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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uj/uj:12589 |
| Date | 13 October 2014 |
| Creators | Van der Walt, Frederik Christoffel |
| Source Sets | South African National ETD Portal |
| Detected Language | English |
| Type | Thesis |
| Rights | University of Johannesburg |
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