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
本文提出基于显式有限和公式的分层Copula聚合方法，用于市场-信用风险度量，推导了聚合分布、分位数和尾部损失的确定性表达式，并分析尾部依赖传播，为模拟方法提供确定性替代方案。
AI 中文摘要
分层Copula模型广泛用于跨多层投资组合结构聚合市场风险和信用风险。现有方法通常依赖蒙特卡洛模拟、递归样本重排序或高维数值程序。本文开发了一个基于显式有限和表示的分析框架，用于分层Copula聚合，针对具有经验叶级边际分布的高斯和镜像Clayton Copula的两级市场-信用聚合，推导了聚合损失分布和尾部风险度量的确定性公式。我们推导了聚合分布函数、分位数、期望尾部损失和市场-信用尾部贡献的确定性公式，以及连接局部分层Copula和全局叶级依赖结构的兼容性条件。分位数和期望尾部损失的估计误差表达式也以有限和形式获得。本文进一步分析了在增加树深度下分层聚合的定性渐近行为。高斯层级被认为保持多样化主导，而镜像Clayton层级递归传播上尾依赖，并可能在聚合级别放大极端损失。所得公式为基于模拟的聚合方法提供了确定性替代方案，并阐明了尾部依赖如何通过分层市场-信用投资组合传播，对投资组合风险测量和资本评估具有直接相关性。
英文摘要
Hierarchical copula models are widely used for aggregating market and credit risks across multi-level portfolio structures. Existing approaches often rely on Monte Carlo simulation, recursive sample reordering, or high-dimensional numerical procedures. This paper develops an analytical framework for hierarchical copula aggregation based on explicit finite-sum representations of aggregate loss distributions and tail-risk measures for two-level market-credit aggregation with Gaussian and mirrored Clayton copulas under empirical leaf-level marginals. We derive deterministic formulas for aggregate distribution functions, quantiles, expected tail losses, and market-credit tail contributions, together with a compatibility condition linking local hierarchical copulas and global leaf-level dependence structures. Estimation-error expressions for quantiles and expected tail losses are also obtained in finite-sum form. The paper further analyzes the qualitative asymptotic behavior of hierarchical aggregation under increasing tree depth. Gaussian hierarchies are argued to remain diversification-dominated, whereas mirrored Clayton hierarchies propagate upper-tail dependence recursively and may amplify extreme losses across aggregation levels. The resulting formulas provide a deterministic alternative to simulation-based aggregation methods and clarify how tail dependence propagates through hierarchical market-credit portfolios, with direct relevance for portfolio risk measurement and capital assessment.
