Credit risk for large portfolios of green and brown loans: Extending the ASRF model

• Extension of the ASRF/Vasicek framework to credit portfolios containing two exogenous classes of loans (green and brown), allowing distinct return distributions and correlation structures within a unified asymptotic model. • Incorporation of skew-normal borrower return dynamics, providing a flexible structural mechanism to model empirically documented asymmetries in log-returns while preserving analytical tractability. • Generalization of Vasicek’s convergence result to heterogeneous portfolios with nonuniform exposures, including empirically motivated power-law concentration structures. • Integration of Green Loan Principles (GLP) as the practical basis for loan-type classification, clarifying the financial rationale for distinguishing green and brown exposures. • Scenario-based numerical analysis illustrating loss distributions, sensitivity to key parameters (PDs, correlations, skewness), and the impact of portfolio composition under realistic concentration patterns. • Assessment of robustness of the extended ASRF formula by comparing asymptotic results to finite-portfolio simulations under heterogeneous and skewed structural specifications. • Methodological contribution with regulatory relevance, showing how a green-brown differentiation could be embedded in the ASRF architecture once borrower-level data become available. Inspired by the classical Vasicek approach to credit risk, we propose an extended model for portfolios composed of green and brown loans, widening the Asymptotic Single Risk Factor framework via a two-factor copula structure. Systematic risk is modeled using potentially skewed distributions, allowing for asymmetric creditworthiness effects, while idiosyncratic risk remains Gaussian. Under a non-uniform exposure setting, we establish convergence in quadratic mean of the portfolio loss to a limit reflecting the distinct characteristics of the two loan segments. Numerical results confirm the theoretical findings and illustrate how value-at-risk is affected by portfolio granularity, default probabilities, factor loadings, and skewness. Our model accommodates differential sensitivity to systematic shocks and offers a tractable basis for further developments in credit risk modeling, including granularity adjustments, collateralized default obligations pricing, and empirical analysis of green loan portfolios.