A hypothesis test for the long-term calibration in rating systems with overlapping time windows

Patrick Kurth, Max Nendel and Jan Streicher
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Patrick Kurth: Center for Mathematical Economics, Bielefeld University
Max Nendel: Center for Mathematical Economics, Bielefeld University
Jan Streicher: Center for Mathematical Economics, Bielefeld University

No 735, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: We present a statistical test that can be used to verify supervisory re- quirements concerning overlapping time windows for the long-term calibration in rating systems. In a first step, we show that the long-run default rate is approximately normally distributed with respect to random effects in default realization. We then perform a detailed analysis of the correlation effects caused by the overlapping time windows and solve the problem of an unknown distribution of default probabilities for the long-run default rate. In this context, we present several methods for a conservative calibration test that can deal with the unknown variance in the test statistic. We present a test for individual rating grades, and then pass to the portfolio level by suitably adapting the test statistic. We conclude with comparative statics analysing the effect of persisting customers and the number of customers per reference date.

Pages: 29
Date: 2025-08-14
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https://pub.uni-bielefeld.de/download/3006162/3006163 First Version, 2023 (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:735

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