Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods
Autor(a) principal: | |
---|---|
Data de Publicação: | 2022 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Revista de Engenharia Química e Química |
Texto Completo: | https://periodicos.ufv.br/jcec/article/view/15223 |
Resumo: | Black–Scholes partial differential equation is a generally acceptable model in financial markets for option pricing. However, without variable transformations, the provision of symbolic solutions to the variable coefficient partial differential equation is not a straight-forward task. Moreover, the coefficients of the Black–Scholes can depend on the time and the asset price which makes the analytical solution of the Black–Scholes model very difficult to develop. In this paper, analytical solutions of the model of valuations of financial options are presented using Laplace and differential transform methods. The results of the solutions of the Laplace and differential transformation methods are compared with the results of the exact analytical solutions. Moreover, numerical examples for different options pricing are presented to establish the applications, speed and accuracy of the hybrid methods. |
id |
UFV-4_c56bc43ceb31eb0236d6aadf3eb4ce40 |
---|---|
oai_identifier_str |
oai:ojs.periodicos.ufv.br:article/15223 |
network_acronym_str |
UFV-4 |
network_name_str |
Revista de Engenharia Química e Química |
repository_id_str |
|
spelling |
Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation MethodsBlack–Scholes model; Partial differential Equation; Financial Market; Option pricing; Laplace-differential transformation method.Black–Scholes partial differential equation is a generally acceptable model in financial markets for option pricing. However, without variable transformations, the provision of symbolic solutions to the variable coefficient partial differential equation is not a straight-forward task. Moreover, the coefficients of the Black–Scholes can depend on the time and the asset price which makes the analytical solution of the Black–Scholes model very difficult to develop. In this paper, analytical solutions of the model of valuations of financial options are presented using Laplace and differential transform methods. The results of the solutions of the Laplace and differential transformation methods are compared with the results of the exact analytical solutions. Moreover, numerical examples for different options pricing are presented to establish the applications, speed and accuracy of the hybrid methods.Universidade Federal de Viçosa - UFV2022-06-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtigo, Manuscrito, Eventosapplication/pdfhttps://periodicos.ufv.br/jcec/article/view/1522310.18540/jcecvl8iss1pp15223-01iThe Journal of Engineering and Exact Sciences; Vol. 8 No. 1 (2022); 15223-01iThe Journal of Engineering and Exact Sciences; Vol. 8 Núm. 1 (2022); 15223-01iThe Journal of Engineering and Exact Sciences; v. 8 n. 1 (2022); 15223-01i2527-1075reponame:Revista de Engenharia Química e Químicainstname:Universidade Federal de Viçosa (UFV)instacron:UFVenghttps://periodicos.ufv.br/jcec/article/view/15223/7743Copyright (c) 2022 The Journal of Engineering and Exact Scienceshttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessDere, Zainab OlabisiSobamowo, Gbeminiyi MusibauSiqueira, Antonio Marcos de Oliveira2023-01-12T14:29:48Zoai:ojs.periodicos.ufv.br:article/15223Revistahttp://www.seer.ufv.br/seer/rbeq2/index.php/req2/indexONGhttps://periodicos.ufv.br/jcec/oaijcec.journal@ufv.br||req2@ufv.br2446-94162446-9416opendoar:2023-01-12T14:29:48Revista de Engenharia Química e Química - Universidade Federal de Viçosa (UFV)false |
dc.title.none.fl_str_mv |
Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods |
title |
Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods |
spellingShingle |
Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods Dere, Zainab Olabisi Black–Scholes model; Partial differential Equation; Financial Market; Option pricing; Laplace-differential transformation method. |
title_short |
Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods |
title_full |
Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods |
title_fullStr |
Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods |
title_full_unstemmed |
Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods |
title_sort |
Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods |
author |
Dere, Zainab Olabisi |
author_facet |
Dere, Zainab Olabisi Sobamowo, Gbeminiyi Musibau Siqueira, Antonio Marcos de Oliveira |
author_role |
author |
author2 |
Sobamowo, Gbeminiyi Musibau Siqueira, Antonio Marcos de Oliveira |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Dere, Zainab Olabisi Sobamowo, Gbeminiyi Musibau Siqueira, Antonio Marcos de Oliveira |
dc.subject.por.fl_str_mv |
Black–Scholes model; Partial differential Equation; Financial Market; Option pricing; Laplace-differential transformation method. |
topic |
Black–Scholes model; Partial differential Equation; Financial Market; Option pricing; Laplace-differential transformation method. |
description |
Black–Scholes partial differential equation is a generally acceptable model in financial markets for option pricing. However, without variable transformations, the provision of symbolic solutions to the variable coefficient partial differential equation is not a straight-forward task. Moreover, the coefficients of the Black–Scholes can depend on the time and the asset price which makes the analytical solution of the Black–Scholes model very difficult to develop. In this paper, analytical solutions of the model of valuations of financial options are presented using Laplace and differential transform methods. The results of the solutions of the Laplace and differential transformation methods are compared with the results of the exact analytical solutions. Moreover, numerical examples for different options pricing are presented to establish the applications, speed and accuracy of the hybrid methods. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-06-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Artigo, Manuscrito, Eventos |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://periodicos.ufv.br/jcec/article/view/15223 10.18540/jcecvl8iss1pp15223-01i |
url |
https://periodicos.ufv.br/jcec/article/view/15223 |
identifier_str_mv |
10.18540/jcecvl8iss1pp15223-01i |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://periodicos.ufv.br/jcec/article/view/15223/7743 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2022 The Journal of Engineering and Exact Sciences https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2022 The Journal of Engineering and Exact Sciences https://creativecommons.org/licenses/by/4.0 |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Federal de Viçosa - UFV |
publisher.none.fl_str_mv |
Universidade Federal de Viçosa - UFV |
dc.source.none.fl_str_mv |
The Journal of Engineering and Exact Sciences; Vol. 8 No. 1 (2022); 15223-01i The Journal of Engineering and Exact Sciences; Vol. 8 Núm. 1 (2022); 15223-01i The Journal of Engineering and Exact Sciences; v. 8 n. 1 (2022); 15223-01i 2527-1075 reponame:Revista de Engenharia Química e Química instname:Universidade Federal de Viçosa (UFV) instacron:UFV |
instname_str |
Universidade Federal de Viçosa (UFV) |
instacron_str |
UFV |
institution |
UFV |
reponame_str |
Revista de Engenharia Química e Química |
collection |
Revista de Engenharia Química e Química |
repository.name.fl_str_mv |
Revista de Engenharia Química e Química - Universidade Federal de Viçosa (UFV) |
repository.mail.fl_str_mv |
jcec.journal@ufv.br||req2@ufv.br |
_version_ |
1800211186716770304 |