Use of radial basis functions for meshless numerical solutions applied to financial engineering barrier options

Detalhes bibliográficos
Autor(a) principal: Santos,Gisele Tessari
Data de Publicação: 2009
Outros Autores: Souza,Maurício Cardoso de, Fortes,Mauri
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Pesquisa operacional (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382009000200009
Resumo: A large number of financial engineering problems involve non-linear equations with non-linear or time-dependent boundary conditions. Despite available analytical solutions, many classical and modified forms of the well-known Black-Scholes (BS) equation require fast and accurate numerical solutions. This work introduces the radial basis function (RBF) method as applied to the solution of the BS equation with non-linear boundary conditions, related to path-dependent barrier options. Furthermore, the diffusional method for solving advective-diffusive equations is explored as to its effectiveness to solve BS equations. Cubic and Thin-Plate Spline (TPS) radial basis functions were employed and evaluated as to their effectiveness to solve barrier option problems. The numerical results, when compared against analytical solutions, allow affirming that the RBF method is very accurate and easy to be implemented. When the RBF method is applied, the diffusional method leads to the same results as those obtained from the classical formulation of Black-Scholes equation.
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spelling Use of radial basis functions for meshless numerical solutions applied to financial engineering barrier optionsfinancial engineeringradial basis functionsdiffusional methodbarrier optionsA large number of financial engineering problems involve non-linear equations with non-linear or time-dependent boundary conditions. Despite available analytical solutions, many classical and modified forms of the well-known Black-Scholes (BS) equation require fast and accurate numerical solutions. This work introduces the radial basis function (RBF) method as applied to the solution of the BS equation with non-linear boundary conditions, related to path-dependent barrier options. Furthermore, the diffusional method for solving advective-diffusive equations is explored as to its effectiveness to solve BS equations. Cubic and Thin-Plate Spline (TPS) radial basis functions were employed and evaluated as to their effectiveness to solve barrier option problems. The numerical results, when compared against analytical solutions, allow affirming that the RBF method is very accurate and easy to be implemented. When the RBF method is applied, the diffusional method leads to the same results as those obtained from the classical formulation of Black-Scholes equation.Sociedade Brasileira de Pesquisa Operacional2009-08-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382009000200009Pesquisa Operacional v.29 n.2 2009reponame:Pesquisa operacional (Online)instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)instacron:SOBRAPO10.1590/S0101-74382009000200009info:eu-repo/semantics/openAccessSantos,Gisele TessariSouza,Maurício Cardoso deFortes,Maurieng2009-10-02T00:00:00Zoai:scielo:S0101-74382009000200009Revistahttp://www.scielo.br/popehttps://old.scielo.br/oai/scielo-oai.php||sobrapo@sobrapo.org.br1678-51420101-7438opendoar:2009-10-02T00:00Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)false
dc.title.none.fl_str_mv Use of radial basis functions for meshless numerical solutions applied to financial engineering barrier options
title Use of radial basis functions for meshless numerical solutions applied to financial engineering barrier options
spellingShingle Use of radial basis functions for meshless numerical solutions applied to financial engineering barrier options
Santos,Gisele Tessari
financial engineering
radial basis functions
diffusional method
barrier options
title_short Use of radial basis functions for meshless numerical solutions applied to financial engineering barrier options
title_full Use of radial basis functions for meshless numerical solutions applied to financial engineering barrier options
title_fullStr Use of radial basis functions for meshless numerical solutions applied to financial engineering barrier options
title_full_unstemmed Use of radial basis functions for meshless numerical solutions applied to financial engineering barrier options
title_sort Use of radial basis functions for meshless numerical solutions applied to financial engineering barrier options
author Santos,Gisele Tessari
author_facet Santos,Gisele Tessari
Souza,Maurício Cardoso de
Fortes,Mauri
author_role author
author2 Souza,Maurício Cardoso de
Fortes,Mauri
author2_role author
author
dc.contributor.author.fl_str_mv Santos,Gisele Tessari
Souza,Maurício Cardoso de
Fortes,Mauri
dc.subject.por.fl_str_mv financial engineering
radial basis functions
diffusional method
barrier options
topic financial engineering
radial basis functions
diffusional method
barrier options
description A large number of financial engineering problems involve non-linear equations with non-linear or time-dependent boundary conditions. Despite available analytical solutions, many classical and modified forms of the well-known Black-Scholes (BS) equation require fast and accurate numerical solutions. This work introduces the radial basis function (RBF) method as applied to the solution of the BS equation with non-linear boundary conditions, related to path-dependent barrier options. Furthermore, the diffusional method for solving advective-diffusive equations is explored as to its effectiveness to solve BS equations. Cubic and Thin-Plate Spline (TPS) radial basis functions were employed and evaluated as to their effectiveness to solve barrier option problems. The numerical results, when compared against analytical solutions, allow affirming that the RBF method is very accurate and easy to be implemented. When the RBF method is applied, the diffusional method leads to the same results as those obtained from the classical formulation of Black-Scholes equation.
publishDate 2009
dc.date.none.fl_str_mv 2009-08-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382009000200009
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382009000200009
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0101-74382009000200009
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Pesquisa Operacional
publisher.none.fl_str_mv Sociedade Brasileira de Pesquisa Operacional
dc.source.none.fl_str_mv Pesquisa Operacional v.29 n.2 2009
reponame:Pesquisa operacional (Online)
instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
instacron:SOBRAPO
instname_str Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
instacron_str SOBRAPO
institution SOBRAPO
reponame_str Pesquisa operacional (Online)
collection Pesquisa operacional (Online)
repository.name.fl_str_mv Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
repository.mail.fl_str_mv ||sobrapo@sobrapo.org.br
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