arXiv subjects

Christophe Hurlin

Publications and source records attributed to Christophe Hurlin.

4 recordsLinked to original sources

arXiv2026

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

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.

econ.EM↗

arXiv2026

Reverse Stress Testing Geopolitical Risk in Corporate Credit Portfolios: A Formal and Operational Framework

This paper proposes a formal framework for reverse stress testing geopolitical risk in corporate credit portfolios. A joint macro-financial scenario vector, augmented with an explicit geopolitical risk factor, is mapped into stressed probabilities of default and losses given default. These stresses are then propagated to portfolio tail losses through a latent factor structure and translated into a stressed CET1 ratio, jointly accounting for capital depletion and risk-weighted asset dynamics. Reverse stress testing is formulated as a constrained maximum likelihood problem over the scenario space. This yields a geopolitical point reverse stress test, or design point, defined as the most probable scenario that breaches a prescribed capital adequacy constraint under a reference distribution. The framework further characterises neighbourhoods and near optimal sets of reverse stress scenarios, allowing for sensitivity analysis and governance oriented interpretation. The approach is compatible with internal rating based models and supports implementation at the exposure or sector level.

econ.EM↗

arXiv2024

Backtesting Expected Shortfall: Accounting for both duration and severity with bivariate orthogonal polynomials

We propose an original two-part, duration-severity approach for backtesting Expected Shortfall (ES). While Probability Integral Transform (PIT) based ES backtests have gained popularity, they have yet to allow for separate testing of the frequency and severity of Value-at-Risk (VaR) violations. This is a crucial aspect, as ES measures the average loss in the event of such violations. To overcome this limitation, we introduce a backtesting framework that relies on the sequence of inter-violation durations and the sequence of severities in case of violations. By leveraging the theory of (bivariate) orthogonal polynomials, we derive orthogonal moment conditions satisfied by these two sequences. Our approach includes a straightforward, model-free Wald test, which encompasses various unconditional and conditional coverage backtests for both VaR and ES. This test aids in identifying any mis-specified components of the internal model used by banks to forecast ES. Moreover, it can be extended to analyze other systemic risk measures such as Marginal Expected Shortfall. Simulation experiments indicate that our test exhibits good finite sample properties for realistic sample sizes. Through application to two stock indices, we demonstrate how our methodology provides insights into the reasons for rejections in testing ES validity.

q-fin.RM↗

arXiv2022

The Fairness of Credit Scoring Models

In credit markets, screening algorithms aim to discriminate between good-type and bad-type borrowers. However, when doing so, they can also discriminate between individuals sharing a protected attribute (e.g. gender, age, racial origin) and the rest of the population. This can be unintentional and originate from the training dataset or from the model itself. We show how to formally test the algorithmic fairness of scoring models and how to identify the variables responsible for any lack of fairness. We then use these variables to optimize the fairness-performance trade-off. Our framework provides guidance on how algorithmic fairness can be monitored by lenders, controlled by their regulators, improved for the benefit of protected groups, while still maintaining a high level of forecasting accuracy.

stat.ML↗