Analyzing the use of generalized hyperbolic distributions to value at risk calculations
Autor(a) principal: | |
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Data de Publicação: | 2005 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Economia Aplicada |
Texto Completo: | https://www.revistas.usp.br/ecoa/article/view/221386 |
Resumo: | The goal of this paper is to analyze the use of the Generalized Hyperbolic (GH) Distributions to model the US Dollar/Brazilian Real exchange rate in a way to produce more accurate VaR (Value at Risk) measurements. After the GH parameters estimation, several distances were calculated to verify the fitting quality of Normal distribution and GH distribution family to empirical data. The GH Distributions had shown to be more adequate for modeling the US Dollar/Brazilian Real exchange rate, since they produced smaller distances, especially in tails. Additionally, several methodologies for VaR calculation were compared using the Kupiec test: Historical Simulation, RiskMetrics®, unconditional Normal, GH, Normal Inverse Gaussian (NIG) and Hyperbolic, and GARCH models using Normal, GH, Hyperbolic and NIG. The GH Distribution and its subclasses showed better results than unconditional Normal. The use of a GARCH model for volatility forecasting produced satisfactory results, being the main factor of success. Two estimation methods were used: Maximum Log-Likelihood and Minimization of the FOF distance; but both produced similar results. As the Maximum Log-Likelihood showed to be faster we recommend this method. Overall, our recommendation the use of a GH family distribution re-scaled by a GARCH volatility and estimated by Maximum Log-Likelihood. |
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Economia Aplicada |
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Analyzing the use of generalized hyperbolic distributions to value at risk calculationsvalue at riskgeneralized hyperbolic distributionsbacktestingThe goal of this paper is to analyze the use of the Generalized Hyperbolic (GH) Distributions to model the US Dollar/Brazilian Real exchange rate in a way to produce more accurate VaR (Value at Risk) measurements. After the GH parameters estimation, several distances were calculated to verify the fitting quality of Normal distribution and GH distribution family to empirical data. The GH Distributions had shown to be more adequate for modeling the US Dollar/Brazilian Real exchange rate, since they produced smaller distances, especially in tails. Additionally, several methodologies for VaR calculation were compared using the Kupiec test: Historical Simulation, RiskMetrics®, unconditional Normal, GH, Normal Inverse Gaussian (NIG) and Hyperbolic, and GARCH models using Normal, GH, Hyperbolic and NIG. The GH Distribution and its subclasses showed better results than unconditional Normal. The use of a GARCH model for volatility forecasting produced satisfactory results, being the main factor of success. Two estimation methods were used: Maximum Log-Likelihood and Minimization of the FOF distance; but both produced similar results. As the Maximum Log-Likelihood showed to be faster we recommend this method. Overall, our recommendation the use of a GH family distribution re-scaled by a GARCH volatility and estimated by Maximum Log-Likelihood.Universidade de São Paulo, FEA-RP/USP2005-02-20info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://www.revistas.usp.br/ecoa/article/view/22138610.11606/1413-8050/ea221386Economia Aplicada; Vol. 9 No. 1 (2005); 25-38Economia Aplicada; v. 9 n. 1 (2005); 25-38Economia Aplicada; Vol. 9 Núm. 1 (2005); 25-381980-53301413-8050reponame:Economia Aplicadainstname:Universidade de São Paulo (USP)instacron:USPenghttps://www.revistas.usp.br/ecoa/article/view/221386/202524Copyright (c) 2005 Economia Aplicadahttp://creativecommons.org/licenses/by-nc/4.0info:eu-repo/semantics/openAccessBarbadian, José Santiago Fajardo Farias, Aquiles Rocha de Ornelas, José Renato Haas 2024-01-17T17:39:15Zoai:revistas.usp.br:article/221386Revistahttps://www.revistas.usp.br/ecoaPUBhttps://www.revistas.usp.br/ecoa/oai||revecap@usp.br1980-53301413-8050opendoar:2024-01-17T17:39:15Economia Aplicada - Universidade de São Paulo (USP)false |
dc.title.none.fl_str_mv |
Analyzing the use of generalized hyperbolic distributions to value at risk calculations |
title |
Analyzing the use of generalized hyperbolic distributions to value at risk calculations |
spellingShingle |
Analyzing the use of generalized hyperbolic distributions to value at risk calculations Barbadian, José Santiago Fajardo value at risk generalized hyperbolic distributions backtesting |
title_short |
Analyzing the use of generalized hyperbolic distributions to value at risk calculations |
title_full |
Analyzing the use of generalized hyperbolic distributions to value at risk calculations |
title_fullStr |
Analyzing the use of generalized hyperbolic distributions to value at risk calculations |
title_full_unstemmed |
Analyzing the use of generalized hyperbolic distributions to value at risk calculations |
title_sort |
Analyzing the use of generalized hyperbolic distributions to value at risk calculations |
author |
Barbadian, José Santiago Fajardo |
author_facet |
Barbadian, José Santiago Fajardo Farias, Aquiles Rocha de Ornelas, José Renato Haas |
author_role |
author |
author2 |
Farias, Aquiles Rocha de Ornelas, José Renato Haas |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Barbadian, José Santiago Fajardo Farias, Aquiles Rocha de Ornelas, José Renato Haas |
dc.subject.por.fl_str_mv |
value at risk generalized hyperbolic distributions backtesting |
topic |
value at risk generalized hyperbolic distributions backtesting |
description |
The goal of this paper is to analyze the use of the Generalized Hyperbolic (GH) Distributions to model the US Dollar/Brazilian Real exchange rate in a way to produce more accurate VaR (Value at Risk) measurements. After the GH parameters estimation, several distances were calculated to verify the fitting quality of Normal distribution and GH distribution family to empirical data. The GH Distributions had shown to be more adequate for modeling the US Dollar/Brazilian Real exchange rate, since they produced smaller distances, especially in tails. Additionally, several methodologies for VaR calculation were compared using the Kupiec test: Historical Simulation, RiskMetrics®, unconditional Normal, GH, Normal Inverse Gaussian (NIG) and Hyperbolic, and GARCH models using Normal, GH, Hyperbolic and NIG. The GH Distribution and its subclasses showed better results than unconditional Normal. The use of a GARCH model for volatility forecasting produced satisfactory results, being the main factor of success. Two estimation methods were used: Maximum Log-Likelihood and Minimization of the FOF distance; but both produced similar results. As the Maximum Log-Likelihood showed to be faster we recommend this method. Overall, our recommendation the use of a GH family distribution re-scaled by a GARCH volatility and estimated by Maximum Log-Likelihood. |
publishDate |
2005 |
dc.date.none.fl_str_mv |
2005-02-20 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://www.revistas.usp.br/ecoa/article/view/221386 10.11606/1413-8050/ea221386 |
url |
https://www.revistas.usp.br/ecoa/article/view/221386 |
identifier_str_mv |
10.11606/1413-8050/ea221386 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://www.revistas.usp.br/ecoa/article/view/221386/202524 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2005 Economia Aplicada http://creativecommons.org/licenses/by-nc/4.0 info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2005 Economia Aplicada http://creativecommons.org/licenses/by-nc/4.0 |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Universidade de São Paulo, FEA-RP/USP |
publisher.none.fl_str_mv |
Universidade de São Paulo, FEA-RP/USP |
dc.source.none.fl_str_mv |
Economia Aplicada; Vol. 9 No. 1 (2005); 25-38 Economia Aplicada; v. 9 n. 1 (2005); 25-38 Economia Aplicada; Vol. 9 Núm. 1 (2005); 25-38 1980-5330 1413-8050 reponame:Economia Aplicada instname:Universidade de São Paulo (USP) instacron:USP |
instname_str |
Universidade de São Paulo (USP) |
instacron_str |
USP |
institution |
USP |
reponame_str |
Economia Aplicada |
collection |
Economia Aplicada |
repository.name.fl_str_mv |
Economia Aplicada - Universidade de São Paulo (USP) |
repository.mail.fl_str_mv |
||revecap@usp.br |
_version_ |
1800221692736307200 |