Basel requirements of downturn loss given default: modeling and estimating probability of default and loss given default correlations

Basel II requires that banks use downturn loss given default (LGD) estimates in regulatory capital calculations, citing the fact that the probability of default (PD) and LGD correlations are not captured. We show that the lack of correlation can be taken care of by incorporating a certain degree of conservatism in cyclical LGD in a point-in-time (PIT) framework. We examine a model that can capture the PD and LGD correlation in its entirety, differentiating the different components of correlations in question. Using historical LGD and default data of a loan portfolio, we calibrate our model and, through the simulation of economic capital, we show that the mean LGD needs to be increased by about 35% to 41% for a corporate portfolio and about 16% for a mid-market portfolio in order to compensate for the lack of correlations. Our hope is to provide a framework that the banks can use based on their internal data to estimate and justify their LGD choices for different portfolios. Although the paper is presented within the context of Basel II, the applications could be widened to include structured finance, credit derivatives, economic capital and portfolio modeling in general, where PD and LGD correlations need to be estimated and modeled.