Mixture models for consumer credit risk

Abstract

The three papers in this thesis comprise the development of three types of Basel models – a Probability of Default (PD), Loss Given Default (LGD) and Exposure at Default (EAD) model for consumer credit risk, using mixture model methods. Mixture models consider the underlying population as being composed of different sub-populations that are modelled separately. In the first paper (Chapter 2), mixture cure models are introduced to the area of PD/credit scoring. A large proportion of the dataset may not experience the event of interest during the loan term, i.e. default. A mixture cure model predicting (time to) default on a UK personal loan portfolio was developed and its performance compared to industry standard models. The mixture cure model's ability to distinguish between two subpopulations can offer additional insights by estimating the parameters that determine susceptibility to default in addition to parameters that influence time to default of a borrower. The second paper (Chapter 3) considers LGD modelling. One of the key problems in building regression models to estimate loan-level LGD in retail portfolios such as mortgage loans relates to the difficulty in modelling its distribution, which typically contains an extensive amount of zeroes. An alternative approach is proposed in which a mixed discrete-continuous model for the total loss amount incurred on a defaulted loan is developed. The model simultaneously accommodates the probability of zero loss and the loss amount given that loss occurs. This zero-adjusted gamma model is shown to present an alternative and competitive approach to LGD modelling. The third paper (Chapter 4) considers EAD models for revolving credit facilities with variable exposure. The credit conversion factor (CCF), the proportion of the current undrawn amount that will be drawn down at time of default, is used to calculate the EAD and poses modelling challenges with challenging bimodal distributions. We explore alternative EAD models which ignore the CCF formulation and target the EAD distribution directly. We propose a mixture model with the zero-adjusted gamma distribution and compare performance with CCF based models. We find the mixture model to be more accurate in calibration than the CCF models and that segmented approaches offer further performance improvements.

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Identifiers

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

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