Time dynamic and hierarchicaldependence modelling of an aggregatedportfolio of trading books –a multivariate nonparametric approach

From a banking supervisory perspective, this paper analyses aspects of market risk of anaggregated trading portfolio comprised of the trading books of 11 German banks with aregulatory approved internal market risk model. Based on real, clean prot and loss dataand Value-at-Risk estimates of the 11 banks, the paper specically models and analyzesthe portfolio's dependence and diversication structure, indispensable for nancial stabilitystudies. The high sensitivity of market risk measurements with respect to the dependencestructure of the underlying portfolio is nowadays a well-known fact. However, only few techniquesfor high-dimensional and hierarchical dependence analysis have been proposed andstudied in the nancial literature so far. One reason is certainly the increasing complexityof the statistical theory, which is commonly referred to as the curse of high-dimensionality.The present paper develops and applies multidimensional (asymptotic) test statistics basedon the copula theory with the aim of detecting signicant long-term level changes in thesupervisory portfolio's dependence over time. Furthermore, a statistical hypothesis test isproposed to identify the distinct contributions of sub-portfolios towards the overall dependencelevel in a hierarchical manner. The utilized techniques are distribution-free and, inparticular, are invariant with respect to the marginal return distribution[...]