Statistical Inference in the Asymptotic Single Risk Factor Model

Quant Talk
Wednesday, 20 January 2010
6.30 pm, room 21

No registration necessary. Just turn up and enjoy!

After the development of advanced credit portfolio models, financial institutions are now challenged to implement meaningful stress tests in order to improve their risk management. From a statistical point of view, stress-testing considers unfavourable changes in the parameters of the underlying credit portfolio model. Using the Basel II asymptotic single risk factor (ASRF) model, which is a standard credit portfolio model in the banking industry, the model parameters of interest are default probabilities and correlations (asset, default or survival time correlations). The crucial question is how stress scenarios for these model parameters can be identified. To this end, three versions of the ASRF model are considered: (a) known default probabilities but unknown asset correlations, (b) known asset correlations but unknown default probabilities and (c) all model parameters are unknown. Firstly, for each version of the ASRF model, model-inherent worst-case scenarios for the unknown model parameters are derived and their impact on the economic capital is analyzed. If, for example, the ASRF model with known default probabilities is considered, then higher asset correlations do not always lead to higher stress and increased economic capital, i. e. worst-case correlations less than one exist. Secondly, individual and simultaneous confidence intervals for the unknown model parameters are developed. These confidence intervals are analytically describable and are not based on simulation or bootstrap methods. Since the length of these confidence intervals depends on the confidence level chosen and on the data, confidence intervals can be used to identify data-based stress scenarios for the model parameters