How Well Does the Vasicek-Basel Airb Model Fit the Data? Evidence from a Long Time Series of Corporate Credit Rating Data

I develop methods that produce consistent estimates of the Vasicek-Basel IRB (VAIRB) credit risk model parameters. I apply these methods to Moody's data on corporate defaults over the period 1920–2008 and assess the model fit and construct hypothesis tests using bootstrap methods. The results show that the VAIRB does not capture the variability in Moody's default data: there are numerous episodes in which obligors default with much greater frequency than predicted. This pattern is consistent with a missing common factor that affects default correlation only intermittently — a missing factor similar to the frailty covariate in Duffie et al. (2009). Unlike Lopez (2004), I find the VAIRB correlation parameter to be larger for lower-rated credits. I use estimates of the VAIRB error distribution to construct capital allocations for model risk and find that the capital buffers for model risk are substantial, especially for lower-graded credits. VAIRB common factor estimates exhibit positive autocorrelation and thus long time series are usually necessary to produce reliable model estimates. Alternatively, I use common factor and correlation parameter estimates from the 1920-2008 data to control for common factor realizations when estimating unconditional default rates (PDs) from short samples. I estimate PDs and confidence intervals using default data for Moody's alpha-numeric rating grades (1998-2008). After correcting for common factor effects, sample average default rates are shown to overstate the PD for most credit grades in this sample period