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Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

   
 
 

 

Reverse stress testing in skew-elliptical models


Authors: Jonathan von Schroeder, Thorsten Dickhaus and Taras Bodnar
Journal: Theor. Probability and Math. Statist. 109 (2023), 101-127
MSC (2020): Primary 62E15; Secondary 62P05
DOI: https://doi.org/10.1090/tpms/1199
Published electronically: October 3, 2023
MathSciNet review: 4652996
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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.


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Additional Information

Jonathan von Schroeder
Affiliation: University of Bremen, Institute for Statistics, Bremen, Germany
Email: j.von.schroeder@gmail.com

Thorsten Dickhaus
Affiliation: University of Bremen, Institute for Statistics, Bremen, Germany
Email: dickhaus@uni-bremen.de

Taras Bodnar
Affiliation: Stockholm University, Department of Mathematics, Stockholm, Sweden
Email: taras.bodnar@math.su.se

Keywords: Bank regulation, constrained optimization, empirical likelihood, most likely scenario, parametric bootstrap, risk management
Received by editor(s): March 31, 2022
Accepted for publication: October 28, 2022
Published electronically: October 3, 2023
Additional Notes: The first author was supported by the Deutsche Forschungsgemeinschaft (DFG, http://dx.doi.org/10.13039/501100001659) within the framework of RTG 2224, entitled “$\pi ^3$: Parameter Identification – Analysis, Algorithms, Applications”.
Article copyright: © Copyright 2023 Taras Shevchenko National University of Kyiv