发表机构
University of Torino; Core Dynamics GmbH; Signal Iduna Reinsurance（都灵大学; Core Dynamics有限公司; Signal Iduna再保险公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种递归层级Copula框架，通过局部依赖指定和秩重排传播，在保留边际分布的同时实现多层级依赖建模，并用Kendall's tau校准，实证显示压力下依赖增强且随信用质量变化，为风险聚合提供透明可扩展工具。
AI 中文摘要
风险聚合是金融风险管理和监管资本评估中的一个核心问题。尽管基于Copula的方法因其易处理性和可解释性而被广泛使用，但标准实现依赖于平坦的依赖结构，可能无法捕捉风险组成部分之间的层级交互。本文提出了一种在树上进行风险聚合的层级Copula框架，其中依赖关系在每个聚合节点局部指定，并通过递归的基于秩的重排进行传播。该方法保留了边际分布，同时能够在多个聚合层级上实现灵活且经济上可解释的依赖建模。Copula参数使用Kendall's tau从经验数据中校准，并使用市场和信用风险代理来说明该方法。鲁棒性在替代信用细分领域进行评估，包括投资级和高收益指数。数值结果表明，依赖强度在压力下增加，并随信用质量系统性变化，这对风险测量具有重要意义。所提出的框架结合了基于Copula的聚合的透明性与层级模型的结构丰富性，为企业风险管理提供了一个实用且可扩展的工具。这有助于弥合自下而上和自上而下的风险聚合方法。关键词：层级Copula；依赖建模；Kendall's tau校准；高斯和Clayton Copula；尾部依赖；风险聚合。关键信息：- 递归层级Copula聚合市场和信用组合。- 经验依赖校准与样本重排相结合。- 该框架透明地计算VaR和期望损失。- 尾部依赖显著影响层级风险聚合。
英文摘要
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.
