Stochastic loss given default and exposure at default in a structural model of portfolio credit risk

Florian Kaposty, Matthias Löderbusch and Jakob Maciag

Abstract

In this paper, we develop a factor-type latent variable model for portfolio credit risk that accounts for stochastically dependent probability of default (PD), loss given default (LGD) and exposure at default (EAD) at both the systematic and borrower specific levels. By employing a comprehensive simulation study, we set our results in contrast to those obtained using the asymptotic single risk factor (ASRF) model that underlies Basel II and III. Several sensitivity and robustness analyses for different parameter assumptions are conducted to break down our results. As required by the regulator, we show how to map our portfolio credit loss quantiles with correlated PD, LGD and EAD into values for downturn LGD and EAD. Our analyses reveal that stochastically dependent defaults, LGD and EAD increase a credit portfolio’s tail risk significantly. Estimating risk markups separately can therefore lead to substantially underestimating the inherent risk of a portfolio with nondeterministic exposures. Further, we show that relative downturn markups on LGD and EAD depend strongly on asset correlations and, in particular, that credit portfolios with low asset correlations might be prone to an underestimation of additional capital charges for stochastically dependent LGD and EAD. Thus, our results are of economic significance for banks and regulators when setting up minimum capital requirements.