Pricing perpetual put options 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/10400.5/16343
Resumo: We investigate qualitative and quantitative behavior of a solution to the problem of pricing American style of perpetual put options. We assume the option price is a solution to a stationary generalized Black-Scholes equation in which the volatility may depend on the second derivative of the option price itself. We prove existence and uniqueness of a solution to the free boundary problem. We derive a single implicit equation for the free boundary position and the closed form formula for the option price. It is a generalization of the well-known explicit closed form solution derived by Merton for the case of a constant volatility. We also present results of numerical computations of the free boundary position, option price and their dependence on model parameters.
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spelling Pricing perpetual put options by the Black-Scholes equation with a nonlinear volatility functionOption pricingnonlinear Black-Scholes equationperpetual American put optionearly exercise boundaryWe investigate qualitative and quantitative behavior of a solution to the problem of pricing American style of perpetual put options. We assume the option price is a solution to a stationary generalized Black-Scholes equation in which the volatility may depend on the second derivative of the option price itself. We prove existence and uniqueness of a solution to the free boundary problem. We derive a single implicit equation for the free boundary position and the closed form formula for the option price. It is a generalization of the well-known explicit closed form solution derived by Merton for the case of a constant volatility. We also present results of numerical computations of the free boundary position, option price and their dependence on model parameters.ISEG - REM - Research in Economics and MathematicsRepositório da Universidade de LisboaGrossinho, Maria do RosárioKord, Yaser FaghanŠevčovič, Daniel2018-11-14T14:26:40Z2017-122017-12-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/16343engGrossinho, Maria do Rosário, Yaser Faghan Kord e Daniel Ševčovič (2017). "Pricing perpetual put options by the Black-Scholes equation with a nonlinear volatility function". Instituto Superior de Economia e Gestão – REM Working paper nº 019 - 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:RCAAP2023-03-06T14:46:10Zoai:www.repository.utl.pt:10400.5/16343Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:01:46.410773Repositório 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 perpetual put options by the Black-Scholes equation with a nonlinear volatility function
title Pricing perpetual put options by the Black-Scholes equation with a nonlinear volatility function
spellingShingle Pricing perpetual put options by the Black-Scholes equation with a nonlinear volatility function
Grossinho, Maria do Rosário
Option pricing
nonlinear Black-Scholes equation
perpetual American put option
early exercise boundary
title_short Pricing perpetual put options by the Black-Scholes equation with a nonlinear volatility function
title_full Pricing perpetual put options by the Black-Scholes equation with a nonlinear volatility function
title_fullStr Pricing perpetual put options by the Black-Scholes equation with a nonlinear volatility function
title_full_unstemmed Pricing perpetual put options by the Black-Scholes equation with a nonlinear volatility function
title_sort Pricing perpetual put options 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 Option pricing
nonlinear Black-Scholes equation
perpetual American put option
early exercise boundary
topic Option pricing
nonlinear Black-Scholes equation
perpetual American put option
early exercise boundary
description We investigate qualitative and quantitative behavior of a solution to the problem of pricing American style of perpetual put options. We assume the option price is a solution to a stationary generalized Black-Scholes equation in which the volatility may depend on the second derivative of the option price itself. We prove existence and uniqueness of a solution to the free boundary problem. We derive a single implicit equation for the free boundary position and the closed form formula for the option price. It is a generalization of the well-known explicit closed form solution derived by Merton for the case of a constant volatility. We also present results of numerical computations of the free boundary position, option price and their dependence on model parameters.
publishDate 2017
dc.date.none.fl_str_mv 2017-12
2017-12-01T00:00:00Z
2018-11-14T14:26:40Z
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/10400.5/16343
url http://hdl.handle.net/10400.5/16343
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 perpetual put options by the Black-Scholes equation with a nonlinear volatility function". Instituto Superior de Economia e Gestão – REM Working paper nº 019 - 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
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