COLLATERALIZED DEBT OBLIGATION VALUATION AND HEDGE THROUGH TWO PERSPECTIVES: CONVOLUTION AND CLASSIC MODELS WITH NORMALITY ASSUMPTIONS

A CDO consists of a portfolio of debt instruments such as bonds, loans and mortgages, which are grouped in different tranches based on risk and return profiles. In this paper, we present the problem of analyzing the risk embedded in a CDO and constructing a proper hedge using VaR and assuming that t...

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Autor principal: CAÁ‘IBANO, Mauro
Formato: Artículo publishedVersion
Lenguaje:Español
Publicado: Centro de Investigación en Métodos Cuantitativos Aplicados a la Economía y la Gestión (CMA) 2016
Acceso en línea:https://ojs.economicas.uba.ar/RIMF/article/view/1489
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=modelfin&d=1489_oai
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Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires
id I28-R145-1489_oai
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spelling I28-R145-1489_oai2025-02-11 CAÁ‘IBANO, Mauro 2016-07-05 A CDO consists of a portfolio of debt instruments such as bonds, loans and mortgages, which are grouped in different tranches based on risk and return profiles. In this paper, we present the problem of analyzing the risk embedded in a CDO and constructing a proper hedge using VaR and assuming that the components of the CDO are correlated to each other. In order to complete this task two perspectives are used to value the CDO. First of all, classic models which assume normality in the distribution of the risks are used. Since there is much evidence that these assumptions are not satisfied in real markets a second approach involving a Convolution is introduced. This Convolution assumes no normality in the distribution ofthe risks and incorporates the correlation within the different components of the CDO. Finally, VaR at 99% is used to show the efficiency of each method. As a result of the false normality assumption the VaR based on classic models will underestimate the maximum possible loss, resulting in a VaR lower than the VaR obtained through the Convolution. Un “Collateralized Debt Obligation” (CDO) es una cartera que agrupa a un conjunto de instrumentos financieros de deuda (bonos, préstamos, hipotecas. Representa una cartera de bonos, préstamos o hipotecas) y los divide en distintos tramos según su perfil de riesgo y rendimiento. Se presenta el problema de analizar la cobertura del riesgo inherente en elmismo a través del “Value At Risk”(VaR), sabiendo que los componentes del CDO son interdependientes. Se busca hacer una evaluación de riesgo del CDO desde dos perspectivas distintas. La primera, a través de los modelos clásicos aplicados al área de riesgo financiero que tienen sustento teórico en la distribución normal de los riesgos. Dado que existe cuantiosa evidencia empírica que respalda que este supuesto mencionado no se cumple en los mercados reales, la segunda evaluación será lograda a través de una Convolución de variables aleatorias que muestran una evidente dependencia y distribuciones distintas a la normal. Finalmente, con la herramienta VaR se busca demostrar la eficiencia de cada método empleado, analizando la máxima pérdida esperada, con un 99% de confianza, en el período de evaluación, según sea el método utilizado. Se demuestra que, al sustentarse en supuestos que se alejan de la realidad de los mercados, el VaR que resulta de la aplicación de los métodos clásicos que suponen normalidad subestimará la máxima pérdida posible en el período de evaluación, arrojando un VaR menor al VaR calculado a partir de la Convolución. application/pdf https://ojs.economicas.uba.ar/RIMF/article/view/1489 spa Centro de Investigación en Métodos Cuantitativos Aplicados a la Economía y la Gestión (CMA) https://ojs.economicas.uba.ar/RIMF/article/view/1489/2117 Revista de Investigación en Modelos Financieros; Vol. 1 (2016): Revista de Investigación en Modelos Financieros; 18-47 2250-6861 2250-687X COLLATERALIZED DEBT OBLIGATION VALUATION AND HEDGE THROUGH TWO PERSPECTIVES: CONVOLUTION AND CLASSIC MODELS WITH NORMALITY ASSUMPTIONS VALUACIÓN Y COBERTURA DE UN COLLATERALIZED DEBT OBLIGATION A TRAVÉS DE DOS PERSPECTIVAS: CONVOLUCIÓN Y MODELOS CLÁSICOS QUE SUPONEN NORMALIDAD info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=modelfin&d=1489_oai
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-145
collection Repositorio Digital de la Universidad de Buenos Aires (UBA)
language Español
orig_language_str_mv spa
description A CDO consists of a portfolio of debt instruments such as bonds, loans and mortgages, which are grouped in different tranches based on risk and return profiles. In this paper, we present the problem of analyzing the risk embedded in a CDO and constructing a proper hedge using VaR and assuming that the components of the CDO are correlated to each other. In order to complete this task two perspectives are used to value the CDO. First of all, classic models which assume normality in the distribution of the risks are used. Since there is much evidence that these assumptions are not satisfied in real markets a second approach involving a Convolution is introduced. This Convolution assumes no normality in the distribution ofthe risks and incorporates the correlation within the different components of the CDO. Finally, VaR at 99% is used to show the efficiency of each method. As a result of the false normality assumption the VaR based on classic models will underestimate the maximum possible loss, resulting in a VaR lower than the VaR obtained through the Convolution.
format Artículo
publishedVersion
author CAÁ‘IBANO, Mauro
spellingShingle CAÁ‘IBANO, Mauro
COLLATERALIZED DEBT OBLIGATION VALUATION AND HEDGE THROUGH TWO PERSPECTIVES: CONVOLUTION AND CLASSIC MODELS WITH NORMALITY ASSUMPTIONS
author_facet CAÁ‘IBANO, Mauro
author_sort CAÁ‘IBANO, Mauro
title COLLATERALIZED DEBT OBLIGATION VALUATION AND HEDGE THROUGH TWO PERSPECTIVES: CONVOLUTION AND CLASSIC MODELS WITH NORMALITY ASSUMPTIONS
title_short COLLATERALIZED DEBT OBLIGATION VALUATION AND HEDGE THROUGH TWO PERSPECTIVES: CONVOLUTION AND CLASSIC MODELS WITH NORMALITY ASSUMPTIONS
title_full COLLATERALIZED DEBT OBLIGATION VALUATION AND HEDGE THROUGH TWO PERSPECTIVES: CONVOLUTION AND CLASSIC MODELS WITH NORMALITY ASSUMPTIONS
title_fullStr COLLATERALIZED DEBT OBLIGATION VALUATION AND HEDGE THROUGH TWO PERSPECTIVES: CONVOLUTION AND CLASSIC MODELS WITH NORMALITY ASSUMPTIONS
title_full_unstemmed COLLATERALIZED DEBT OBLIGATION VALUATION AND HEDGE THROUGH TWO PERSPECTIVES: CONVOLUTION AND CLASSIC MODELS WITH NORMALITY ASSUMPTIONS
title_sort collateralized debt obligation valuation and hedge through two perspectives: convolution and classic models with normality assumptions
publisher Centro de Investigación en Métodos Cuantitativos Aplicados a la Economía y la Gestión (CMA)
publishDate 2016
url https://ojs.economicas.uba.ar/RIMF/article/view/1489
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=modelfin&d=1489_oai
work_keys_str_mv AT caaibanomauro collateralizeddebtobligationvaluationandhedgethroughtwoperspectivesconvolutionandclassicmodelswithnormalityassumptions
AT caaibanomauro valuacionycoberturadeuncollateralizeddebtobligationatravesdedosperspectivasconvolucionymodelosclasicosquesuponennormalidad
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