Advances in Multivariate Back-testing for Credit Risk Underestimation

35 Pages Posted: 5 Jul 2016

See all articles by François Coppens

François Coppens

National Bank of Belgium

Manuel Mayer

Oesterreichische Nationalbank (OeNB)

Laurent Millischer

European Central Bank (ECB)

Florian Resch

Oesterreichische Nationalbank (OeNB)

Stephan Sauer

European Central Bank (ECB)

Klaas Schulze

Deutsche Bundesbank

Date Written: February 24, 2016

Abstract

When back-testing the calibration quality of rating systems two-sided statistical tests can detect over- and under-estimation of credit risk. Some users though, such as risk-averse investors and regulators, are primarily interested in the under-estimation of risk only, and thus require one-sided tests. The established one-sided tests are multiple tests, which assess each rating class of the rating system separately and then combine the results to an overall assessment. However, these multiple tests may fail to detect under-performance of the whole rating system. Aiming to improve the overall assessment of rating systems, this paper presents a set of one-sided tests, which assess the performance of all rating classes jointly. These joint tests build on the method of Sterne [1954] for ranking possible outcomes by probability, which allows to extend back-testing to a setting of multiple rating classes. The new joint tests are compared to the most established one-sided multiple test and are further shown to outperform this benchmark in terms of power and size of the acceptance region.

Keywords: credit ratings, probability of default, back-testing, one-sided

JEL Classification: C12, C52, G21, G24

Suggested Citation

Coppens, Francois and Mayer, Manuel and Millischer, Laurent and Resch, Florian and Sauer, Stephan and Schulze, Klaas, Advances in Multivariate Back-testing for Credit Risk Underestimation (February 24, 2016). ECB Working Paper No. 1885, Available at SSRN: https://ssrn.com/abstract=2737358 or http://dx.doi.org/10.2139/ssrn.2737358

Francois Coppens (Contact Author)

National Bank of Belgium ( email )

Brussels, B-1000
Belgium

Manuel Mayer

Oesterreichische Nationalbank (OeNB) ( email )

Otto-Wagner-Platz 3, PO Box 61
Vienna,
1010 Vienna, A-1011
Austria

Laurent Millischer

European Central Bank (ECB) ( email )

Sonnemannstrasse 22
Frankfurt am Main, 60314
Germany

Florian Resch

Oesterreichische Nationalbank (OeNB) ( email )

Otto-Wagner-Platz 3, PO Box 61
Vienna,
1010 Vienna, A-1011
Austria

Stephan Sauer

European Central Bank (ECB) ( email )

Sonnemannstrasse 22
Frankfurt am Main, 60314
Germany

HOME PAGE: http://www.ecb.int

Klaas Schulze

Deutsche Bundesbank ( email )

Wilhelm-Epstein-Str. 14
Frankfurt/Main, 60431
Germany

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