Truncated regular vines in high dimensions with application to financial data

Abstract

Using only bivariate copulas as building blocks, regular vine copulas constitute a flexible class of high‐dimensional dependency models. However, the flexibility comes along with an exponentially increasing complexity in larger dimensions. In order to counteract this problem, we propose using statistical model selection techniques to either truncate or simplify a regular vine copula. As a special case, we consider the simplification of a canonical vine copula using a multivariate copula as previously treated by Heinen & Valdesogo (2009) and Valdesogo (2009). We validate the proposed approaches by extensive simulation studies and use them to investigate a 19‐dimensional financial data set of Norwegian and international market variables. The Canadian Journal of Statistics 40: 68–85; 2012 © 2012 Statistical Society of Canada

Factor Copula Models for Item Response Data

“…Without a priori knowledge of the subgroups of items, a more general approach makes use of truncated vine copula models, conditional on latent variables, to model the residual dependence with O(d) dependence parameters for d items. Truncated vine models are studied in Brechmann et al (2012) for continuous response variables and in Panagiotelis et al (2012) Derivatives of the univariate probability π jy with respect to the cutpoint a jk , and of the bivariate probability π j1j2,y1y2 with respect to the cutpoint a jk and the copula parameter θ j for the 1-factor model for j, j 1 , j 2 = 1, . .…”

Application of Vine Copulas to Credit Portfolio Risk Modeling

“…Consequently, very complex and asymmetric dependence structures can be modeled. The specific definition of pair-copulas leads to three fundamental estimation and selection tasks (see e.g., [35]): firstly, estimation of copula parameters for a chosen vine tree structure and pair copula families (for details on estimation of vine copulas like SSP or ML (maximum likelihood) estimation, we refer to [29,[36][37][38] or [39]); secondly, selection of the parametric copula family for each pair copula term and estimation of the corresponding parameters for a chosen vine tree structure; and, thirdly, selection and estimation of all three model components.…”

Multivariate VaRs for operational risk capital computation: a vine structure approach

“…• In a second step, we estimate the dependence structures between these severities using nested copulas and vine architectures (Brechmann et al (2010)). We use a pseudo maxi- 4 Other distributions have been tested but we only provide some results obtained using the Generalized Pareto Distribution in the fifth section mum likelihood method to estimate the copulas parameters (Mendes et al (2007), Weiss (2010) providing the value of the corresponding AIC (Akaike (1974)) in order to discriminate between different classes of copulas.…”

“…In the literature, it has often been mentioned that the use of copulas is difficult in high dimensions apart from when one uses an elliptic structure (Gaussian or Student) (Di Clemente and Romano (2004)). In this paper we release these restrictions by considering recent developments on copulas: nested copulas (Morillas (2005), Savu and Trede (2006)) and vine copulas , Berg and Aas (2009), Guégan and Maugis (2010), Brechmann et al (2010) and Dissmann et al (2011)). …”

“…The optimal strategy to employ is not considered in this paper. We instead refer the interested reader to Antoch and Hanousek (2000), Bedford and Cooke (2002), Brechmann et al (2010) and Guégan and Maugis (2011).…”