Correlation between default events and loss given default and downturn loss given default in Basel II

ABSTRACT We derive analytically the effects of PD-LGD correlation on portfolio credit VaR and economic capital with a structural form model and show that under certain assumptions, an approximate linear relationship between downturn loss given default and expected loss given default exists. Thus we provide a model-theoretic justification of the formula in the US Basel II NPR (2006) that relates downturn loss given default to expected loss given default, a formula that has become rather controversial in the implementation of Basel II in the US.