Estimating Probabilities of Default for Low Default Portfolios

24 Pages Posted: 27 Dec 2004

See all articles by Dirk Tasche

Dirk Tasche

Swiss Financial Market Supervisory Authority (FINMA)

Katja Pluto

Deutsche Bundesbank

Date Written: December 2004


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 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 without too much effort.

Keywords: Probability of default, low default portfolio, most prudent estimation, confidence bound

JEL Classification: C14, C15

Suggested Citation

Tasche, Dirk and Pluto, Katja, Estimating Probabilities of Default for Low Default Portfolios (December 2004). Available at SSRN: or

Dirk Tasche (Contact Author)

Swiss Financial Market Supervisory Authority (FINMA) ( email )

Einsteinstrasse 2
Bern, 3003

Katja Pluto

Deutsche Bundesbank ( email )

Wilhelm-Epstein-Str. 14
Frankfurt/Main, 60431

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