Modelling credit card exposure at default using vine copula quantile regression

Abstract

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.