Hierarchical Copulae and the Aggregation of Market and Credit Risk: A Mathematical Perspective

This paper proposes a framework for the aggregation of risks in financial portfolios exposed to both market and credit risk. It employs copula functions to model the dependence structure between these risks without requiring simulation of their joint distribution. The methodology follows a hierarchical aggregation scheme: market and credit losses are first aggregated at the individual portfolio level and subsequently combined across multiple portfolios using copula functions. We specifically analyze the properties and practical applications of Gaussian and mirrored Clayton copulae, demonstrating their effectiveness in representing dependencies within hierarchical risk frameworks. By incorporating recent developments in copula theory, the paper provides actionable insights and methodologies to enhance risk management practices in financial institutions.