Granularity adjustment for default risk factor model with cohorts

This paper examines granularity adjustments to parameter estimators in a default risk model with cohorts. The model is an extension of the Vasicek model (Vasicek, 1991) and includes a general factor and cohort specific factors. The granularity adjustments derived in the paper concern the mean and/or the variance of observed default frequencies and are easy to implement in practice. For illustration, the method is applied to the S&P corporate ratings. The Granularity Adjusted (GA) estimators are compared to the unadjusted estimators in terms of their asymptotic properties and in finite sample.