Stress Tests: From Arts to Science

29 Pages Posted: 10 Jan 2010 Last revised: 28 Sep 2010

See all articles by Thomas Breuer

Thomas Breuer

University of Applied Sciences Vorarlberg

Imre Csiszar

Hungarian Academy of Sciences (HAS) - Alfréd Rényi Institute of Mathematics

Date Written: September 27, 2010

Abstract

Stress tests with handpicked scenarios might misrepresent risks either because the scenarios considered are too implausible or because some dangerous scenarios are not considered. Systematic search for the worst case within some set of plausible scenarios is introduced to overcome these two pitfalls. For arbitrary loss functions we determine explicitly the worst case scenario over Kullback-Leibler spheres of plausible scenarios. Practical implementations of this method do not require any numerical optimisation. The method is illustrated in a number of example applications: linear and quadratic portfolios, stressed credit default probabilities, stressed rating transition correlations.

Keywords: scenario analysis, worst case, risk measures, multiple priors, model risk, ambiguity aversion, relative entropy, maximum entropy principle, Levenberg-Marquardt algorithm

JEL Classification: C18, C44, C60, G01, G32, M48

Suggested Citation

Breuer, Thomas and Csiszar, Imre, Stress Tests: From Arts to Science (September 27, 2010). Available at SSRN: https://ssrn.com/abstract=1328022 or http://dx.doi.org/10.2139/ssrn.1328022

Thomas Breuer (Contact Author)

University of Applied Sciences Vorarlberg ( email )

Hochschulstr. 1
Dornbirn, A-6850
Austria

Imre Csiszar

Hungarian Academy of Sciences (HAS) - Alfréd Rényi Institute of Mathematics

Realtanoda u 13-15
Budapest
Hungary

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