Theory of Probability and Mathematical Statistics
Reverse stress testing in skew-elliptical models
Jonathan von Schroeder, Thorsten Dickhaus and Taras Bodnar
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Abstract: Stylized facts about financial data comprise skewed and heavy-tailed (log-)returns. Therefore, we revisit previous results on reverse stress testing under elliptical models, and we extend them to the broader class of skew-elliptical models. In the elliptical case, an explicit formula for the solution is provided. In the skew-elliptical case, we characterize the solution in terms of an easy-to-implement numerical optimization problem. As specific examples, we investigate the classes of skew-normal and skew-t models in detail. Since the solutions depend on population parameters, which are often unknown in practice, we also tackle the statistical task of estimating these parameters and provide confidence regions for the most likely scenarios.
Keywords: Bank regulation, constrained optimization, empirical likelihood, most likely scenario, parametric bootstrap, risk management
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