Generalized Impulse Responses of Portfolio Default Probabilities: A Modular Framework with an Application to Geopolitical Risk

Abstract

Credit stress testing requires impulse responses of portfolio default probabilities, not only macro-financial drivers. We derive closed-form generalized impulse responses for the mean, quantiles (PD-at-Risk), and expected shortfall in a modular framework combining a Bayesian VAR, a Gaussian satellite, and the Merton-Vasicek model underlying Basel IRB regulation. Results extend to any probit-Gaussian mapping of a latent factor. Nonlinearity makes responses depend on conditional means and variances; plug-in evaluations understate projected default probability levels by 6-8% and miss tail quantiles. For U.S. geopolitical risk shocks, 99%-quantile responses exceed mean responses by 50%, and peak responses vary 4.6-fold across the credit cycle.