Estimating Long-Run PD, Asset Correlation, and Portfolio Level PD by Vasicek Models

In this paper, we propose a Vasicek-type of models for estimating portfolio level probability of default (PD). With these Vasicek models, asset correlation and long-run PD for a risk homogenous 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 square regression, which greatly simplifies parameter estimation. The analytical formula for long-run PD, for example, explicitly quantifies the contribution of uncertainty to an increase of long-run PD. 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 13 industry sectors using corporate annual default rates from S&P for years 1981-2011, and long-run PD and asset correlation for a US commercial portfolio, using US delinquent rate for commercial and industry loans from US Federal Reserve.