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

Paper: arXiv 2506.12510

Authors: Alessandro Ramponi, Sergio Scarlatti

Abstract

We propose a credit risk model for portfolios composed of green and brown loans, extending the ASRF 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, CDO pricing, and empirical analysis of green loan portfolios.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical extension of the Vasicek ASRF model to mixed green and brown loan portfolios using a two-factor skew-normal copula structure and proving convergence in quadratic mean. However, its empirical rigor is limited, relying mostly on theoretical formulation and numerical/synthetic experiments rather than extensive real-world backtesting on proprietary loan datasets.

Research Flowchart

  flowchart TD
    A[Research Goal: Model credit risk for green/brown loan portfolios using extended ASRF] --> B[Inputs: Non-uniform exposures, PDs, Factor Loadings & Skewed Distributions]
    B --> C[Methodology: Develop Two-Factor Copula with Skewed Systematic & Gaussian Idiosyncratic Risks]
    C --> D[Computation: Prove convergence in quadratic mean of portfolio loss & calculate VaR]
    D --> E[Outcomes: Validated framework showing VaR sensitivity to granularity, skewness, and sector shocks]
    E --> F[Applications: Granularity adjustments, CDO pricing & empirical green loan analysis]