Contributions to the analysis of credit risk data using advanced survival analysis techniques.

The Basel Accords, a set of recommendations for regulating the banking industry, have changed the strategies of financial institutions significantly. These accords allowed banks to use risk assessment based on their own models to determine the size of the buffer capital they need to hold against unexpected losses. This gave rise to a more model-based focus in the banking industry. With typically a major focus on basic regression techniques such as logistic regression for modelling ``good'' versus ``bad'' customers, growing interest in methods from other areas of statistics and machine learning was a result. One of these areas is survival analysis. Survival analysis deals with the analysis of the duration time until a certain event, such as the time of death in biological organisms. A typical property of survival analysis is the survival function S(t)=P(T>t), which is the probability that the time of the event of interest has not occurred by a stated time t. Defining loan “default” (or, by extension, “early repayment”) as the event of interest, the appropriateness of using survival analysis in the credit risk content becomes apparent. The advantage of using this method here, as opposed to more frequently used classification techniques, is that (1) It is possible to compute a ``probability of default'' or a PD-estimate at every point in time during the loan term. (2) One can predict the expected time of default. Despite the fact that there are certain analogies between medical survival and survival in a credit loan context, there are also differences that might make the standard survival approach inappropriate for the analysis of credit data. A basic assumption of survival analysis is that each subject will eventually experience the event of interest, but in reality, default will only take place for a small proportion of the population. To model a so-called ``insusceptible'' part of the loan population, mixture cure models can be used. In this thesis, we explain the mixture cure model in more detail in Chapter 1. As there is there is a missing data-issue since there is incomplete information on which part of the population is ``susceptible'' to default (or early repayment) and which part is not, an appropriate version of Akaike's information criterion (AIC) for variable selection is derived and applied to these models. Certain loan applicant characteristics that would affect the time of default or early repayment, might not be observed. In Chapter 2, this problem is addressed by incorporating ``unobserved heterogeneity'' in the mixture cure model. For model fitting purposes, a hierarchical expectation-maximization algorithm is derived. In Chapter 3, we take a step outside the mixture cure framework, and perform a benchmark study comparing several survival techniques (both mixture and non-mixture survival models). These survival analysis techniques are applied to ten different data sets from five Belgian financial institutions, and evaluated using three different types of evaluation metrics: receiver operating characteristics curves, default time prediction and expected future values of the loan. Chapter 4 extends the mixture cure model such that time-dependent covariates can be included. The method is applied to real life credit data including both personal (time-independent) information of the loan applicants and macro-economic factors that change over time, such as the unemployment and interest rates.status: publishe