Eurozone Sovereign Default Risk and Capital: A Bayesian Approach

Abstract

Using a Bayesian generalized linear mixed model (GLMM), we analyze Eurozone sovereign real-world default probabilities and correlations, and compare regulatory and economic capital requirements. The approach combines prior information and sparse sovereign historical default data. One main finding is that capital under the Basel internal ratings based approach (IRBA) is higher than under the standardized approach (SA) by a factor of 2.06 to 8.86, depending on the method for estimating the probability of default. This divergence is driven mainly by zero capital charges for highly rated securities under the SA. Furthermore, under the Bayesian model, Basel IRBA capital is roughly equivalent to economic capital using the expected shortfall at a 99% confidence level. The results suggest that the zero risk weights under the SA are not consistent with economic risk and offer opportunities for regulatory arbitrage.