An empirical analysis of multivariate copula models

Fischer, Matthias; Köck, Christian; Schlüter, Stephan; Weigert, Florian

doi:10.1080/14697680802595650

Cited by 128 publications

(49 citation statements)

References 15 publications

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“…Kurowicka and Cooke (2006) focused on vine distributions with Gaussian pair-copulae, but Aas et al (2009) allowed for different pair-copula families, such as the bivariate Student-t copula, bivariate Gumbel and bivariate Clayton copula. While D-vine based models are started to be used in many applications (Fischer et al (2009), Min and Czado (2010), Chollete et al (2009), Hofmann and Czado (2010), Mendes et al (2010), Salinas-Gutiérrez et al (2010), Erdorf et al (2011), Mercier and Frison (2009), Smith et al (2010)), C-vines are less commonly used , Czado et al (2010)); Nikoloulopoulos et al (2012) consider both classes.…”

Section: Introductionmentioning

confidence: 99%

Selecting and estimating regular vine copulae and application to financial returns

DiíMann

Brechmann

Czado

et al. 2013

Computational Statistics & Data Analysis

586

551

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Regular vine distributions which constitute a flexible class of multivariate dependence models are discussed. Since multivariate copulae constructed through pair-copula decompositions were introduced to the statistical community, interest in these models has been growing steadily and they are finding successful applications in various fields. Research so far has however been concentrating on so-called canonical and D-vine copulae, which are more restrictive cases of regular vine copulae. It is shown how to evaluate the density of arbitrary regular vine specifications. This opens the vine copula methodology to the flexible modeling of complex dependencies even in larger dimensions. In this regard, a new automated model selection and estimation technique based on graph theoretical considerations is presented. This comprehensive search strategy is evaluated in a large simulation study and applied to a 16-dimensional financial data set of international equity, fixed income and commodity indices which were observed over the last decade, in particular during the recent financial crisis. The analysis provides economically well interpretable results and interesting insights into the dependence structure among these indices.

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Section: Introductionmentioning

confidence: 99%

Selecting and estimating regular vine copulae and application to financial returns

DiíMann

Brechmann

Czado

et al. 2013

Computational Statistics & Data Analysis

586

551

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“…Provided its existence, c denotes the corresponding density. In contrast to the wide-spread class of elliptical copulas, our focus is on vine copulas henceforth (For a detailed treatment of multivariate copula models, we refer to [23] or [24], for instance). Vine copulas (Comprehensive contributions to vine copulas are provided by [25,26], [9] or [10]) are a flexible class of dependence models consisting of bivariate building blocks and have proven to be particularly useful in high dimensions.…”

Section: A Short Primer On Pair-copulas Including Specification and Ementioning

confidence: 99%

Application of Vine Copulas to Credit Portfolio Risk Modeling

Geidosch¹,

Fischer

2016

JRFM

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Abstract:In this paper, we demonstrate the superiority of vine copulas over conventional copulas when modeling the dependence structure of a credit portfolio. We show statistical and economic implications of replacing conventional copulas by vine copulas for a subportfolio of the Euro Stoxx 50 and the S&P 500 companies, respectively. Our study includes D-vines and R-vines where the bivariate building blocks are chosen from the Gaussian, the t and the Clayton family. Our findings are (i) the conventional Gauss copula is deficient in modeling the dependence structure of a credit portfolio and economic capital is seriously underestimated; (ii) D-vine structures offer a better statistical fit to the data than classical copulas, but underestimate economic capital compared to R-vines; (iii) when mixing different copula families in an R-vine structure, the best statistical fit to the data can be achieved which corresponds to the most reliable estimate for economic capital.

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“…For related recent studies, see [46,116]. Other constructions can be found in [162] (direct compatibility), [95] (nested constructions), and [17,66,115,123].…”

Section: Copulas With Given Lower Dimensional Marginalsmentioning

confidence: 99%