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Square, Inc.

Industry researchnorthamerica · us
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Research library2linked papers
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Selected work

Representative Papers

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

Aug 05, 2026

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.

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

Jan 07, 2026

This study addresses the need to enhance the resilience of credit portfolios against extreme geopolitical shocks by quantifying scenarios most likely to drive a bank’s Common Equity Tier 1 (CET1) capital ratio below regulatory thresholds. It proposes a novel “geopolitical point reverse stress testing” framework that embeds explicit geopolitical risk factors into a macro-financial joint scenario vector, which is then mapped—via a latent factor model—to stressed default probabilities and losses, ultimately propagating to tail losses and CET1 impacts. The approach formulates the problem as a constrained maximum likelihood estimation in scenario space and characterizes a near-optimal scenario set to support sensitivity analysis and governance decisions. Compatible with Internal Ratings-Based (IRB) frameworks, the method is interpretable, actionable, and applicable at both individual exposure and sectoral levels, thereby strengthening regulatory compliance and forward-looking risk management.

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Recent publications

Latest Papers

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

Aug 05, 2026

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.

0 citationsRead paper

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

Jan 07, 2026

This study addresses the need to enhance the resilience of credit portfolios against extreme geopolitical shocks by quantifying scenarios most likely to drive a bank’s Common Equity Tier 1 (CET1) capital ratio below regulatory thresholds. It proposes a novel “geopolitical point reverse stress testing” framework that embeds explicit geopolitical risk factors into a macro-financial joint scenario vector, which is then mapped—via a latent factor model—to stressed default probabilities and losses, ultimately propagating to tail losses and CET1 impacts. The approach formulates the problem as a constrained maximum likelihood estimation in scenario space and characterizes a near-optimal scenario set to support sensitivity analysis and governance decisions. Compatible with Internal Ratings-Based (IRB) frameworks, the method is interpretable, actionable, and applicable at both individual exposure and sectoral levels, thereby strengthening regulatory compliance and forward-looking risk management.

0 citationsRead paper