Quantifying tail dependence is an important issue in insurance and risk management. The prevalent tail dependence coefficient (TDC), however, is known to underestimate the degree of tail dependence and it does not capture non-exchangeable tail dependence since it evaluates the limiting tail probability only along the main diagonal. To overcome these issues, two novel tail dependence measures called the maximal tail concordance measure (MTCM) and the average tail concordance measure (ATCM) are proposed. Both measures are constructed based on tail copulas and possess clear probabilistic interpretations in that the MTCM evaluates the largest limiting probability among all comparable rectangles in the tail, and the ATCM is a normalized average of these limiting probabilities. In contrast to the TDC, the proposed measures can capture non-exchangeable tail dependence. Analytical forms of the proposed measures are also derived for various copulas. A real data analysis reveals striking tail dependence and tail non-exchangeability of the return series of stock indices, particularly in periods of financial distress.

翻译：量化尾部相依性是保险与风险管理领域的重要议题。然而，广泛使用的尾部相依系数（TDC）既会低估尾部相依程度，又因仅沿主对角线评估极限尾部概率而无法捕捉非可交换尾部相依性。为克服这些问题，本文提出两种新型尾部相依测度：最大尾部一致性测度（MTCM）与平均尾部一致性测度（ATCM）。两种测度均基于尾部Copula构建，具有清晰的概率解释——MTCM评估尾部所有可比矩形中最大的极限概率，而ATCM则是这些极限概率的归一化平均值。相较于TDC，所提测度能捕捉非可交换尾部相依性。本文还推导了多种Copula下所提测度的解析表达式。实际数据分析揭示股票指数收益率序列（尤其在金融困境时期）存在显著的尾部相依性与尾部非可交换性。