Recursive Copula Aggregation for Market and Credit Portfolios

Risk aggregation is a central problem in financial risk management and regulatory capital assessment. While copula-based approaches are widely used due to their tractability and interpretability, standard implementations rely on flat dependence structures that may fail to capture hierarchical interactions across risk components. This paper introduces a hierarchical copula framework for risk aggregation on trees, in which dependence is specified locally at each aggregation node and propagated through recursive rank-based reordering. The approach preserves marginal distributions while enabling flexible and economically interpretable modeling of dependence across multiple aggregation levels. Copula parameters are calibrated from empirical data using Kendalls tau, and the methodology is illustrated using market and credit risk proxies. Robustness is assessed across alternative credit segments, including investment-grade and high-yield indices. Numerical results show that dependence strength increases under stress and varies systematically across credit quality, with important implications for risk measurement. The proposed framework combines the transparency of copula-based aggregation with the structural richness of hierarchical models, providing a practical and scalable tool for enterprise risk management. This contributes to bridging bottom-up and top-down approaches to risk aggregation. Keywords: hierarchical copulae; dependence modelling; Kendalls tau calibration; Gaussian and Clayton copulae; tail dependence; risk aggregation. Key Messages: - Recursive hierarchical copulas aggregate market and credit portfolios. - Empirical dependence calibration is combined with sample reordering. - The framework computes VaR and Expected Shortfall transparently. - Tail dependence significantly affects hierarchical risk aggregation.