Dynamics of Probabilities of Default

64 Pages Posted: 19 Aug 2024

See all articles by Peter Bednarek

Peter Bednarek

Deutsche Bundesbank

Guenter Franke

University of Konstanz - Department of Economics

Date Written: June 10, 2024

Abstract

Probabilities of default (PDs) of loans are of central importance for financial stability. We analyze the PDs, reported quarterly by German financial institutions to Deutsche Bundesbank. The development of PDs is modelled as an AR process of PD changes and an initial PD. Panel regressions show mean diversion of the PDs in the short-run and mean reversion to target-PDs over longer time intervals. The expected PD does not converge monotonically to the target PD, but overshoots and oscillates with declining amplitude. The PD converges faster to the target PD starting at a high relative to a low PD. The target PD is lower when more than one institution reports a PD, also in the case if the borrower exhibits unlimited liability. To bypass instabilities in PD time series, due to systematic factors, we also rank firms within an industry according to their PDs. This rank order is driven mostly by idiosyncratic firm factors and portrays competitiveness of debtors. Migrations are defined by changes in this rank order. We also find mean diversion of migrations in the short-run and mean reversion over longer time intervals.

Keywords: Dynamics of probabilities of default, systematic and idiosyncratic factors, mean diversion and reversion, overshooting, oscillations

JEL Classification: D25, E51, G11, G14, G17, G21, G32

Suggested Citation

Bednarek, Peter and Franke, Guenter, Dynamics of Probabilities of Default (June 10, 2024). Deutsche Bundesbank Discussion Paper No. 32/2024, Available at SSRN: https://ssrn.com/abstract=4930492

Peter Bednarek (Contact Author)

Deutsche Bundesbank ( email )

Wilhelm-Epstein-Str. 14
Frankfurt/Main, 60431
Germany
004969 9566-8972 (Phone)

HOME PAGE: http://www.bundesbank.de

Guenter Franke

University of Konstanz - Department of Economics ( email )

Fach 147
Konstanz, 78457
Germany
+49 7531 88 2545 (Phone)
+49 7531 88 3559 (Fax)

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