Ph.D. (Mathematical Statistics) / This thesis considers the modelling and prediction of consumer credit risk events. We model consumer credit risk events (like a missed payment, a repayment or a default) by means of a discrete, real time, staggered entry counting process. Merton s (1974) structural approach is the foundation of numerous credit-risk models, as well as the Basel capital accords. The underlying assumptions of this approach are that both liability and asset levels are observable to some extent and that default, which occurs if liability levels are larger than asset levels, can occur only once. These assumptions are inappropriate for consumer credit risk, where asset and liability levels are not observable and multiple defaults may occur. We nd that the so-called reduced-form models initially developed by Artzner and Delbaen (1995) and Jarrow and Turnbull (1995), which impose no structure on the default event, are better suited to model and predict consumer credit risk. All reduced-form models can be represented as counting processes. Counting processes are continuous in nature, so we discretize these processes before applying them to the regularly spaced, discrete monthly data. We show that the use of survival analysis tech- niques such as Cox s (1972) proportional hazard model, which is a special case in counting processes, are not well suited to model credit risk. This is because survival analysis is mostly concerned with the prediction of the time until a single event occurs. Accordingly, in survival analysis the time domain used is event time . Hence, all observations need to be aligned to some starting time. We prefer to work in calendar time and are concerned with the timing (in calendar time) of multiple events. We identify and implement a dynamic, discrete statistical model based on calendar time that accounts for staggered entries, multiple entries into and exits from the portfolio, as well as multiple default events on an account level. This approach, from Arjas and Haara (1987), makes use of both idiosyncratic and systematic covariates, which facilitates stress-testing. This approach has, to our knowledge, never been applied to credit risk before and we apply it to a mortgage loan portfolio of a major bank in South Africa.

The objective of this research is to investigate the existence of structural changes in unsecured lending time series data and analyse the impact thereof on trends in consumer demand for unsecured credit spanning the years from 2008 to 2015. This is achieved by identifying dates when structural changes occurred over this period. The identified structural break date is linked to an influential economic event or monetary policy change that took place in South Africa of which the impact on three unsecured credit categories are analysed. Unsecured credit growth in South Africa has been subjected to intensive scrutiny since the inception of the National Credit Act (Act No. 34 of 2005) by various regulatory bodies. In 2012 the National Credit Regulator (NCR) commissioned a research study into examining the impact that the National Credit Act (Act No. 34 of 2005) has had on the consumer credit market. The empirical part of this study involved the gathering of time series data on unsecured loans approved, unsecured credit granted per income category and unsecured credit granted from the National Credit Regulator (NCR) database and performing descriptive and econometric analysis. The Zivot-Andrews (1992) and augmented Dickey-Fuller tests determined the break dates which were linked to a significant economic event while the one sample t-test of means compared average loan values before and after the break date. Results of the study indicate that the break dates determined coincided with economic events and monetary policy changes in South Africa, such as the collapse of African Bank, the implementation of the National Credit Amendment Act, prime interest rate movements and the introduction of a debt counselling program by the government. These events, coupled with stricter lending criteria and no further loans being granted to customers already more than three months in arrears, restrained the uptake of unsecured loans to lower and middle income groups. The introduction of new affordability criteria and increasing interest rates in 2014 further negatively impacted demand for unsecured loans. However, higher income earners had the advantage of being able to apply for higher loan amounts. Findings could be used by monetary policymakers and financial institutions to constantly monitor credit trends, improve credit assessment techniques and review lending criteria. / Business Management / M. Com. (Financial Management)