Modelling Credit Card Exposure at Default: Novel Applications of Additive Models and Copula Regression

Abstract

The thesis comprises three papers that contribute to the consumer credit risk literature by studying the Exposure At Default (EAD) of credit card portfolios. Three novel EAD modelling approaches are proposed, each tackling different practical prediction and interpretation challenges.

The first paper distinguishes between two groups of card borrowers — those whose balance hits the limit as they approach default time, and those who do not. We conjecture that the level of EAD as well as its risk drivers could be significantly different between the two groups. Hence, we propose a two-component mixture model that conditions EAD on these two respective scenarios, using the Generalised Additive Models for Location, Scale and Shape (GAMLSS) framework. Having fitted our proposed model to a real-life dataset of credit card defaults, we find that the mean and dispersion of EAD in the two respective submodels are indeed impacted by different risk factors. More importantly, we find that the proposed model produces a clear improvement in predictive performance.

The second paper studies the dependence between the Probability of Default (PD) and credit card balance, and investigates how this dependence impacts EAD and, thus, expected loss estimation. A joint model for PD and balance is introduced by applying the bivariate Copula Generalised Additive Models for Location, Scale and Shape framework. Using this framework, the two responses can be modelled flexibly under the GAMLSS setting while their association can be captured by a suitable copula. The proposed method also addresses potential sample selection bias by extending the analysis to outstanding balance (rather than simply balance at default time, or EAD) over a sample of both defaults and non-defaults. The proposed model is shown to produce more accurate and sufficiently conservative expected loss estimates, at both individual account and portfolio level.

Most EAD modelling research thus far has focused on point estimation approaches, whilst information on extreme quantiles, rather than the mean, can have greater implications in practice. In order to produce conditional quantiles and interval estimates for EAD, the third paper proposes the use of vine copula-based quantile regression. The proposed method automatically avoids the quantile crossing and multicollinearity problems associated with conventional quantile regression and allows relationships between all of the variables of interest (including EAD) to be modelled through a series of pair-copulas. The analysis shows that the proposed model provides better point and interval EAD estimates and more accurately reflects its actual distribution compared to other models.

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Identifiers

ORCID for Christophe Mues: orcid.org/0000-0002-6289-5490

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