Accurately modelling the dependence structure between financial assets in a portfolio optimization framework has attracted growing attention in statistical and financial literature. Since in these assets several types of tail dependence might occur simultaneously, it is fundamental for parametric models to adequately replicate their whole tail dependence structure. This article investigates the effectiveness of Vine copulas in modelling counterdiagonal/nonpositive tail dependence, so far overlooked. We obtain expressions for their corresponding general tail dependence function which accounts for all dependences. This generalises the well-known approach of using the survival copula to study upper tail dependence, rather than using rotations on the data. We prove that, further to the already known flexibility to model asymmetric lower and upper tail dependence, Vine copulas can model all multivariate types of tail dependence simultaneously. In an empirical application, using a D-Vine copula with appropriate choices of bivariate linking copulas, we are able to capture the tail dependence structure of a portfolio of financial data in which different types of tail dependence coexist. Further to this, we test to what extent Vine copulas are able to model different types of tail dependence.

在投资组合优化框架中对金融资产之间的依存关系结构进行准确建模已引起统计和金融文献越来越多的关注。由于在这些资产中可能同时发生几种类型的尾部依赖，因此参数模型充分复制其整个尾部依赖结构是基础。本文研究了藤蔓copulas在建模对角线/非阳性尾巴依赖方面的有效性，至今仍被忽略。我们获得了它们对应的一般尾部依赖函数的表达式，该函数解释了所有依赖性。这概括了众所周知的方法，即使用生存系来研究上尾巴依赖性，而不是对数据进行旋转。我们证明 除了已知的灵活性，可以对不对称的上下尾部依赖性进行建模之外，Vine copulas可以同时对所有多元类型的尾部依赖性进行建模。在经验应用中，使用D-Vine copula和适当的二元连接copulas选择，我们能够捕获金融数据组合的尾部依赖结构，其中不同类型的尾部依赖共存。进一步地，我们测试藤蔓copus在多大程度上能够建模不同类型的尾巴依赖性。我们能够捕获不同类型的尾部依赖关系共存的金融数据组合的尾部依赖结构。进一步地，我们测试藤蔓copus在多大程度上能够建模不同类型的尾巴依赖性。我们能够捕获其中不同类型的尾部依赖共存的财务数据组合的尾部依赖结构。进一步地，我们测试藤蔓copus在多大程度上能够建模不同类型的尾巴依赖性。