Estimating long-run probability of default, asset correlation and portfolio-level probability of default using Vasicek models

ABSTRACT In this paper, we propose Vasicek-type models for estimating portfolio-level probability of default (PD). With these Vasicek models, asset correlation and long-run PD (LRPD) for a risk-homogeneous portfolio both have analytical solutions, longer external time series for market and macroeconomic variables can be included, and the traditional asymptotic maximum likelihood approach can be shown to be equivalent to least squares regression, which greatly simplifies parameter estimation. The analytical formula for LRPD, for example, explicitly quantifies the contribution of uncertainty to an increase of LRPD. We recommend the bootstrap approach to addressing the serial correlation issue for a time series sample. To validate the proposed models, we estimate the asset correlations for thirteen industry sectors, using corporate annual default rates from S&P for 1981-2011, and LRPD and asset correlation for a US commercial portfolio, using US delinquent rate for commercial and industry loans from US Federal Reserve.