Estimating Probabilities of Default for Low Default Portfolios

TL;DR

This paper proposes a conservative method for estimating probabilities of default in low-default credit portfolios, ensuring prudence and respecting credit quality differences, with applicability under independent and correlated default assumptions.

Contribution

It introduces the 'most prudent estimation' principle, using upper confidence bounds to improve PD estimates for portfolios with few or no defaults.

Findings

Provides a methodology for conservative PD estimation

Ensures PD ordering respects credit ratings

Applicable to both independent and correlated defaults

Abstract

For credit risk management purposes in general, and for allocation of regulatory capital by banks in particular (Basel II), numerical assessments of the credit-worthiness of borrowers are indispensable. These assessments are expressed in terms of probabilities of default (PD) that should incorporate a certain degree of conservatism in order to reflect the prudential risk management style banks are required to apply. In case of credit portfolios that did not at all suffer defaults, or very few defaults only over years, the resulting naive zero or close to zero estimates would clearly not involve such a sufficient conservatism. As an attempt to overcome this issue, we suggest the "most prudent estimation" principle. This means to estimate the PDs by upper confidence bounds while guaranteeing at the same time a PD ordering that respects the differences in credit quality indicated by the rating grades. The methodology is most easily applied under an assumption of independent default events but can be adapted to the case of correlated defaults.