Dynamics of Probabilities of Default

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