Rating frailty, Bayesian updates, and portfolio credit risk analysis

This paper studies how to utilize individual ratings and credit performance for portfolio credit risk analysis and surveillance. We model the default intensity of firms using a proportional form, with rating specific individual frailty to account for heterogeneity within a rating group, as well as rating specific exposure to observable macro covariates, industries and a latent mean-reverting macro frailty factor. To estimate the model, we take the Bayesian approach and develop a Markov chain Monte Carlo-based algorithm. This approach enables us to quantify parameter uncertainty which is crucial for forecasting and it also provides a convenient tool for performing updates. Using a large default dataset spanning a period of 45 years including the 2008 financial crisis, we provide strong evidence for the dependence of individual frailty and exposure to systematic risk factors on credit rating. In out-of-sample testing, we showcase the ability of our model to forecast the number of defaults through business cycles and particularly in the financial crisis. Furthermore, by monitoring a collateralized loan obligation (CLO), we show that our model can perform reasonably well for the surveillance purpose with timely updates, even if the data used for the initial calibration of the model does not contain the firms in the CLO.