Options valuation by using radial basis function approximation
This paper describes the valuation scheme of European, barrier, and Asian options of single asset by using radial basis function approximation. The option prices are governed with Black–Scholes equation. The equation is discretized with Crank–Nicolson scheme and then, the option price is approximate...
Gespeichert in:
| Veröffentlicht in: | Engineering analysis with boundary elements 2007-10, Vol.31 (10), p.836-843 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 843 |
|---|---|
| container_issue | 10 |
| container_start_page | 836 |
| container_title | Engineering analysis with boundary elements |
| container_volume | 31 |
| creator | Goto, Yumi Fei, Zhai Kan, Shen Kita, Eisuke |
| description | This paper describes the valuation scheme of European, barrier, and Asian options of single asset by using radial basis function approximation. The option prices are governed with Black–Scholes equation. The equation is discretized with Crank–Nicolson scheme and then, the option price is approximated with the radial basis functions with unknown parameters. In the European and the barrier options, the prices are governed with Black–Scholes equation. The governing option of the Asian option, however, is different from them of the others. In that case, one has to adopt the other radial basis functions than that for the original Black–Scholes equation.
Finally, numerical results are compared with theoretical and finite difference solutions in order to confirm the validity of the present formulation. |
| doi_str_mv | 10.1016/j.enganabound.2007.02.001 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1082194867</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0955799707000550</els_id><sourcerecordid>1082194867</sourcerecordid><originalsourceid>FETCH-LOGICAL-c450t-a56eac4b1b2530090463f2861879b7ff82a3b52527d035a40cd567d8902eb47d3</originalsourceid><addsrcrecordid>eNqNkF9LwzAUxYMoOKffoT4IvrTepE3TvAgy_AeDvSj4Fm7TdGR06UzW4b696Sboo0_3wv1xzrmHkGsKGQVa3q0y45bosO4H12QMQGTAMgB6Qia0EnlKpfg4JROQnKdCSnFOLkJYRSAHKCfkfrHZ2t6FZIfdgOOa1PtkCNYtE4-NxS6pMdiQtIPThzNuNr7_susDfEnOWuyCufqZU_L-9Pg2e0nni-fX2cM81QWHbYq8NKiLmtaMR18JRZm3rCpjQlmLtq0Y5jVnnIkGco4F6IaXoqkkMFMXosmn5PaoG70_BxO2am2DNl2HzvRDUBQqRmVRlSKi8ohq34fgTas2Pqb1-wipsTO1Un86U2NnCpgaK5mSmx8bDBq71qPTNvwKSIiRi5GbHTkTf95Z41XQ1jhtGuuN3qqmt_9w-waBa4fY</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1082194867</pqid></control><display><type>article</type><title>Options valuation by using radial basis function approximation</title><source>Access via ScienceDirect (Elsevier)</source><creator>Goto, Yumi ; Fei, Zhai ; Kan, Shen ; Kita, Eisuke</creator><creatorcontrib>Goto, Yumi ; Fei, Zhai ; Kan, Shen ; Kita, Eisuke</creatorcontrib><description>This paper describes the valuation scheme of European, barrier, and Asian options of single asset by using radial basis function approximation. The option prices are governed with Black–Scholes equation. The equation is discretized with Crank–Nicolson scheme and then, the option price is approximated with the radial basis functions with unknown parameters. In the European and the barrier options, the prices are governed with Black–Scholes equation. The governing option of the Asian option, however, is different from them of the others. In that case, one has to adopt the other radial basis functions than that for the original Black–Scholes equation.
Finally, numerical results are compared with theoretical and finite difference solutions in order to confirm the validity of the present formulation.</description><identifier>ISSN: 0955-7997</identifier><identifier>EISSN: 1873-197X</identifier><identifier>DOI: 10.1016/j.enganabound.2007.02.001</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Applied sciences ; Approximation ; Asian ; Asian option ; Barrier option ; Barriers ; Black-Scholes equation ; Boundary element method ; Decision theory. Utility theory ; European option ; Exact sciences and technology ; Mathematical analysis ; Mathematical models ; Operational research and scientific management ; Operational research. Management science ; Option Contract ; Radial basis function</subject><ispartof>Engineering analysis with boundary elements, 2007-10, Vol.31 (10), p.836-843</ispartof><rights>2007 Elsevier Ltd</rights><rights>2007 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c450t-a56eac4b1b2530090463f2861879b7ff82a3b52527d035a40cd567d8902eb47d3</citedby><cites>FETCH-LOGICAL-c450t-a56eac4b1b2530090463f2861879b7ff82a3b52527d035a40cd567d8902eb47d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.enganabound.2007.02.001$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=19061841$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Goto, Yumi</creatorcontrib><creatorcontrib>Fei, Zhai</creatorcontrib><creatorcontrib>Kan, Shen</creatorcontrib><creatorcontrib>Kita, Eisuke</creatorcontrib><title>Options valuation by using radial basis function approximation</title><title>Engineering analysis with boundary elements</title><description>This paper describes the valuation scheme of European, barrier, and Asian options of single asset by using radial basis function approximation. The option prices are governed with Black–Scholes equation. The equation is discretized with Crank–Nicolson scheme and then, the option price is approximated with the radial basis functions with unknown parameters. In the European and the barrier options, the prices are governed with Black–Scholes equation. The governing option of the Asian option, however, is different from them of the others. In that case, one has to adopt the other radial basis functions than that for the original Black–Scholes equation.
Finally, numerical results are compared with theoretical and finite difference solutions in order to confirm the validity of the present formulation.</description><subject>Applied sciences</subject><subject>Approximation</subject><subject>Asian</subject><subject>Asian option</subject><subject>Barrier option</subject><subject>Barriers</subject><subject>Black-Scholes equation</subject><subject>Boundary element method</subject><subject>Decision theory. Utility theory</subject><subject>European option</subject><subject>Exact sciences and technology</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Option Contract</subject><subject>Radial basis function</subject><issn>0955-7997</issn><issn>1873-197X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNqNkF9LwzAUxYMoOKffoT4IvrTepE3TvAgy_AeDvSj4Fm7TdGR06UzW4b696Sboo0_3wv1xzrmHkGsKGQVa3q0y45bosO4H12QMQGTAMgB6Qia0EnlKpfg4JROQnKdCSnFOLkJYRSAHKCfkfrHZ2t6FZIfdgOOa1PtkCNYtE4-NxS6pMdiQtIPThzNuNr7_susDfEnOWuyCufqZU_L-9Pg2e0nni-fX2cM81QWHbYq8NKiLmtaMR18JRZm3rCpjQlmLtq0Y5jVnnIkGco4F6IaXoqkkMFMXosmn5PaoG70_BxO2am2DNl2HzvRDUBQqRmVRlSKi8ohq34fgTas2Pqb1-wipsTO1Un86U2NnCpgaK5mSmx8bDBq71qPTNvwKSIiRi5GbHTkTf95Z41XQ1jhtGuuN3qqmt_9w-waBa4fY</recordid><startdate>20071001</startdate><enddate>20071001</enddate><creator>Goto, Yumi</creator><creator>Fei, Zhai</creator><creator>Kan, Shen</creator><creator>Kita, Eisuke</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20071001</creationdate><title>Options valuation by using radial basis function approximation</title><author>Goto, Yumi ; Fei, Zhai ; Kan, Shen ; Kita, Eisuke</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c450t-a56eac4b1b2530090463f2861879b7ff82a3b52527d035a40cd567d8902eb47d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Applied sciences</topic><topic>Approximation</topic><topic>Asian</topic><topic>Asian option</topic><topic>Barrier option</topic><topic>Barriers</topic><topic>Black-Scholes equation</topic><topic>Boundary element method</topic><topic>Decision theory. Utility theory</topic><topic>European option</topic><topic>Exact sciences and technology</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Operational research and scientific management</topic><topic>Operational research. Management science</topic><topic>Option Contract</topic><topic>Radial basis function</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Goto, Yumi</creatorcontrib><creatorcontrib>Fei, Zhai</creatorcontrib><creatorcontrib>Kan, Shen</creatorcontrib><creatorcontrib>Kita, Eisuke</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Engineering analysis with boundary elements</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Goto, Yumi</au><au>Fei, Zhai</au><au>Kan, Shen</au><au>Kita, Eisuke</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Options valuation by using radial basis function approximation</atitle><jtitle>Engineering analysis with boundary elements</jtitle><date>2007-10-01</date><risdate>2007</risdate><volume>31</volume><issue>10</issue><spage>836</spage><epage>843</epage><pages>836-843</pages><issn>0955-7997</issn><eissn>1873-197X</eissn><abstract>This paper describes the valuation scheme of European, barrier, and Asian options of single asset by using radial basis function approximation. The option prices are governed with Black–Scholes equation. The equation is discretized with Crank–Nicolson scheme and then, the option price is approximated with the radial basis functions with unknown parameters. In the European and the barrier options, the prices are governed with Black–Scholes equation. The governing option of the Asian option, however, is different from them of the others. In that case, one has to adopt the other radial basis functions than that for the original Black–Scholes equation.
Finally, numerical results are compared with theoretical and finite difference solutions in order to confirm the validity of the present formulation.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.enganabound.2007.02.001</doi><tpages>8</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0955-7997 |
| ispartof | Engineering analysis with boundary elements, 2007-10, Vol.31 (10), p.836-843 |
| issn | 0955-7997 1873-197X |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1082194867 |
| source | Access via ScienceDirect (Elsevier) |
| subjects | Applied sciences Approximation Asian Asian option Barrier option Barriers Black-Scholes equation Boundary element method Decision theory. Utility theory European option Exact sciences and technology Mathematical analysis Mathematical models Operational research and scientific management Operational research. Management science Option Contract Radial basis function |
| title | Options valuation by using radial basis function approximation |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T10%3A50%3A06IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Options%20valuation%20by%20using%20radial%20basis%20function%20approximation&rft.jtitle=Engineering%20analysis%20with%20boundary%20elements&rft.au=Goto,%20Yumi&rft.date=2007-10-01&rft.volume=31&rft.issue=10&rft.spage=836&rft.epage=843&rft.pages=836-843&rft.issn=0955-7997&rft.eissn=1873-197X&rft_id=info:doi/10.1016/j.enganabound.2007.02.001&rft_dat=%3Cproquest_cross%3E1082194867%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1082194867&rft_id=info:pmid/&rft_els_id=S0955799707000550&rfr_iscdi=true |