A Rank Estimator Approach to Modeling Default Frequencies

Abstract

This study introduces a non-parametric methodology for estimating expected frequencies of defaults and other credit events. The methodology allows for an independent estimation of a credit-quality variable, referred to as a default rank variable. In a subsequent step, the relationship between the rank variable and the expected default frequency is established. This analysis can be achieved by initially determining the functional dependence between the rank variable and the expected tail default frequencies representing the average default frequencies of entities ranked lower than a given rank value. The expected default frequency can then be derived from a simple linear integral equation. We propose a prototype model for public corporations which establishes generalized logistic function dependencies between the distance-to-default rank variable and the expected default frequencies in the log–log space. This relationship applies to public corporations across different credit rating categories.