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Climate aware lending allocation under NGFS scenarios - A Monte Carlo approach

This paper presents a Monte Carlo-based framework that integrates NGFS climate scenarios into a structural credit risk model to simulate obligor default probabilities and optimize loan portfolio allocation, thereby enabling banks to link climate transition and physical risks to forward-looking credit risk outcomes and stress testing.

Original authors: Marina Palaisti

Published 2026-10-02

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Marina Palaisti

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Banks have long relied on history to predict the future. When deciding who gets a loan, they look at how borrowers have performed in the past, assuming that economic relationships will remain relatively stable. This approach works well for normal times, but it struggles when the world changes in ways that have no historical precedent. Climate change is one such force. It introduces two distinct types of danger for borrowers: physical risks, where extreme weather damages assets and disrupts operations, and transition risks, where the shift toward a low-carbon economy changes costs, regulations, and market demand. Because these forces are forward-looking and driven by policy rather than just market cycles, traditional tools often fail to capture the true risk. Regulators now ask banks to look ahead, to understand how different paths toward a greener future might affect the safety of their loans.

A researcher named Marina Palaisti has developed a new way to answer this question. The work involves building a computer model that simulates how a large group of borrowers might behave over the next three to five years under different climate scenarios. Instead of guessing, the model uses specific, structured stories about the future provided by the Network for Greening the Financial System, a global group of central banks and supervisors. These stories range from a smooth, orderly transition to a low-carbon world, to a chaotic situation where policy changes happen suddenly and physical damage from storms increases. The model takes these broad stories and translates them into specific effects on individual companies, adjusting how fast they grow and how likely they are to fail.

The core of the study is a simulation of one thousand hypothetical companies. The researcher feeds the model different climate scenarios to see how each one changes the companies' financial health. In the model, a company's value is tied to its ability to produce goods and manage its energy use. When a climate scenario hits, it acts like a shock to the company's growth engine. For example, a scenario with strict new carbon taxes might slow down a factory that relies on coal, while a scenario with better technology might help a wind energy firm grow faster. The model calculates the probability that each company will fall below a critical threshold and default on its loan. By running thousands of these simulations, the researcher can see not just the average risk, but how risk is distributed across the entire group of borrowers.

The results show that the choice of climate story matters deeply. Different scenarios produce very different patterns of risk. In one scenario, where policy action is delayed and physical damage from weather rises, the risk is spread out somewhat evenly, with many companies facing moderate challenges. In another scenario, where the transition to a green economy happens in a sudden, abrupt shock, the risk becomes more uneven. Some companies that were previously safe suddenly face high risks, while others remain stable. The study found that the scenario where the transition is orderly and coordinated actually produced the highest average risk for the portfolio in this specific simulation, while a scenario with a sudden wake-up call produced the lowest average risk. This highlights that the severity of a scenario is not just about how bad the weather gets, but how the economy reacts to the changes.

Using these calculated risks, the researcher then asked a practical question: how should a bank lend its money if it wants to maximize returns while staying safe? The model acts as a guide, showing which sectors look most attractive under each climate story. In the scenario where physical disasters are the main threat, the model suggests lending more to resilient infrastructure like wind power and hydroelectricity. In the scenario where the transition is sudden and chaotic, the model shifts its preference toward "bridge" technologies, such as cleaner natural gas and carbon capture systems, which might be more valuable in a rapidly changing market. Interestingly, even in the most extreme scenarios, the model does not completely cut off lending to fossil fuel sectors, but it drastically reduces the amount of money going to them compared to cleaner alternatives.

The study emphasizes that these findings are specific to the simulation and the assumptions built into the model. The results depend on how the climate stories are translated into company-level data, and the model does not yet capture every detail of how individual companies might adapt or how their specific locations might affect them. However, the framework provides a clear, transparent way for banks to link high-level climate narratives to the actual risk of their loan books. It shows that climate risk is not a single number but a complex landscape that changes depending on the path the world takes. By using this kind of forward-looking analysis, banks can move beyond looking only at the past and start preparing for the specific challenges that different climate futures might bring.

Technical Summary: Climate Aware Lending Allocation under NGFS Scenarios

Problem Formulation

The paper addresses the challenge of integrating forward-looking climate risk into credit risk management and capital allocation. Traditional credit risk frameworks rely on historical data and stable economic relationships, rendering them ill-suited for climate risk, which is policy-driven, scenario-dependent, and forward-looking. Regulators increasingly demand tools to translate Network for Greening the Financial System (NGFS) climate scenarios into portfolio-level loss and capital implications for Internal Capital Adequacy Assessment Process (ICAAP) and stress testing.

The core problem is defined as a constrained optimization problem: a financial institution seeks to allocate a total capital budget $K$ across $N$ obligors to maximize expected interest income, subject to default risk and diversification constraints. The objective is to determine the optimal loan amounts $x_i$ for each obligor $i$ such that:
$\max_{x_1, \dots, x_N} \sum_{i=1}^N x_i \eta_i (1 - PD_i)$
subject to $\sum x_i = K$ and $0 \le x_i \le \kappa K$ , where $\eta_i$ is the risk-adjusted interest rate and $PD_i$ is the probability of default. The critical challenge is that $PD_i$ is not static but is a function of climate scenario pathways (transition and physical risks) that alter firm-level dynamics.

Methodology

The paper proposes a structural credit risk framework that embeds NGFS short-term scenarios (2024) into firm-level value dynamics. The methodology proceeds through four main stages:

1. Firm-Level Emission and Production Modeling

Firms are modeled as optimizing agents choosing emission strategies $\gamma_i$ to maximize the net present value of profits.

Cost Structure: Firms face quadratic costs for energy production and regulatory penalties/rewards based on deviations from emission benchmarks.
Production Dynamics: The logarithmic production level $p_t^i$ follows a stochastic differential equation (SDE). The drift term $\mu_i$ is adjusted by climate factors, including emission choices and a leverage penalty ( $x_i \eta_i$ ) representing the cost of capital exposure.
Optimal Strategy: The paper establishes the existence and uniqueness of an optimal emission policy under convex cost structures, deriving a closed-form solution for the optimal strategy under quadratic costs.

2. Structural Default Modeling

Firm value $V_t^i$ is defined as the present value of expected future cash flows (net of climate-related losses) minus expected physical losses (EPL).

Default Condition: Default occurs when the firm's value falls below a liability threshold $L_i(t)$ .
Value Function: The value process is linked to the log-production process via a deterministic function $h_i(t, x)$ , which integrates production growth, costs, and physical losses.
Drift Adjustment: NGFS scenario shocks (transition and physical) are mapped to sector-level adjustments, which modify the drift of the firm's production process. This creates a climate-adjusted drift $\tilde{\mu}_i^\theta$ .

3. Dependence and Simulation (Monte Carlo)

To model joint defaults and systemic risk, the paper employs Principal Component Analysis (PCA) on the covariance matrix of systemic risk factors.

Dimension Reduction: The systemic risk vector $X_t$ is approximated by the first two principal components (eigenvalues $\nu_1, \nu_2$ ), reducing the high-dimensional correlation structure to two orthogonal factors ( $G_1, G_2$ ).
Default Probability Estimation: Using Monte Carlo simulation ( $M=5000$ draws), the model simulates idiosyncratic and systemic shocks to estimate the probability of default ( $PD_i$ ) for each obligor under specific scenarios. The default condition is transformed into a comparison between an idiosyncratic state $A_t^i$ and a systemic threshold $X_t^i$ .

4. Constrained Optimization

The estimated $PD_i$ values are fed into a linear programming solver to determine the optimal lending allocation $x_i$ . The optimization maximizes the risk-adjusted return while adhering to a diversification cap ( $\kappa = 0.05$ ), preventing excessive concentration in any single obligor.

Key Contributions

Structural Integration of NGFS Scenarios: The study embeds NGFS short-term scenarios directly into a structural portfolio credit risk model, linking high-level climate narratives to firm-level default dynamics and capital signals.
Scenario-Dependent Drift Adjustment: It introduces a mechanism where transition and physical risk shocks adjust the drift of firm value dynamics, translating sector-level climate impacts into obligor-specific creditworthiness metrics.
Tractable Portfolio Optimization: The framework provides a computationally feasible approach (using PCA and linear programming) to assess lending allocation patterns across different climate pathways, offering a forward-looking overlay to existing credit models.
Synthetic Portfolio Analysis: By utilizing a synthetic portfolio of 1,000 obligors, the paper demonstrates the mechanics of the framework in the absence of proprietary bank-level data, highlighting model risk and calibration dependencies.

Results

The study simulates outcomes across four NGFS scenarios: Disasters and Policy Stagnation (DAPS), Highway to Paris (HWTP), Sudden Wake-Up Call (SWUC), and Diverging Realities (DiRe).

Default Probability Distributions: While absolute PDs remain low (generally < 1.5%), the cross-sectional distributions vary significantly.
- HWTP (Orderly transition) produces the highest mean, median, and upper-tail PDs.
- SWUC (Abrupt transition) produces the lowest mean and median PDs.
- DAPS and DiRe show dispersed and clustered distributions, respectively, reflecting heterogeneous physical and transition risk exposures.
- Note: These rankings are model-implied and calibration-dependent, not empirical measures of scenario severity.
Lending Allocation Patterns:
- DAPS: Capital concentrates in resilient low-carbon infrastructure (Wind, Hydro, Biomass).
- HWTP: Similar to DAPS, favoring Wind and Hydro, with smaller allocations to transition-supporting sectors (PV, Nuclear, CO2 Capture).
- SWUC and DiRe: These scenarios result in mixed portfolios where "bridge" technologies (Clean Gas) and mitigation technologies (CO2 Capture) receive the largest allocations, alongside transport and manufacturing sectors. Fossil sectors are not fully excluded but receive limited, capped allocations.
Robustness: Sensitivity checks confirm that the diversification cap is essential to avoid degenerate corner solutions. Allocation outcomes are stable across independent Monte Carlo draws, though individual obligor rankings vary due to simulation noise.

Significance and Limitations

Significance:
The paper claims to offer a tractable framework for banks to link NGFS scenarios to sector-level credit risk and portfolio loss outcomes. It supports ICAAP and climate stress testing by identifying exposures most sensitive to climate risk and adding a forward-looking overlay to existing models. It contributes to literature by connecting climate finance, portfolio optimization under uncertainty, and stress testing research.

Limitations:
The author explicitly states that results depend on NGFS scenario design and sector-level impact estimates, which remain uncertain.

Heterogeneity: The model maps shocks by sector classification and does not fully capture within-sector heterogeneity (e.g., firm-level carbon intensity, geographic exposure, adaptation capacity).
Static Liabilities: Firm liabilities are held constant, ignoring dynamic restructuring or refinancing.
Risk Factors: Climate risk enters only through the drift component; volatility changes, fat-tailed outcomes, and jump risks are excluded.
Synthetic Data: The analysis uses a synthetic portfolio; empirical validation with real bank-level data is required for practical application.

The paper concludes that while the framework is a valuable tool for exploring scenario impacts on creditworthiness and portfolio resilience, it should be viewed as a scenario-analysis overlay rather than a replacement for empirical credit models.