A Stochastic Climate Model -- An approach to calibrate the Climate-Extended Risk Model (CERM)

Abstract: The initial Climate-Extended Risk Model (CERM) addresses the estimate of climate-related financial risk embedded within a bank loan portfolio, through a climatic extension of the Basel II IRB model. It uses a Gaussian copula model calibrated with non stationary macro-correlations in order to reflect the future evolution of climate-related financial risks. In this complementary article, we propose a stochastic forward-looking methodology to calibrate climate macro-correlation evolution from scientific climate data, for physical and transition efforts specifically. We assume a global physical and transition risk, likened to persistent greenhouse gas (GHG) concentration in the atmosphere. The economic risk is considered stationary and can therefore be calibrated with a backward-looking methodology. We present 4 key principles to model the GDP and we propose to model the economic, physical and transition effort factors with three interdependent stochastic processes allowing for a calibration with seven well defined parameters. These parameters can be calibrated using public data. This new approach means not only to evaluate climate risks without picking any specific scenario but also allows to fill the gap between current one year approach of regulatory and economic capital models and the necessarily long-term view of climate risks by designing a framework to evaluate the resulting credit loss on each step (typically yearly) of the transition path. This new approach could prove instrumental in the 2022 context of central banks weighing the pros and cons of a climate capital charge.

• The paper proposes a stochastic methodology to calibrate the CERM by incorporating dynamic correlations and cumulative greenhouse gas impacts.
• It employs three interlinked stochastic processes—economic growth, physical damage, and transition costs—to enhance predictive accuracy.
• The calibration redefines macro-correlations, offering valuable insights for assessing credit loss provisions and shaping regulatory strategies amid climate risks.

A Stochastic Approach to Climate-Extended Risk Model Calibration

The paper "A Stochastic Climate Model -- An approach to calibrate the Climate-Extended Risk Model (CERM)" focuses on developing a methodology for calibrating a Climate-Extended Risk Model, addressing the quantification of climate-related financial risk.

Introduction and Objectives

The initial CERM framework attempts to evaluate climate-related risks within bank loan portfolios using a Gaussian copula model to integrate non-stationary macro-correlations reflective of climate risk evolution. This paper proposes a stochastic methodology as an alternative to deterministic scenario-based approaches. The proposed model accounts for the uncertainty and persistence of greenhouse gas (GHG) concentrations, a significant driver of climate change impact and transition risks.

Key Modeling Assumptions

The paper delineates four foundational principles underlying the model:

1. Additivity of Climate Risks: Climate risks are additive to other economic risks, viewed historically.
2. Cumulative Physical Risks: Climatic sensitivity is driven by incremental GHG accumulation, echoing the broad consensus among climate specialists.
3. Mitigating Transition Efforts: Transition efforts are assumed to reduce long-term climate damage by promoting adaptation and lowering GHG emissions.
4. Reactive Transition Efforts: Political and public pressures, exacerbated by climatic extreme events, foster transition activities.

Model Structure and Stochastic Processes

The model's structure involves three interlinked stochastic processes to represent economic growth, physical climate damage, and transition costs. The processes depend on seven parameters derived from accessible public data:

• Economic Growth Process: Stationary, encompassing stochastic variability.
• Physical Damage Process: Dynamic, influenced by ongoing economic activities and mitigative effects of transition efforts.
• Transition Costs: Responsive to past climate impacts, reflecting political and social dynamics.

Mathematically, the GDP growth is modeled as an exponential function of three cumulative factors:

$$GDP^t = GDP^{-t_0} \exp{\left(\tilde{Y}_E^t - \tilde{Y}_T^t - \tilde{Y}_P^t \right)}$$

The stochastic forward-looking model for these factors accounts for autocorrelation and environmental uncertainties.

Calibration and Analysis

The approach redefines macro-correlations by incorporating time-dependent correlation matrices, elevating the original CERM's static assumptions. The study illustrates that incorporating dynamic correlations better reflects persistent climate phenomena. Specifically, the proposed model highlights auto-correlations among physical and transition risks, a departure from the original CERM's independence assumptions.

Application and Implications

Potential applications of this enhanced model include the assessment of credit loss provisions along transition pathways. This innovation might assist central banks deliberating over climate capital charges, aligning short-term regulatory frameworks with the exigencies posed by climate risk.

Further exploration is encouraged through numerical applications, utilizing both historical economic data and forecasts from international financial and climate bodies.

Conclusion

The stochastic climate model for calibrating the CERM presents a robust approach to quantifying climate-related financial risks. By leveraging public data and considering interdependencies in risk factors, this model enhances the predictive power and accuracy of financial risk assessments. However, successful implementation necessitates continuous updating and verification with evolving climate data and economic conditions.