Analytical Path-Integral Pricing of Deterministic Moving-Barrier Options under Non-Gaussian Distributions
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1142/S0219024920500053 http://hdl.handle.net/11449/200071 |
Resumo: | In this work, we present an analytical model, based on the path-integral formalism of statistical mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under possibly non-Gaussian distributions of the underlying object. We adapt to our problem a model originally proposed by De Simone et al. (2011) to describe the formation of galaxies in the universe, which uses cumulant expansions in terms of the Gaussian distribution, and we generalize it to take into account drift and cumulants of orders higher than three. From the probability density function, we obtain an analytical pricing model, not only for vanilla options (thus removing the need of volatility smile inherent to the Black & Scholes (1973) model), but also for fixed or deterministically moving barrier options. Market prices of vanilla options are used to calibrate the model, and barrier option pricing arising from the model is compared to the price resulted from the relative entropy model. |
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Repositório Institucional da UNESP |
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Analytical Path-Integral Pricing of Deterministic Moving-Barrier Options under Non-Gaussian DistributionsBreeden-Litzenberger theoremcumulant expansionfirst-passage timemoving barrier, Black & Scholes modelNon-Gaussian distributionpath integralrelative entropy, Gram-Charlier expansion, Edgeworth expansionstochastic processesIn this work, we present an analytical model, based on the path-integral formalism of statistical mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under possibly non-Gaussian distributions of the underlying object. We adapt to our problem a model originally proposed by De Simone et al. (2011) to describe the formation of galaxies in the universe, which uses cumulant expansions in terms of the Gaussian distribution, and we generalize it to take into account drift and cumulants of orders higher than three. From the probability density function, we obtain an analytical pricing model, not only for vanilla options (thus removing the need of volatility smile inherent to the Black & Scholes (1973) model), but also for fixed or deterministically moving barrier options. Market prices of vanilla options are used to calibrate the model, and barrier option pricing arising from the model is compared to the price resulted from the relative entropy model.Instituto de Física Teórica Universidade Estadual Paulista-UNESP South American Institute for Fundamental Research, R. Dr. Bento Teobaldo Ferraz 271Instituto de Física Teórica Universidade Estadual Paulista-UNESP South American Institute for Fundamental Research, R. Dr. Bento Teobaldo Ferraz 271Universidade Estadual Paulista (Unesp)Catalaõ, André [UNESP]Rosenfeld, Rogério [UNESP]2020-12-12T01:56:54Z2020-12-12T01:56:54Z2020-02-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1142/S0219024920500053International Journal of Theoretical and Applied Finance, v. 23, n. 1, 2020.0219-0249http://hdl.handle.net/11449/20007110.1142/S02190249205000532-s2.0-85079485105Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal of Theoretical and Applied Financeinfo:eu-repo/semantics/openAccess2021-10-23T11:51:55Zoai:repositorio.unesp.br:11449/200071Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-23T11:51:55Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Analytical Path-Integral Pricing of Deterministic Moving-Barrier Options under Non-Gaussian Distributions |
title |
Analytical Path-Integral Pricing of Deterministic Moving-Barrier Options under Non-Gaussian Distributions |
spellingShingle |
Analytical Path-Integral Pricing of Deterministic Moving-Barrier Options under Non-Gaussian Distributions Catalaõ, André [UNESP] Breeden-Litzenberger theorem cumulant expansion first-passage time moving barrier, Black & Scholes model Non-Gaussian distribution path integral relative entropy, Gram-Charlier expansion, Edgeworth expansion stochastic processes |
title_short |
Analytical Path-Integral Pricing of Deterministic Moving-Barrier Options under Non-Gaussian Distributions |
title_full |
Analytical Path-Integral Pricing of Deterministic Moving-Barrier Options under Non-Gaussian Distributions |
title_fullStr |
Analytical Path-Integral Pricing of Deterministic Moving-Barrier Options under Non-Gaussian Distributions |
title_full_unstemmed |
Analytical Path-Integral Pricing of Deterministic Moving-Barrier Options under Non-Gaussian Distributions |
title_sort |
Analytical Path-Integral Pricing of Deterministic Moving-Barrier Options under Non-Gaussian Distributions |
author |
Catalaõ, André [UNESP] |
author_facet |
Catalaõ, André [UNESP] Rosenfeld, Rogério [UNESP] |
author_role |
author |
author2 |
Rosenfeld, Rogério [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Catalaõ, André [UNESP] Rosenfeld, Rogério [UNESP] |
dc.subject.por.fl_str_mv |
Breeden-Litzenberger theorem cumulant expansion first-passage time moving barrier, Black & Scholes model Non-Gaussian distribution path integral relative entropy, Gram-Charlier expansion, Edgeworth expansion stochastic processes |
topic |
Breeden-Litzenberger theorem cumulant expansion first-passage time moving barrier, Black & Scholes model Non-Gaussian distribution path integral relative entropy, Gram-Charlier expansion, Edgeworth expansion stochastic processes |
description |
In this work, we present an analytical model, based on the path-integral formalism of statistical mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under possibly non-Gaussian distributions of the underlying object. We adapt to our problem a model originally proposed by De Simone et al. (2011) to describe the formation of galaxies in the universe, which uses cumulant expansions in terms of the Gaussian distribution, and we generalize it to take into account drift and cumulants of orders higher than three. From the probability density function, we obtain an analytical pricing model, not only for vanilla options (thus removing the need of volatility smile inherent to the Black & Scholes (1973) model), but also for fixed or deterministically moving barrier options. Market prices of vanilla options are used to calibrate the model, and barrier option pricing arising from the model is compared to the price resulted from the relative entropy model. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-12-12T01:56:54Z 2020-12-12T01:56:54Z 2020-02-01 |
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://dx.doi.org/10.1142/S0219024920500053 International Journal of Theoretical and Applied Finance, v. 23, n. 1, 2020. 0219-0249 http://hdl.handle.net/11449/200071 10.1142/S0219024920500053 2-s2.0-85079485105 |
url |
http://dx.doi.org/10.1142/S0219024920500053 http://hdl.handle.net/11449/200071 |
identifier_str_mv |
International Journal of Theoretical and Applied Finance, v. 23, n. 1, 2020. 0219-0249 10.1142/S0219024920500053 2-s2.0-85079485105 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
International Journal of Theoretical and Applied Finance |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1803046885294866432 |