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

2026-08-05

AI Summary

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.

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.

Problem

• credit stress testing
• portfolio default probabilities
• impulse responses
• tail risk
• nonlinearity

Innovation

• Generalized Impulse Responses
• Portfolio Default Probabilities
• Modular Framework
• Bayesian VAR
• PD-at-Risk