To model the Exposure At Default (EAD) of revolving credit facilities, such as credit cards, most of the research thus far has employed point estimation approaches, focusing on the central tendency of the outcomes. However, such approaches may have difficulties coping with the high variance of EAD data and its non-normal empirical distribution, whilst information on extreme quantiles, rather than the mean, can have greater implications in practice. Also, many of the input variables used in EAD models are strongly correlated, which further complicates model building. This paper, therefore, proposes vine copula-based quantile regression, an interval estimation approach, to model the entire distribution of EAD and predict its conditional mean and quantiles. This methodology addresses several drawbacks of classical quantile regression, including quantile crossing and multicollinearity, and it allows the multi-dimensional dependencies between all variables in any EAD dataset to be modelled by a suitable series of (either parametric or non-parametric) pair-copulas. Using a large dataset of credit card accounts, our empirical analysis shows that the proposed non-parametric model provides better point and interval estimates for EAD, and more accurately reflects its actual distribution, compared to a selection of other models.

为了对信用卡等循环信贷设施的违约风险（EAD）进行建模，迄今为止大多数研究都采用点估计方法，重点关注结果的集中趋势。然而，此类方法可能难以应对 EAD 数据的高方差及其非正态经验分布，而极端分位数（而不是均值）的信息在实践中可能具有更大的影响。此外，EAD 模型中使用的许多输入变量都是强相关的，这进一步使模型构建变得复杂。因此，本文提出基于 vine copula 的分位数回归（一种区间估计方法）来对 EAD 的整个分布进行建模并预测其条件均值和分位数。这种方法解决了经典分位数回归的几个缺点，包括分位数交叉和多重共线性，并且它允许通过一系列合适的（参数或非参数）对联结对任何 EAD 数据集中所有变量之间的多维依赖性进行建模。使用信用卡账户的大型数据集，我们的实证分析表明，与选择的其他模型相比，所提出的非参数模型为 EAD 提供了更好的点和区间估计，并且更准确地反映了其实际分布。