Using the Bayesian sampling method to estimate corporate loss given default distribution

Abstract

We use Markov chain Monte Carlo (MCMC) sampling to draw model coefficients to generate LGD distributions. We find that applying this Bayesian method on a sophisticated model, such as the zero-one-inflated beta (ZOIB) model, that accounts for the bi-modal distribution of the LGDs can generate LGD distributions that mimic the observed distributions well. By contrast, applying this Bayesian sampling approach on a simple model such as Tobit cannot capture the bi-modal LGD distributions accurately. Finally, we argue that this Bayesian sampling approach to generate LGD distributions is better fit for the stress testing purpose than the typical approach to estimate LGD model coefficients and then stress the macro variables. The latter approach yields stressed LGDs that may not be conservative enough, even if the macro variables are stressed to their worst historical values.