Generalized Impulse Responses of Portfolio Default Probabilities: A Modular Framework with an Application to Geopolitical Risk
This study addresses the lack of systematic analysis of the dynamic response of portfolio-level probability of default (PD) in existing credit stress-testing frameworks. The authors propose a modular framework that integrates Bayesian vector autoregression, Gaussian latent variable models, and the Merton–Vasicek structural credit model to derive, for the first time, analytical solutions for nonlinear generalized impulse responses of PD mean, quantiles (PD-at-Risk), and expected shortfall. This approach captures the joint influence of conditional mean and variance on PD dynamics, overcoming limitations of conventional interpolation methods that underestimate PD by 6–8% and neglect tail risk. Empirical results demonstrate that under geopolitical shocks, the 99th percentile PD response exceeds the mean response by 50%, with peak responses during credit cycles differing by up to a factor of 4.6.