Climate-Aware Copula Models for Sovereign Rating Migration Risk

TL;DR

This paper introduces a novel copula-based framework incorporating climate risk to model sovereign credit rating migration, demonstrating its effectiveness over traditional models in capturing dependence dynamics.

Contribution

It develops a new mixed-difference transformation and extends copula models to a MAGMAR(1,1) process, improving modeling of sovereign rating dependence with climate data.

Findings

Gumbel MAGMAR(1,1) model outperforms others in empirical tests.

Strong nonlinear dependence and clustering of high-activity years observed.

Climate covariates enhance marginal models but have limited impact on dependence dynamics.

Abstract

This paper develops a copula-based time-series framework for modelling sovereign credit rating activity and its dependence dynamics, with extensions incorporating climate risk. We introduce a mixed-difference transformation that maps discrete annual counts of sovereign rating actions into a continuous domain, enabling flexible copula modelling. Building on a MAG(1) copula process, we extend the framework to a MAGMAR(1,1) specification combining moving-aggregate and autoregressive dependence, and establish consistency and asymptotic normality of the associated maximum likelihood estimators. The empirical analysis uses a multi-agency panel of sovereign ratings and country-level carbon intensity, aggregated to an annual measure of global rating activity. Results reveal strong nonlinear dependence and pronounced clustering of high-activity years, with the Gumbel MAGMAR(1,1) specification delivering the strongest empirical performance among the models considered, while standard Markov copulas and Poisson count models perform substantially worse. Climate covariates improve marginal models but do not materially enhance dependence dynamics, suggesting limited incremental explanatory power of the chosen aggregate climate proxy. The results highlight the value of parsimonious copula-based models for sovereign migration risk and stress testing.