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: Faghan, Yaser Kord, 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/10400.5/24431
Resumo: We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black–Scholes equation in which the volatility function 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.
id RCAP_080e56f1745b3f38b891691c6b160ba1
oai_identifier_str oai:www.repository.utl.pt:10400.5/24431
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
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 of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black–Scholes equation in which the volatility function 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.SpringerRepositório da Universidade de LisboaGrossinho, Maria do RosárioFaghan, Yaser KordŠevčovič, Daniel2022-05-31T09:52:11Z20172017-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/24431engGrossinho, Maria do Rosário, Yaser Kord Faghan and Daniel Ševčovič. (2017). "Pricing perpetual put options by the black–scholes equation with a nonlinear volatility function" . Asia-Pacific Financial Markets. Vol. 24: pp. 291-308. (Search PDF in 2023).info: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:RCAAP2023-04-23T01:30:45Zoai:www.repository.utl.pt:10400.5/24431Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:08:28.817060Repositório 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
Faghan, Yaser Kord
Ševčovič, Daniel
author_role author
author2 Faghan, Yaser Kord
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
Faghan, Yaser Kord
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 of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black–Scholes equation in which the volatility function 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
2017-01-01T00:00:00Z
2022-05-31T09:52:11Z
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/10400.5/24431
url http://hdl.handle.net/10400.5/24431
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Grossinho, Maria do Rosário, Yaser Kord Faghan and Daniel Ševčovič. (2017). "Pricing perpetual put options by the black–scholes equation with a nonlinear volatility function" . Asia-Pacific Financial Markets. Vol. 24: pp. 291-308. (Search PDF in 2023).
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 Springer
publisher.none.fl_str_mv Springer
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
_version_ 1817551778402533376

Registros relacionados