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

TL;DR

This paper introduces an extended credit risk model for green and brown loan portfolios using a two-factor copula, capturing asymmetric effects and providing insights into risk measures like value-at-risk.

Contribution

It extends the ASRF model with a two-factor copula and skewed distributions, enabling more accurate modeling of green and brown loan portfolios with systematic and idiosyncratic risks.

Findings

Convergence of portfolio loss to a limit under non-uniform exposures.

Value-at-risk is influenced by portfolio granularity, default probabilities, and skewness.

Model supports further credit risk analysis including CDO pricing and empirical studies.

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.