Time dynamic and hierarchical dependence modelling of an aggregated portfolio of trading books

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This paper analyzes market risk from a banking supervisory perspective, focusing on an aggregated trading portfolio of 11 German banks using a regulatory-approved internal market risk model. Utilizing real profit and loss data and Value-at-Risk estimates, it models the portfolio's dependence and diversification structure, essential for financial stability studies. The paper highlights the high sensitivity of market risk measurements to the dependence structure, a well-known issue in finance. However, few techniques for high-dimensional and hierarchical dependence analysis have been adequately explored, largely due to the complexities of statistical theory, often referred to as the curse of high-dimensionality. The study develops and applies multidimensional (asymptotic) test statistics based on copula theory to detect significant long-term changes in the supervisory portfolio's dependence over time. Additionally, it proposes a statistical hypothesis test to identify the contributions of sub-portfolios to the overall dependence level in a hierarchical manner. The techniques employed are distribution-free and invariant with respect to the marginal return distributions, emphasizing their robustness in analyzing multivariate dependence.