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

Patrick Kurth, Max Nendel and Jan Streicher

We present a statistical test for the long-term calibration in rating systems that can deal with overlapping time windows as required by the guidelines of the European Banking Authority (EBA), which apply to major financial institutions in the European System. In accordance with regulation, rating systems are to be calibrated and validated with respect to the long-run default rate. The consideration of one-year default rates on a quarterly basis leads to correlation effects which drastically influence the variance of the long-run default rate. In a first step, we show that the long-run default rate is approximately normally distributed. 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.

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Year of publication:	2024
Authors:	Kurth, Patrick ; Nendel, Max ; Streicher, Jan
Subject:	hypothesis test \| credit risk \| rating system \| validation \| backtesting \| long-run default rate \| EBA guidelines \| correlation effects \| Kreditrisiko \| Credit risk \| Statistischer Test \| Statistical test \| Kreditwürdigkeit \| Credit rating \| Theorie \| Theory \| Korrelation \| Correlation

Type of publication:	Article
Type of publication (narrower categories):	Aufsatz in Zeitschrift ; Article in journal
Language:	English
Other identifiers:	10.3390/risks12080131 [DOI]
Classification:	C12 - Hypothesis Testing ; C52 - Model Evaluation and Testing ; G28 - Government Policy and Regulation ; G32 - Financing Policy; Capital and Ownership Structure
Source:	ECONIS - Online Catalogue of the ZBW

Persistent link: https://ebvufind01.dmz1.zbw.eu/10015065887