Worst-Case and Stressed Correlations in the Asymptotic Single Risk Factor Model

Steffi Höse and Stefan Huschens

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. In addition to this internal risk control, stress tests are part of the regulatory requirements of the revised capital adequacy framework, known as Basel II.11Cf, Basel Committee on Banking Supervision (2006, pp. 213–217).

From a statistical point of view, in stress testing, unfavourable changes in the parameters of the underlying credit portfolio model are considered. Using the Basel II asymptotic single risk factor (ASRF) model, the model parameters of interest are the asset correlations and the default probabilities of the obligors. The crucial question is how stress scenarios for these model parameters can be identified.

As most of the literature focuses on stressing default probabilities with given asset correlations,22For example Bühn and Richter (2006) and Deutsche Bundesbank (2007, p. 113). the opposite approach is taken in this contribution.33For a simultaneous consideration of the model parameters based on statistical estimation methods cf, Höse (2007, Chapters 4.3, 6) and Rösch and Scheule

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