Estimating default probabilities for no- and low-default portfolios: parameter specification via floor constraints

Abstract

For low- and no-default portfolios, financial institutions are confronted with the problem to estimate default probabilities for credit ratings for which no default was observed. The Bayesian approach offers a solution but brings the problem of the parameter assignment of the prior distribution. Sequential Bayesian updating allows to settle the question of the location parameter or mean of the prior distribution. This article proposes to use floor constraints to determine the scale or standard deviation parameter of the prior distribution. The floor constraint can also be used to determine the free parameter γ in the Pluto–Tasche approach.