuZRgguBk5UtTiHzmBb9xo5wtBBpXgn9tj-ZuxzDC8LSlmONmlyTnkKiyR5j21VVTgFcRPUMaQUycjnaEcVVxJBrr8nv3xvMu0no21-vy5HZd238mgjrTchjuo1RDfIrFYuRBOV1zZJ8R-Lv-FflMxvWfwDbqCZ4A |
| CitedBy_id | crossref_primary_10_1016_j_cam_2025_116619 crossref_primary_10_1016_j_amc_2020_125811 crossref_primary_10_1016_j_apnum_2024_12_011 crossref_primary_10_1016_j_amc_2018_04_005 crossref_primary_10_1080_17415977_2019_1661410 crossref_primary_10_1016_j_amc_2023_127856 crossref_primary_10_23939_ujit2023_01_025 crossref_primary_10_1029_2019JD030754 crossref_primary_10_1016_j_apnum_2020_08_016 crossref_primary_10_36930_40320510 |
| Cites_doi | 10.1088/1469-7688/3/6/304 10.1007/978-3-642-61798-0 10.1088/0266-5611/21/2/013 10.1088/0266-5611/13/5/001 10.1016/j.jmaa.2005.03.025 10.1088/0266-5611/15/3/201 10.2307/2329207 10.1088/0266-5611/17/1/311 |
| ContentType | Journal Article |
| Copyright | Copyright Taylor & Francis Group, LLC 2006 |
| Copyright_xml | – notice: Copyright Taylor & Francis Group, LLC 2006 |
| DBID | AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| DOI | 10.1080/00036810500475025 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISSN | 1563-504X |
| EndPage | 692 |
| ExternalDocumentID | 10_1080_00036810500475025 147485 |
| GroupedDBID | --Z -~X .7F .QJ 0BK 0R~ 23M 2DF 30N 4.4 5GY 5VS AAENE AAGDL AAHIA AAJMT AALDU AAMIU AAPUL AAQRR ABCCY ABFIM ABHAV ABJNI ABLIJ ABPAQ ABPEM ABTAI ABUFD ABXUL ABXYU ACAGQ ACGEJ ACGFS ACGOD ACIWK ACTIO ADCVX ADGTB ADXPE AEISY AENEX AEOZL AEPSL AEYOC AFKVX AFRVT AGDLA AGMYJ AGROQ AHDZW AHMOU AIJEM AIYEW AJWEG AKBVH AKOOK ALCKM ALMA_UNASSIGNED_HOLDINGS ALQZU AMEWO AQRUH AQTUD AVBZW AWYRJ BLEHA CAG CCCUG CE4 COF CRFIH CS3 DGEBU DKSSO DMQIW EBS EJD E~A E~B F5P GTTXZ H13 HZ~ H~P IPNFZ J.P KYCEM M4Z NA5 NY~ O9- P2P PQQKQ QCRFL RIG RNANH ROSJB RTWRZ S-T SNACF TASJS TBQAZ TDBHL TEJ TFL TFT TFW TN5 TOXWX TTHFI TUROJ TWF UPT UT5 UU3 WH7 ZGOLN ~S~ 07G 1TA 6TJ AAIKQ AAKBW AAYXX ACGEE ACTCW AEUMN AFFNX AGCQS AGLEN AMVHM AMXXU BCCOT BPLKW C06 CITATION DWIFK HF~ H~9 IVXBP LJTGL NUSFT TAQ TFMCV UB9 UU8 V3K V4Q ZY4 7SC 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c292t-a0e14e7f0c69719b8ce9c6351f6f78f63323d2ee471b08f1759c1210d804a283 |
| ISSN | 0003-6811 |
| IngestDate | Thu Oct 02 06:57:51 EDT 2025 Thu Apr 24 22:57:54 EDT 2025 Wed Oct 01 03:24:33 EDT 2025 Mon May 13 12:10:01 EDT 2019 Mon Oct 20 23:44:46 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 6-7 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c292t-a0e14e7f0c69719b8ce9c6351f6f78f63323d2ee471b08f1759c1210d804a283 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 29174441 |
| PQPubID | 23500 |
| PageCount | 12 |
| ParticipantIDs | informaworld_taylorfrancis_310_1080_00036810500475025 crossref_primary_10_1080_00036810500475025 proquest_miscellaneous_29174441 crossref_citationtrail_10_1080_00036810500475025 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 20060601 |
| PublicationDateYYYYMMDD | 2006-06-01 |
| PublicationDate_xml | – month: 06 year: 2006 text: 20060601 day: 01 |
| PublicationDecade | 2000 |
| PublicationTitle | Applicable analysis |
| PublicationYear | 2006 |
| Publisher | Taylor & Francis Group |
| Publisher_xml | – name: Taylor & Francis Group |
| References | Gilbarg D (CIT0005) 2001 CIT0011 Wilmottm P (CIT0012) 1998 Adams RA (CIT0001) 1975 Dupire B (CIT0004) 1994; 7 Tikhonov AN (CIT0013) 1977 Lagnado R (CIT0008) 1996; 1 CIT0003 CIT0002 CIT0007 CIT0006 CIT0009 Wang YB (CIT0010); 312 |
| References_xml | – volume: 1 start-page: 13 year: 1996 ident: CIT0008 publication-title: Journal of Computational Finance – volume-title: Sobolev Spaces year: 1975 ident: CIT0001 – ident: CIT0006 doi: 10.1088/1469-7688/3/6/304 – volume-title: Derivatives, The Theory and Practice of Financial Engineering year: 1998 ident: CIT0012 – volume: 7 start-page: 32 year: 1994 ident: CIT0004 publication-title: Risk – volume-title: Solutions of Ill-posed Problems year: 1977 ident: CIT0013 – volume-title: Elliptic Partial Differential Equations of Second Order year: 2001 ident: CIT0005 doi: 10.1007/978-3-642-61798-0 – ident: CIT0011 doi: 10.1088/0266-5611/21/2/013 – ident: CIT0002 doi: 10.1088/0266-5611/13/5/001 – volume: 312 start-page: 121 ident: CIT0010 publication-title: Journal of Mathematical Analysis and Applications doi: 10.1016/j.jmaa.2005.03.025 – ident: CIT0003 doi: 10.1088/0266-5611/15/3/201 – ident: CIT0009 doi: 10.2307/2329207 – ident: CIT0007 doi: 10.1088/0266-5611/17/1/311 |
| SSID | ssj0012856 |
| Score | 1.6786637 |
| Snippet | In this article, a numerical method for recovering the local volatility in Black-Scholes model is proposed based on the Dupire formula in which the numerical... |
| SourceID | proquest crossref informaworld |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 681 |
| SubjectTerms | AMS Subject Classifications: 65M32 Black-Scholes model Dupire formula Local volatility Numerical differentiation Tikhonov regularization |
| Title | Recovering the local volatility in Black-Scholes model by numerical differentiation |
| URI | https://www.tandfonline.com/doi/abs/10.1080/00036810500475025 https://www.proquest.com/docview/29174441 |
| Volume | 85 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVLSH databaseName: aylor and Francis Online customDbUrl: mediaType: online eissn: 1563-504X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0012856 issn: 0003-6811 databaseCode: AHDZW dateStart: 19970201 isFulltext: true providerName: Library Specific Holdings – providerCode: PRVAWR databaseName: Taylor & Francis Science and Technology Library-DRAA customDbUrl: eissn: 1563-504X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0012856 issn: 0003-6811 databaseCode: 30N dateStart: 19970101 isFulltext: true titleUrlDefault: http://www.tandfonline.com/page/title-lists providerName: Taylor & Francis |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3LbtQwFLWgbGABbQExfVAvuqIycuLEsZeoAlVI7WoqtasocWxppFGKmExVuuIf-EO-hOtHPDOZMqJsopGdeB73zH3Z91yEjouk0iZvGgLWOSNZqjQRYEiJNFxbRikpK1vgfH7Bzy6zr1f51aL2xFWXdPVHdf9gXcn_SBXGQK62SvYRko2LwgC8BvnCFSQM13-SsY0dbx2XoPMfnV06AX0D0867nrQnLkHXn2hglnNzqkP_G-t5tnO_YzONnVK6JVn17LR-k9vWWFWBwyQqi9DufdLWkwiza5ckvZ7f22T0MK3QH3-KqpIRLoIm1EE7ckZy6o9U9urTd9wJMOGkWNKGXCRLhpX7pndrOjsecmSWGy23_JU59dXQq_zYA7sVTxMmkeZ0sMRT9CwFZW87ejB6ETeXUuGa-sZv2G92W8r14RIr7soKme2a8XYeyXgbvQyhBP7kcbGDnuh2F70KYQUOSnu2i16cR2re2Wt0uQANhmHsQIMXoMGTFjvQ_P75K8AFO7jg-geOcMEDuLxB4y-fx6dnJPTWICqVaUcqqpNMF4YqLotE1kJpqcD5TAw3hTCcsZQ1qdbgu9RUGHAypbJcc42gWQUu6Vu01d60-h3CdpLnDYQNSmYwKYy2NIlZVTGYadgI0f4XLFXgnbftT6blX-U2Qh_iI9886cqmm-myWMrOZbqMb0uzfnvZ3XUjlG94hG14q6Ne5CVoYbu1VrX6Zj4rUwmRPUQWe4_55Pvo-eKfd4C2uu9zfQguble_d4D9A2T4m-Q |
| linkProvider | Taylor & Francis |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT8MwDLZgHIAD4ynGazlwQgr0veaIENN4bBeGtFvVpomEmDpEOwT8euy0nXhph11rJ30kjr_Y6WeA044dK-2nKUfv7HHPkYqH6Ei50IEiRikhYvrBuT8Ieo_e7cgfVQG3vDpWSXtoXRJFmLWajJuC0fWRuAvDohIiMiCuQx-99jKs-Aj0qYKBaw1mWQQnNNVbSZ2jvl1nNf_r4odf-sFa-meVNq6n24SofujyxMnz-bRIzuXnLz7Hxd9qEzYqVMouy2m0BUsq24ZmhVBZZf_5Nqz3Zyyv-Q480N71zXAZMrzMjF9kuN6hnNA9e8qYCRBy4vocq5yZujss-WDZtMwUjVldoaUo58guDLvXw6ser4o0cOkIp-CxpWxPdbQlA9GxRRJKJSSiGFsHuhPqwHUdN3WUQieYWKFGtCIkkZaloeXFiG32oJFNMrUPjISBnyL-lMJDYagV8e15ceyiJHVbYNUjFMmKwJzqaIwje8Zz-usLtuBs1uSlZO-Yp2x9H_aoMCETXdY3-aseFe9FC_w5Tdw5t2rXUypCc6YcTZypyTSPHNw-ewhRDxbsuQ2rvWH_Prq_GdwdwloZMKKY0RE0itepOkYIVSQnxk6-AIE4DQc |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT8MwDLZgSAgOPAaI8VoOnJACfa85ImAarwmJIXGr2jSREFM30Q4Bvx47bSde2oFr7aRqE8dfYuczwGHHjpX205Sjd_a450jFQ3SkXOhAEaOUEDFdcL7tB70H7-rRf6xyc_IqrZL20LokijBrNRn3ONV1RtyJIVEJERgQ1aGPTnseFgKKiNENDqs_DSI4oSneSuoc9e06qPlXF9_c0jfS0l-LtPE83dWyvGpuCAsp4eT5eFIkx_LjB53jvz9qDVYqTMpOy0m0DnMqa8JqhU9ZZf15E5Zvpxyv-Qbc08711TAZMnzMjFdkuNqhnLA9e8qYOR7kxPQ5VDkzVXdY8s6ySRknGrK6PktRzpBNGHQvBmc9XpVo4NIRTsFjS9me6mhLBqJjiySUSkjEMLYOdCfUges6buoohS4wsUKNWEVIoixLQ8uLEdlsQSMbZWobGAkDP0X0KYWHwlArYtvz4thFSeq2wKoHKJIVfTlV0RhG9pTl9McfbMHRtMm45O6YpWx9HfWoMAcmuqxu8ls9Kt6KFvgzmrgzXtWuZ1SExkwRmjhTo0keObh59hCg7vyz5zYs3p13o5vL_vUuLJWnRXRgtAeN4mWi9hE_FcmBsZJPGmkLqw |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Recovering+the+local+volatility+in+Black%E2%80%93Scholes+model+by+numerical+differentiation&rft.jtitle=Applicable+analysis&rft.au=Yin%2C+Binbin&rft.au=Ye%2C+Yuzhang&rft.date=2006-06-01&rft.issn=0003-6811&rft.eissn=1563-504X&rft.volume=85&rft.issue=6-7&rft.spage=681&rft.epage=692&rft_id=info:doi/10.1080%2F00036810500475025&rft.externalDBID=n%2Fa&rft.externalDocID=10_1080_00036810500475025 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0003-6811&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0003-6811&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0003-6811&client=summon |