Pricing american call option by the Black-Scholes equation with a nonlinear volatility function

Detalhes bibliográficos
Autor(a) principal: Grossinho, Maria do Rosário
Data de Publicação: 2017
Outros Autores: Kord, Yaser Faghan, Ševčovič, Daniel
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.5/15991
Resumo: In this paper we analyze a nonlinear Black-Scholes equation for pricing American style call option in which the volatility may depend on the underlying asset price and the Gamma of the option. We study the generalized Black-Scholes equation by means of transformation of the free boundary problem (variational inequalities) into the so-called Gamma equation for the new variable H = S@2SV . Moreover, we reformulate our new problem with PSOR method and construct an effective numerical scheme for discretization of the Gamma equation. Finally,we solve numerically our nonlinear complementarity problem applying PSOR method.
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spelling Pricing american call option by the Black-Scholes equation with a nonlinear volatility functionAmerican option pricingnonlinear Black-Scholes equationvariable transaction costsPSOR methodIn this paper we analyze a nonlinear Black-Scholes equation for pricing American style call option in which the volatility may depend on the underlying asset price and the Gamma of the option. We study the generalized Black-Scholes equation by means of transformation of the free boundary problem (variational inequalities) into the so-called Gamma equation for the new variable H = S@2SV . Moreover, we reformulate our new problem with PSOR method and construct an effective numerical scheme for discretization of the Gamma equation. Finally,we solve numerically our nonlinear complementarity problem applying PSOR method.ISEG - REM - Research in Economics and MathematicsRepositório da Universidade de LisboaGrossinho, Maria do RosárioKord, Yaser FaghanŠevčovič, Daniel2018-09-27T15:00:19Z2017-122017-12-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/15991engGrossinho, Maria do Rosário, Yaser Faghan Kord e Daniel Ševčovič (2017). "Pricing american call option by the Black-Scholes equation with a nonlinear volatility function". Instituto Superior de Economia e Gestão – REM Working paper nº 018 - 20172184-108Xinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-03-06T14:45:51Zoai:www.repository.utl.pt:10400.5/15991Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:01:30.362359Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Pricing american call option by the Black-Scholes equation with a nonlinear volatility function
title Pricing american call option by the Black-Scholes equation with a nonlinear volatility function
spellingShingle Pricing american call option by the Black-Scholes equation with a nonlinear volatility function
Grossinho, Maria do Rosário
American option pricing
nonlinear Black-Scholes equation
variable transaction costs
PSOR method
title_short Pricing american call option by the Black-Scholes equation with a nonlinear volatility function
title_full Pricing american call option by the Black-Scholes equation with a nonlinear volatility function
title_fullStr Pricing american call option by the Black-Scholes equation with a nonlinear volatility function
title_full_unstemmed Pricing american call option by the Black-Scholes equation with a nonlinear volatility function
title_sort Pricing american call option by the Black-Scholes equation with a nonlinear volatility function
author Grossinho, Maria do Rosário
author_facet Grossinho, Maria do Rosário
Kord, Yaser Faghan
Ševčovič, Daniel
author_role author
author2 Kord, Yaser Faghan
Ševčovič, Daniel
author2_role author
author
dc.contributor.none.fl_str_mv Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Grossinho, Maria do Rosário
Kord, Yaser Faghan
Ševčovič, Daniel
dc.subject.por.fl_str_mv American option pricing
nonlinear Black-Scholes equation
variable transaction costs
PSOR method
topic American option pricing
nonlinear Black-Scholes equation
variable transaction costs
PSOR method
description In this paper we analyze a nonlinear Black-Scholes equation for pricing American style call option in which the volatility may depend on the underlying asset price and the Gamma of the option. We study the generalized Black-Scholes equation by means of transformation of the free boundary problem (variational inequalities) into the so-called Gamma equation for the new variable H = S@2SV . Moreover, we reformulate our new problem with PSOR method and construct an effective numerical scheme for discretization of the Gamma equation. Finally,we solve numerically our nonlinear complementarity problem applying PSOR method.
publishDate 2017
dc.date.none.fl_str_mv 2017-12
2017-12-01T00:00:00Z
2018-09-27T15:00:19Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.5/15991
url http://hdl.handle.net/10400.5/15991
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Grossinho, Maria do Rosário, Yaser Faghan Kord e Daniel Ševčovič (2017). "Pricing american call option by the Black-Scholes equation with a nonlinear volatility function". Instituto Superior de Economia e Gestão – REM Working paper nº 018 - 2017
2184-108X
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv ISEG - REM - Research in Economics and Mathematics
publisher.none.fl_str_mv ISEG - REM - Research in Economics and Mathematics
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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