Selecting and estimating regular vine copulae and application to financial returns

Abstract

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.

Forecasting portfolio-Value-at-Risk with nonparametric lower tail dependence estimates

“…We nevertheless believe our findings from the analysis of bivariate copulas to be highly relevant. Recent work by Aas et al (2009) and Dissmann et al (2013) emphasizes that so-called pair-copula constructions are extremely well suited for modeling financial returns in high dimensions. As these hierarchical models are built from bivariate copulas as buildings blocks, our findings should be directly applicable to high-dimensional pair-copula models.…”

Application of Vine Copulas to Credit Portfolio Risk Modeling

“…In order to select the vine structure, two construction strategies have been proposed in the literature: a top-down approach by [7] and a bottom-up method by [38]. In our setting, the heuristic is to use the basis tree which captures the strongest dependencies as measured by pairwise Kendall's τ, which means that in a D-vine we have to find pairs of variables and arrange them one after another so that the sum of the absolute pairwise Kendall's τ is maximized.…”

“…Standard procedures to tackle this problem have been studied and evolved over the past (see [7], for instance). In our analysis, we show how these approaches can be applied in the credit portfolio risk context to provide a robust estimation of economic capital.…”

The relationship between WIG-subindexes: evidence from the Warsaw Stock Exchange

“…The second tree is constructed so that the set of nodes contains a set of pairs of all indexes, and the set of edges is built of pairs of pairs of indexes, etc. Formally, the definition of a regular vine (R-vine) is as follows (see Dißmann et al 2013):…”

“…The proximity condition allows us to identify each edge e = (a e ,b e |D e ), where {ae, be} is the conditioned set and De is conditioning set of edge e Here a e , b e ∈ {1, ... An n-dimensional regular vine copula is based on the R-vine structure and is used to specify bivariate copulas in PCC, pair-copula construction ). A formal definition of the R-vine copula specification is as follows (Dißmann et al 2013, Czado et al 2013). …”