Recursive Hierarchical Copula Aggregation for Market and Credit Portfolio Risk

01 ABSTRACT

To address the inability of standard flat copula structures to capture hierarchical interactions in risk aggregation, the paper proposes a recursive hierarchical copula framework in which dependence is specified locally at each tree node and propagated through recursive rank-based reordering. The authors calibrate copula parameters from empirical data using Kendall's tau and illustrate the method with market and credit risk proxies, assessing robustness across credit segments such as investment-grade and high-yield indices. Numerical results show that dependence strengthens under stress and varies systematically with credit quality, which the authors argue has important implications for risk measurement; these are the paper's claims and have not been independently verified.

02 KEY FINDINGS

1. Proposes a tree-based recursive hierarchical copula aggregation method where dependence is specified locally at nodes and propagated recursively while preserving marginal distributions.
2. Calibrates copula parameters from empirical data using Kendall's tau and illustrates the approach with market and credit risk proxies and robustness checks across credit segments.
3. Reports numerical results indicating that dependence strengthens under stress and varies systematically with credit quality, and that tail dependence significantly affects hierarchical aggregation risk.