Bridging the Last Mile: A Transmission Channel Framework for Derivatives Stress Testing Under Climate Scenarios

Abstract

Climate risk is increasingly recognized as an important factor in financial modelling, with applications including stress testing where climate risk factors are used to influence market risk and credit risk. However, this “transmission channel” modelling faces several challenges, particularly in terms of data availability and the mismatch between the time horizons of climate risks and financial risks. Recent research, especially from central banks and regulatory bodies, is beginning to address these challenges. The International Swaps and Derivatives Association (ISDA) has developed methodologies to compute very short-term scenarios. In this paper, we illustrate how outputs from ISDA and other sources can be integrated for climate stress testing of key products listed on the Singapore Exchange (SGX). The main contribution of this study is the development of a structured “last-mile modelling” framework that combines country-level climate sensitivity scaling, stressed correlation inference modelling, and direct carbon cost transmission mechanisms to bridge macro-level climate scenarios with product-level financial risk. It provides a practical and extensible approach for climate stress testing across both listed and over the counter (OTC) markets.

1. Introduction

The global awareness of climate change, coupled with the Paris Agreement established at COP 21 in 20151, has significantly influenced the formation of green alliances. Notably, the Glasgow Financial Alliance for Net Zero (GFANZ) was established during COP 26 in 2021. This coalition comprises financial institutions such as banks, insurers, asset managers, and other financial service providers. All are committed to transitioning the global economy towards net-zero GHG emissions by 2050. These institutions collaborate to set rigorous targets and develop credible transition plans. Their aim is to address climate risks through financial mechanisms and to promote green financing and product innovation.

Green financing pertains to the allocation of capital to projects that yield positive environmental impact. Examples include renewable energy initiatives and energy efficiency projects. Instruments like green bonds and loans are utilized for this purpose. Green financing not only helps mitigate climate change but also offers financial returns. This makes it attractive to investors who are conscious of sustainability.

Financial product innovation is also gaining momentum. This includes the development of green indices, green funds, ETFs, and carbon markets. These financial assets are designed to channel capital towards companies contributing to the green transition. They thereby provide a monetary incentive to divest from sectors and activities that are high in carbon emissions.

Climate risk is increasingly recognized as a significant emerging risk factor within financial institutions. It has the potential to contribute to systemic risk in the global financial system. This recognition has spurred the development of regulations, which require financial institutions to measure, manage, and disclose climate risks. This is particularly important for banks that finance the green transition. The financialization of climate risk entails integrating climate considerations into financial decision-making and risk management.

Despite these developments, a key challenge remains in translating these climate scenarios into granular shocks for individual financial products, often referred to by practitioners as “last-mile modelling.” This paper proposes a practical framework for extending climate stress scenarios to granular market products. The framework consists of three components: (i) scaling for country-specific assets, (ii) inference using stressed correlations, and (iii) direct impact calculation for products directly exposed to carbon costs or physical disruptions. The objective is to provide a practical stress-testing framework under limited climate data and short market risk horizons.

2. Literature Review

Leading central banks have pioneered the development of models to measure climate risks, one of which is industry-wide climate stress testing. Climate stress testing involves assessing the resilience of financial institutions to climate-related risks under various hypothetical scenarios. These stress tests enable institutions to understand the potential impacts of future climate change on their portfolios and make informed decisions to mitigate these risks proactively.

Climate scenario design examines the types of climate risks that are believed to affect economic activity: physical risks, such as those from the physical manifestations of climate change (e.g., coastal flooding, heat stress, wildfires), and transition risks, which stem from regulatory interventions (e.g., carbon taxes, renewable energy subsidies) or changes in technologies and preferences. Transition risks typically operate over shorter time horizons, while physical risks extend beyond a decade. These risks may interact and differ substantially in their impact on overall economic activity and the sectoral distribution of effects.

Climate risk modelling in finance has developed across two main paths: macro climate–economy models, and asset pricing- and market-based models. A third related area focuses on climate stress-testing frameworks used by financial institutions.

2.1. Macro Climate–Economy Models

Modelling the impact of climate risk on the global economy is complex and nuanced. Transition risks from carbon taxes and renewable subsidies are dynamic choices made by policymakers, who balance the benefits and costs of various interventions while considering their political feasibility. Climate risks also exhibit compound effects.

There is ongoing debate among academic researchers regarding whether states experiencing significant climate risk realizations will see high or low GDP outcomes. Dynamic Integrated Climate–Economy (DICE) models, such as those developed by Nordhaus and Boyer (2000), posit that climate change is an unintended consequence of economic growth. In these models, the damages from climate change, often conceptualized as a tax on consumption, are most substantial when GDP levels are at their peak.

In contrast, the models proposed by Weitzman (2012, 2014) and Barro (2015) account for the potential of low-probability, high-impact climate events, which could lead to reduced GDP in countries and regions facing such physical climate risk disasters. Barnett et al. (2023) and Giglio et al. (2024) further highlight the importance of long-run climate uncertainty and its implications for macroeconomic outcomes.

While these models provide important theoretical insights, they operate at a highly aggregated level. They are also calibrated over long horizons. As a result, they are not directly applicable to financial instruments or short-term risk measurement.

2.2. Asset Pricing- and Market-Based Models

A second path of research examines how climate risks are reflected in financial asset prices. Research suggests that climate risks may not yet be fully priced. If climate risks are significantly underpriced, shifts in investor perception could trigger abrupt and severe asset repricing. This may result in a climate-related “black swan” event, even if the underlying probabilities of risk remain unchanged.

Stroebel and Wurgler (2021) provide early anecdotal evidence of underpricing. More recent studies focus on equity markets and find that climate risks are at least partially incorporated into stock prices. Bolton and Kacperczyk (2023) find that companies with higher carbon emissions tend to earn higher stock returns across sectors and major countries. Similarly, Pankratz et al. (2023) show that transition risks increasingly affect firm valuation and returns.

Despite these advances, this literature is largely backward-looking and does not provide a forward-looking stress-testing framework.

2.3. Climate Risk Stress-Testing Frameworks

Climate stress testing provides a forward-looking approach to assess financial risk. The modelling of climate risk impacts on banking institutions is predominantly conducted through two primary channels: the credit risk channel, which pertains to the banks’ loan portfolios, and the market risk channel, which involves the banks’ financial asset portfolios.

Climate scenario analysis begins with the selection of a set of severe but plausible scenarios. These scenarios are typically developed by climate modelling consortia such as the Network for Greening the Financial System (NGFS) and the Intergovernmental Panel on Climate Change (IPCC). These institutions use integrated assessment models (IAMs) to generate a combination of macroeconomic and financial variables over extended periods, often projecting up to the end of the century, and these projections are commonly referred to as “indicator pathways”.

The next step is transmission channel modelling. This step links scenario variables to financial risk outcomes. It typically employs statistical models, including regressions, to translate macro indicators into credit and market risk factors. At this stage, the analysis becomes more granular. It takes into account the specific structure of individual banks’ balance sheets and income statements. Supervisory stress tests focus on individual banks. In contrast, macroprudential stress tests account for potential feedback loops within the financial system, such as contagion and spillover effects between the financial systems and the real economy.

At a more granular level, two significant modelling challenges arise. The first challenge is data availability. The variable pathways provided by the modelling consortia typically consist of broad macroeconomic indicators, such as national GDP, inflation rates, and the consumption of key commodities. These variables are often too general to assess the microeconomic impact on individual firms. Firm-level stress testing requires more detailed data that reflects specific business models.

The second challenge is the mismatch in time horizons. Climate scenarios typically extend to the year 2100, with data in five-year intervals. In contrast, financial risk is assessed over much shorter periods. The credit risk horizon is usually one year, as seen in banks’ loan books. The market risk horizon is even shorter, often less than ten days, as observed in trading books. It is difficult to translate long-term climate scenarios into short-term financial market shocks.

Currently, the majority of scenarios employed are derived from the NGFS with some modifications. The NGFS, comprising central banks, supervisors, and observers, is dedicated to advancing environmental and climate risk management within the financial sector and promoting mainstream finance to facilitate the transition towards a sustainable economy (NGFS, 2019). For instance, the Bank of England applies three core scenarios: the Net Zero 2050, Delayed Transition, and Current Policies scenarios, each adjusting the temperature targets to 1.8 °C, 1.8 °C, and 3.3 °C by 2050, respectively (Bank of England, 2021). Similarly, the Federal Reserve System incorporates the NGFS Current Policies and Net Zero 2050 scenarios in its transition risk module. It complements these with the IPCC SSP2–4.5 and RCP4.5 and SSP5–8.5 and RCP8.5 scenarios in its physical risk module (Board of Governors of the Federal Reserve System, 2023). A survey conducted by Acharya et al. (2023) on climate stress test initiatives by major central banks reveals that the results are typically projected over a five-year horizon or longer, such as for the years 2030 and 2050. These outputs predominantly include country GDP, sector productivity, and carbon prices. Recognizing the necessity for short-term scenarios and more detailed outputs for the banking sector, the NGFS published a more recent paper (NGFS, 2025). Four narratives model divergent pathways: regional extreme weather events, global green transitions, abrupt policy shifts, and uneven regional actions. The scenarios emphasize compound climate hazards and cross-regional spillovers via trade/finance linkages, highlighting significant GDP losses in vulnerable regions and elevated default risks in energy-intensive sectors. While calibrated to IMF projections, the framework excludes tipping points and sovereign default risks, focusing instead on actionable insights for financial institutions and policymakers navigating transition and physical risks. However, the paper does not fully bridge the gap required for financial stress testing, as the financial variable outputs remain overly generic and medium-term in nature, providing only annual projections from 2025 to 2030.

More practically, the International Swaps and Derivatives Association (ISDA, 2024) published a climate scenario analysis featuring very short-term shocks for various key asset classes, suitable for investment banks to stress test their trading books. These macro risk shocks span from 1 to 12 months, while market risks, volatilities, and probability of default shocks range from 2 days to 1 year.

The short-term climate scenario framework proposed by ISDA represents an important step toward bridging long-term climate narratives with near-term market risk shocks. However, the framework primarily provides shocks for a limited set of core asset classes and does not offer a systematic methodology for extending these shocks to a broader universe of financial instruments. As a result, the practical application of these scenarios for comprehensive stress testing is still constrained. This may be interpreted as a “last-mile modelling” problem. This paper seeks to address this problem by proposing a structured inference modelling framework that extends ISDA scenario variables to granular, product-level stress testing.

3. Extension of ISDA Climate Scenarios to Granular Market Shocks

The ISDA paper describes a short-term climate catastrophe involving the abrupt thawing of Arctic permafrost, which releases a significant amount of CO₂ gas. It proposes three short-term climate scenarios for the trading book: (i) a physical risk scenario, (ii) a transition risk scenario and (iii) a combined physical and transition risk scenario.

3.1. ISDA Three Climate Scenarios for Trading Books

(i)

The physical risk scenario considers an abrupt climate event, such as the thawing of Arctic permafrost, which releases a significant amount of CO₂ into the atmosphere. This scenario is realistic and grounded in scientific evidence. Boreal permafrost is estimated to contain approximately twice the amount of CO₂e currently found in the atmosphere. McKay et al. (2022) identified 15 climate tipping points, several of which are already active. Among these, Boreal permafrost collapse is a tipping point with a median timescale of approximately 50 years.

(ii)

The transition risk scenario models a sudden and a concerted effort to combat climate change, in which governments impose a global tax of $200 per tonne of CO₂e worldwide. Given the current lack of global coordination in decarbonization and the geopolitical division surrounding the climate change agenda, such a scenario would represent a policy U-turn that would undoubtedly surprise the markets.

(iii)

The combined scenario links these two areas, where a physical climate event triggers an immediate and unexpected global policy response. While this provides a comprehensive narrative of interacting risks, we exclude the “combined scenario” from this paper as our focus is on a very short risk horizon of 1–2 days. Within such a horizon, it is unlikely that a physical climate event and a coordinated global policy response would materialize simultaneously. In practice, physical events can occur abruptly, whereas transition risk typically involves institutional processes, consultations, and implementations. As a result, policy responses are more likely to materialize with a lag of several weeks after the initial physical catastrophe.

3.2. The Transmission Channel Framework for ISDA Climate Scenarios

The ISDA paper simulates climate-related factors such as temperature changes, carbon dioxide levels, and carbon tax policies, transforming them into a set of macroeconomic variables. This creates a detailed mapping of how climate scenarios affect various industry sectors and economies over the long term, spanning multiple years. Subsequently, financial models are used to model the transmission to market and credit risk factors with a much shorter horizon price shock.

Table 1. Transmission channel models.

Asset Class	Product	Financial Model
Equity	Japan Nikkei 225	[by ISDA] Fama French 5 Factor Model
	US S&P 500
	UK FTSE 100
	FTSE China A50 Index	[by this paper] Scaling of ISDA shocks using country sensitivity to climate risk
	FTSE Taiwan RIC Capped Index *
	India Nifty 50 Index
	MSCI Singapore Index
FX	USD/INR, USD/JPY, USD/BRL	[by ISDA] XGBoost Regressor–GBP Purchasing Power Parity
	USD/CNH, USD/SGD, etc.	[by this paper] Inference using Broken Arrow Stress Test
Commodities	Coal	[by ISDA] Regression on agent-based model macroeconomic outputs
	WTI Crude
	Iron Ore	[by this paper] Inference using Broken Arrow Stress Test
	Petrochemical, e.g., Paraxylene	[by this paper] Inference using Broken Arrow Stress Test
	Dairy Product	[by this paper] Inference using Broken Arrow Stress Test
	Freight Futures (also for FFA)	[by this paper] Congestion modelling, carbon tax calculation

* Note: Certain index names (e.g., “FTSE Taiwan RIC Capped Index”) are retained solely for consistency with official index-provider naming conventions.

highlights the quantitative models used for risk transmission.

We use the latest ISDA climate scenarios outputs to calculate the financial shocks on various products listed on the SGX Derivatives Exchange. This step is also known as “last-mile modelling” or inference modelling. Three methods are employed to derive the final shocks:

(i)

Scaling method for assets that are country-specific (such as equities);

(ii)

Inference method using stressed correlation for assets that are international in nature (such as commodities and foreign exchange);

(iii)

Direct calculation of loss for assets whose valuation is affected by carbon taxation or physical loss.

We exclude from our study all asset classes that are unaffected by climate risk or exhibit a response time to climate risk that exceeds the risk horizon of interest. Examples include interest rates and bonds, which may reasonably be assigned zero climate stress shocks over a two-day horizon. Additionally, to identify these sectors and assets for exclusion, one may utilize the Transition Exposure Coefficients (TECs) as defined in the EU Taxonomy for sustainable activities. The TEC, as proposed by Alessi and Battiston (2022), is calculated by integrating carbon intensity data with policy impact analysis, resulting in a coefficient that reflects the sector’s sensitivity to transition risks. The potential application of TEC in climate stress testing is left for future research.

The inference framework implicitly assumes that historical relationships among market variables will remain informative under future climate stress conditions. However, climate scenarios are often projections of hypothetical future stressful events that have not occurred and hence may not be adequately captured in the historical data set. Hence, a good practice is to subject the outcomes of such inference models to screening by expert judgement because of inherent data incompleteness. For example, we note that in the ISDA (2024), the modelled outcomes are overlaid with subject matter experts’ input through a crowdsourcing exercise.

4. Scaling Shocks Using Country Sensitivity to Climate Risk

We expand the ISDA climate stress shocks from the core equity markets (US, UK and Japan) to cover other Asian markets including Singapore, India, China and the Taiwan region, etc. This can be done by scaling the stress shocks by the relative sensitivity of countries to physical risk and transition risk. For physical climate risk, we use the Swiss Re’s Climate Economics Index (source: Swiss Re Institute (2021)) which ranks how climate change will impact 48 countries or regions. The index accounts for GDP impact, extreme weather and adaptive capacity of each country or region, where the GDP impact considers sea level rise, heat stress, crop yield, health and tourism. A higher score indicates that a country is more vulnerable to the economic risks caused by physical damage. For transition risk, we use the Bloomberg Government Climate score (2024 data). The score gauges a government’s preparedness to meet global climate goals set out in the Paris Agreement, and considers carbon transition, power transition and climate policies. A higher score translates to higher transition risks.

Developed countries that invest heavily in decarbonization may face relatively higher transition risks, reflecting their stronger capacity to invest in mitigation and adaptation. Conversely, developing countries tend to be more exposed to physical risks, such as extreme weather events, while being less susceptible to transition risks arising from regulations or stranded assets. As a result, an inverse relationship between physical risk scores and transition risk scores is generally expected, as illustrated in Figure 1.

ISDA shocks are only available to three major equity markets (US, UK and Japan), denoted R_i. We derive the “core shock” as a sum of these shocks weighted by their scores:

$$R_{core}={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^3}{I}_i·R_i}{{\displaystyle {\sum }_{i=1}^3}{I}_i}}$$

(1)

where

• $R_i$ is the equity shock of country $i$;
• $I_i$ is the score for country $i$.

We derive the shock for another country $k$ by scaling $R_{core}$ by the score of that country:

$$R_k={\displaystyle \frac{I_k}{I_{core}}}·R_{core}$$

(2)

where

• $I_k$ is the score of country $k$;
• $I_{core}={\displaystyle \frac{1}{3}}{\displaystyle {\sum }_{i=1}^3}{I}_i$.

The results of the scaling are depicted in Figure 2. According to a study by Swiss Re, climate change is projected to result in a 10% loss of total economic value globally by 2050. The index quantifies the long-term GDP impact on individual countries; see details in Appendix A. The scaling approach adopted in this paper should be interpreted as a reduced-form approximation rather than a strict proportional mapping between country-level GDP impacts and short-horizon equity returns. Equity prices reflect expected cash flows and discount rates, both of which may be affected by climate shocks through disruptions to production, trade, infrastructure, and risk premia. While countries with higher climate vulnerability are expected to exhibit greater equity market sensitivity on average, the relationship is not assumed to be one-for-one, as equity returns may also reflect valuation effects, multinational revenue exposure, and market structure differences. Accordingly, the country climate score is used as a parsimonious proxy for relative climate sensitivity rather than as a structural asset pricing model.

The ISDA results do not exhibit meaningful differentiation among the three major equity markets, the United States, the United Kingdom, and Japan, likely due to the application of expert judgement overlays in the final modelled outputs. In light of this, we adopt the average of these three markets as a reference benchmark for scaling purposes.

The scaling methodology assumes that relative climate vulnerability provides a first-order approximation for cross-country differences in equity market sensitivity to climate stress scenarios. To assess robustness, we conduct sensitivity tests by perturbing climate-risk scores by ±10% and ±20%, applying alternative core-market weighting and leave-one-out specifications for the US, UK, and Japan, and comparing the baseline linear scaling against logarithmic and percentile-based scaling. As shown in

Table 2. Robustness analysis of climate risk scaling assumptions.

Robustness Test	Change to Assumption	Result
Climate score perturbation	±10%, ±20%	Ranking broadly unchanged
Alternative core weights	Equal-weight vs. leave-one-out	Similar shock magnitudes
Log scaling	Log(1 + x) transformation	Reduced tail magnitude
Percentile scaling	Rank-based scaling	Preserves relative ordering

, while nonlinear approaches compress the magnitude of shocks for highly vulnerable countries, the relative ranking and qualitative conclusions remain broadly unchanged, suggesting that the framework is reasonably stable as a practical stress-testing approximation rather than a precise prediction model.

This paper distinguishes between the modelling approaches of physical and transition climate risk scenarios across countries. Substantial scientific uncertainty surrounds the triggers, spatial transmission, and timing of climate tipping point events—such as abrupt permafrost thaw—rendering the sequencing of extreme weather events effectively unknowable. Accordingly, ISDA (2024) does not model event timelines.

We therefore assume that physical climate disasters affect countries idiosyncratically due to geographical separation. As a result, in a “physical-risk-only” scenario, short-term (one- to two-day) losses across countries are not aggregated but treated as separate sub-scenarios for stress-testing purposes. For the transition risk scenario, countries are classified into two tiers. Given limited global coordination in decarbonisation and persistent geopolitical frictions, we do not assume a simultaneous policy response across all jurisdictions. Tier 1 countries are assumed to implement a coordinated carbon pricing shock—specifically, a USD 200 per tonne CO₂e increase—within weeks of the physical event, while Tier 2 countries are assumed to follow with a substantial delay. Accordingly, in stress test implementation, short-term (one- to two-day) equity losses are aggregated separately for Tier 1 and Tier 2 countries.

Tier 1 classification is based on legal and institutional readiness to implement a sudden carbon price increase, proxied by the presence of a functioning emissions trading system. This group includes the European Union, the United Kingdom, China, the United States, South Korea, Japan, and New Zealand. All remaining countries are assigned to Tier 2, reflecting anticipated implementation delays due to technical constraints. While political attitudes toward climate policy may further influence response timing, this dimension is not modelled in this paper.

For non-equity asset classes, market reactions are assumed to occur on the announcement date of the Tier 1 policy response. Consequently, stress losses for these asset classes are aggregated with Tier 1 equity losses under the transition risk scenario. We further assume that the announcement constitutes an unanticipated policy shock.

The scaling method provides a parsimonious first-order approximation for extending climate stress shocks from core to non-core equity markets. It assumes that markets may experience larger short-term equity shocks on average, while recognizing that the relationship may not fully capture nonlinearities, threshold effects, or structural market differences. Accordingly, the results should be interpreted as indicative stress sensitivities rather than precise market forecasts or equilibrium asset pricing estimates.

5. Inference Using Broken Arrow Stress Test Model

For other asset classes (non-equity), we employ an inference model based on multi-factor regression, which reflects the historical relationship between dependent variables (core assets provided by ISDA output) and independent variables (herein termed “peripheral” assets) that need to be forecasted. However, this approach assumes that historical covariance is a reliable predictor of price movements during stressful periods, despite the well-documented phenomenon of “correlation breakdown” during crises.

As an improvement, we model correlations during stress periods to better reflect real-world conditions. This approach mitigates the underestimation of risk that can occur when relying solely on historical data, which predominantly contains “normal time” price fluctuations. The Broken Arrow Stress Test approach, as described by Kim and Finger (2000), posits that asset returns follow two multivariate normal distributions. The original approach used the S&P 500 as the single core asset. In the context of ISDA climate risk scenarios, there are multiple core assets. We thereby extend the approach by fitting the Gaussian Mixture Model (GMM) to the data of historical returns of multiple core assets. Instead of the univariate mixed-normal distributions in Kim and Finger’s (2000) work, we adapt multivariate mixed-normal distributions and estimate their mixture using maximum likelihood estimation (MLE).

5.1. Two Regime Specification

The Broken Arrow framework assumes a two-regime structure, quiet vs. hectic. Formally, we model the joint distribution of core asset returns as a mixture of two multivariate normal distributions. On most days, asset returns are drawn from a quiet day’s distribution characterized by lower volatility and relatively mild correlations. However, during periods of market stress, returns may instead be generated from a hectic day’s distribution, exhibiting higher volatility and stronger cross-asset dependencies. By analyzing historical data of core assets, the model estimates the conditional probability that a given observation belongs to the hectic day’s distribution.

This probabilistic weighting mechanism allows the model to remain data-efficient: rather than discarding observations or imposing arbitrary thresholds to define stress periods, all data points are retained and weighted according to their likelihood of being generated under the stressed regime. The resulting regime-dependent correlation structure is then used to infer the conditional expectation of peripheral asset returns, given observed stress movements in the core assets.

5.2. Linear Inference Model

Having obtained the stressed correlation structure from the Gaussian Mixture Model, the next step is to translate the stress shocks observed in core assets into corresponding shocks for peripheral assets. To achieve this, we adopt a linear multi-factor inference method, in which peripheral asset returns are modelled as a function of core asset returns. The core assets identified in the ISDA scenario variables, such as equity indices and key commodities, serve as systematic risk drivers, while peripheral assets respond through historical transmission channels.

To better reflect stress conditions, the conditional expectation of peripheral asset returns is estimated via weighted least squares (WLS):

$$Y=X\beta +\epsilon$$

(3)

where

• $Y$ denotes the vector of the estimated number of peripheral asset shocks $m$.
• $X$ denotes the vector of the number of core asset shocks $n$.
• $\beta$ denotes the matrix of transmission coefficients.
• $\epsilon$ denotes the vector of residuals with mean zero and covariance matrix $\mathsf{\Sigma }$.

Under the Broken Arrow framework, the core asset shocks $X$ follow a mixture of two multivariate normal distributions corresponding to quiet and hectic market regimes:

$$X=\left[\begin{array}{c}\begin{array}{c}{x}_1\\ ⋮\end{array}\\ x_n\end{array}\right]~\left\{\begin{array}{c}{MVN}_q\left(\left[\begin{array}{c}\begin{array}{c}\begin{array}{c}{\mu }_1\end{array}\\ ⋮\end{array}\\ {\mu }_n\end{array}\right],\left[\begin{array}{ccc}{\sigma }_1^2& \dots & {\sigma }_1·{\rho }_{1n}·{\sigma }_n\\ ⋮& \ddots & ⋮\\ {\sigma }_1·{\rho }_{1n}·{\sigma }_n& \dots & {\sigma }_n^2\end{array}\right]\right),quietdayprobability\\ {MVN}_h\left(\left[\begin{array}{c}\begin{array}{c}\begin{array}{c}{\mu }_{h1}\end{array}\\ ⋮\end{array}\\ {\mu }_{hn}\end{array}\right],\left[\begin{array}{ccc}{\sigma }_{h1}^2& \dots & {\sigma }_{h1}·{\rho }_{h1n}·{\sigma }_{hn}\\ ⋮& \ddots & ⋮\\ {\sigma }_{h1}·{\rho }_{h1n}·{\sigma }_{hn}& \dots & {\sigma }_{hn}^2\end{array}\right]\right),hecticdayprobability\end{array}\right.$$

where

• ${MVN}_q$ denotes the multivariate normal distribution on quiet days.
• ${MVN}_h$ denotes the multivariate normal distribution on hectic days.
• $\mu$ denotes the mean, $\sigma$ denotes the standard deviation, and $\rho$ denotes the correlation.

Using the estimated parameters of the two regimes, the conditional probability that a given observation belongs to the hectic regime can be computed via Bayes’ rule. These probabilities are then used to weight observations in the inference model. Specifically, observations are weighted according to their likelihood of belonging to the hectic regime. This ensures that periods of market stress, characterized by stronger co-movements and higher volatility, are given greater influence in estimating the transmission mechanism. As a result, the inferred relationships are more representative of stress dynamics rather than normal market conditions.

The transmission coefficient $\beta$ is estimated using the WLS framework. The weighting structure reflects both heteroskedasticity and the likelihood of stress regimes:

$$\beta ={\left[{\left(X{P}_h\right)}^{T}W\left(X{P}_h\right)\right]}^{-1}{\left(X{P}_h\right)}^{T}WY$$

(4)

where

• $W$ is a diagonal matrix containing weights that are the reciprocal of each error variance.

$$W=\left[\begin{array}{ccc}{\displaystyle \frac{1}{{\sigma }_1^2}}& 0& 0\\ 0& \ddots & 0\\ 0& 0& {\displaystyle \frac{1}{{\sigma }_m^2}}\end{array}\right]$$

In addition, $P_h$ denotes the vector of hectic probability on each day. In the hectic day distribution, both core assets are more volatile, and their correlations are higher than the quiet distribution. These probabilities are obtained from the Gaussian Mixture Model using Bayes’ rule. Specifically, the posterior probability that a given observation belongs to the hectic regime is given by

$$P_h(X)={\displaystyle \frac{\omega {\varphi }_h\left(X\right)}{\omega {\varphi }_h\left(X\right)+(1-\omega ){\varphi }_q\left(X\right)}}$$

(5)

where

• $\omega \in (0,1)$ is the weight of hectic multivariate normal distribution in the Gaussian Mixture Model.
• $\varphi \left(X\right)$ denotes the multivariate normal density, e.g., hectic-regime density ${\varphi }_h\left(X\right)$:

  $${\varphi }_h(X)={\displaystyle \frac{1}{{(2\pi )}^{n/2}{\mid {\mathsf{\Sigma }}_h\mid }^{1/2}}}\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{1}{2}}(X-{\mu }_h{)}^{\mathrm{\top }}{\mathsf{\Sigma }}_h^{-1}(X-{\mu }_h)\right)$$

  (6)
• $\mathsf{\Sigma }$ is the covariance matrix, and $\left|\mathsf{\Sigma }\right|$ is the matrix determinant.
• $\mu$ is the mean vector.

This weighting scheme ensures that observations more likely to occur under stressed market conditions—characterized by higher volatility and stronger correlations—receive greater influence in the estimation of $\beta$. Consequently, the estimated transmission coefficients better capture stress dynamics and provide a more realistic mapping from core asset shocks to peripheral asset responses.

Lastly, $\epsilon$ denotes the matrix of error variances. It is assumed to be multivariate normally distributed with zero mean and covariance:

$$\epsilon =\left[\begin{array}{ccc}{\sigma }_1^2& 0& 0\\ 0& \ddots & 0\\ 0& 0& {\sigma }_m^2\end{array}\right]$$

5.3. Numerical Example

As an example, we consider two core assets ($n=2$), namely the S&P 500 and EUA (European Union Allowance) Futures, over the data period from 1 November 2018 to 31 October 2024. The EUA is the proxy for shadow carbon price that represents the all-in-cost for green transition2. The EUA Futures is chosen despite the existence of multiple carbon markets with fragmented pricing around the world. Owing to its market liquidity and long history, the EUA provides price discovery for the most developed and liquid carbon compliance market and is influenced by various factors, including expectations of climate change policies, demand for emission reduction driven by global political and economic decarbonization, and the supply of carbon allowances within the ETS. The core variables, comprising 1541 daily data points, are used to estimate the parameters of the multivariate mixed-normal distributions, shown in

Table 3. Mixture of two multivariate normal distributions.

Model	Weight, $\mathsf{\omega }$	Mean, $\mathsf{{\rm M}}$	Covariance Matrix, $\mathsf{\Sigma }$	Log-Likelihood
Unconditional, $MVN$	1.00	[0.2985, 0.4457]	[6.6609, 2.9267] [2.9267, 28.3043]	−8374.21
Conditional on quiet days, ${MVN}_q$	0.81	[0.6995, 0.3506]	[1.9454, 1.3539] [1.3539, 17.7022]	−8203.29
Conditional on hectic days, ${MVN}_h$	0.19	[−0.3474, 0.5988]	[13.5813, 5.6208] [5.6208, 45.3461]

.

Figure 3 displays the hectic probability, with each dot representing a single-day shock. In this example, the hectic probability is derived from the daily returns of two core assets: S&P 500 and EUA Futures. Hectic days are observed near the fringe of the distribution, indicating high volatility.

We extend the two-asset example to include six core assets (S&P 500, EUA Futures, USD/INR, Nikkei 225, Brent Crude Oil, and Coal) to capture the climate impact on a broader market dynamic.

The right panel of

Table 4. Unconditional vs. conditional correlations in the Broken Arrow Model.

	Unconditional Correlation						Correlation Conditional on Hectic Days
	EUA	USDINR	Nikkei	S&P	Brent Crude	Coal	EUA	USDINR	Nikkei	S&P	Brent Crude	Coal
Iron Ore	0.002	−0.022	−0.002	0.082	0.050	0.045	−0.075	−0.003	0.066	0.133	0.090	−0.010
USDCNH	−0.011	0.015	−0.023	−0.110	−0.045	−0.023	−0.035	0.030	−0.078	−0.161	−0.069	0.039
USDSGD	−0.033	−0.008	−0.074	−0.181	−0.079	0.018	−0.064	0.011	−0.215	−0.284	−0.178	0.095
KRWUSD	0.030	0.018	0.030	0.119	0.003	−0.026	0.051	0.036	0.095	0.175	0.042	−0.067
Marine Oil	−0.034	−0.031	0.031	0.101	0.249	0.021	−0.095	−0.020	0.053	0.145	0.279	0.029
Paraxylene	−0.039	−0.063	0.033	0.104	0.219	0.025	−0.103	−0.017	0.083	0.165	0.285	0.039
Rubber	0.030	−0.054	0.026	0.137	0.123	0.004	0.049	−0.050	0.104	0.224	0.187	0.002
Lithium	0.042	0.013	0.037	0.024	0.059	0.077	0.015	0.043	0.056	0.052	0.124	0.151
Milk Powder	−0.009	0.000	0.012	0.032	0.089	0.070	−0.028	0.004	0.049	0.099	0.162	0.032

demonstrates that correlations on hectic days are generally higher than unconditional correlations, as expected. Subsequently, this “stressed correlation” matrix will be used to infer the shocks for peripheral assets. In terms of transition risk, a given peripheral asset is influenced directly by the carbon price (EUA) and indirectly, as a secondary knock-on effect, by other core factors from the ISDA model.

In the physical risk scenario, we assume that carbon price shocks are zero, to reflect the view that physical and transition risks do not materialize simultaneously over the very short horizon. The scenarios and associated shocks are presented in Table 9. The inferred shocks for global traded commodities are relatively small, suggesting that extreme weather events, arising from the abrupt thawing of Arctic permafrost, may have limited immediate impact on commodity prices.

In contrast, the transition climate risk scenario considers the imposition of a sudden $200/tonne CO₂e tax, which directly increases production costs across the commodity value chain. This may introduce upward pressure on commodity prices, when the cost impact of the carbon tax outweighs the expected decline in demand caused by climate-induced GDP contraction. The demand-side effect is likely to unfold over longer horizons.

To provide a simple empirical validation of the regime-switching inference model, we compare unconditional correlations with conditional correlations on hectic days, as shown in Table 4, and evaluate the GMM against a single multivariate normal benchmark using log-likelihood. The results suggest that the GMM-WLS framework captures stress-state dependence more effectively than a static correlation model while remaining suitable for practical stress-testing applications.

Nevertheless, the inference model remains subject to limited hectic day data and the assumption that historical relationships remain informative under future climate stress conditions. Such relationships may weaken under unprecedented structural breaks or nonlinear market responses. Accordingly, the inferred shocks should be interpreted as first-order approximations and complemented by sensitivity analysis and expert judgement.

6. Direct Impact Calculation for Freight Markets

Certain asset classes are directly influenced by carbon pricing, particularly when the asset’s valuation incorporates a carbon price input or when the production or sales of the asset incur significant carbon costs. These assets are typically produced by industries covered by the Emission Trading System (ETS), such as electricity, iron and steel. In such cases, the price impact on the asset itself due to an imposition of a $200 per tonne CO₂e tax liability stress can be calculated. If we understand the emission amount and cost for a unit of asset produced, its transition stress loss can be derived without relying on historical data, which often does not contain the relevant climate price discovery. We explore whether the freight futures contracts of Baltic indices traded on the SGX (or its FFA equivalent) may be affected by transition given that the EU ETS was expanded to include maritime transport effective 2024.

6.1. Transition Risk (Carbon Cost Calculation)

According to the European Commission (2024), emissions are considered flag-neutral and route-based. EU ETS rules stipulate that 100% of emissions from a ship performing a voyage between two EU member states are accounted for, as well as 100% of emissions while the ship is at a port in an EU member state. Additionally, 50% of emissions from a voyage where only one port of call is in an EU member state are included. The actual implementation mechanism is still evolving at the time of writing.

After consultation with the market, the Baltic Exchange published guidance3 which requires panellists to include EU ETS costs into the dry voyage assessments. However, in the case of time charters, the situation is more nuanced. Generally, the responsibility for monitoring and reporting GHG emission data lies with the ship owner but under the “polluter-pays” principle4, the ship charterer should pay for the emission allowance. In some cases, charterers could opt to use a special contractual clause, for example, the Emission Trading Scheme Allowances Clause (ETSA) for Time Charter Parties from BIMCO, which obliges the charterer to procure EUA and transfer this to the ship owner. In the absence of an industry-wide standard today, any material EU ETS cost will likely be passed through to the charterer in terms of higher fixtures and daily rates.

Under our stress scenario, the EU ETS has emergency powers to set prices. Hypothetically, the EUA Futures market would be expected to react to an unexpected EU carbon price hike announcement, causing a shock in freight prices. This section illustrates how these shocks are calculated for the case of the Capesize Five-Route Time Charter index. Capesize vessels are large, gearless dry bulk carriers, typically ranging from 130,000 to 210,000 deadweight tonnage (DWT). The five routes that make up the index are depicted in Figure 4.

For the below calculations, we used prices for 21 May 2025: EUA price of EUR73 per tonne; EUR/USD exchange rate of 1.13. The data sources required are as follows:

• The weights and voyage durations of each route in the Baltic indices were sourced from Baltic Exchange Information Services Ltd. (2025);
• CO₂ emission for each route5 (https://emissions.balticexchange.com/en/calculators.html, accessed on 3 February 2026);
• EUA Futures price and rules for EU ETS guidelines for maritime transport (https://climate.ec.europa.eu/, accessed on 1 October 2024).

Table 5. Carbon emission analysis of Capesize Five-Route Time Charter.

Routes	Index Weight (a)	CO2 Ton per Day (b)	EU ETS Accounting (c)	CO2 Cost/Day = (a) $\times$ (b) $\times$ (c) $\times$ USD 82.5
C8_14: Gibraltar/Hamburg transatlantic round voyage	25.0%	111.56	50%	USD 1150
C9_14: Continent/Mediterranean trip China–Japan	12.5%	107.35	50%	USD 553
C10_14: China–Japan transpacific round voyage	25.0%	97.27	0%	-
C14: China–Brazil round voyage	25.0%	118.52	0%	-
C16: Revised backhaul	12.5%	106.01	50%	USD 547
	Total weight 100%			Total CO2 cost/day = USD 2250

illustrates the calculation of total carbon emission cost per day for the asset “Baltic Capesize Time Charter Average (Five Routes)” futures.

The carbon accounting is estimated by applying the EU ETS rules for maritime transport. Consider the C16 route in Table 5 as an example: the starting port is somewhere in North China-South Japan range, and the final port is a port within the EU (Skaw-Passero range); hence only 50% of the emissions need to be accounted for.

The impact of the carbon tax on the index can be calculated using the following formula:

$$\begin{array}{cc}\hfill Impactonindex& =\left({\displaystyle \frac{PolicyCarbonPrice}{CurrentEUAPrice\times EUR/USD}}-1\right)\times Total{CO}_{2}costperday\hfill \\ \hfill & =\left({\displaystyle \frac{USD200}{EUR73\times 1.13}}-1\right)\times \$2250=\$3206\hfill \end{array}$$

(7)

Given a Capesize Five-Route Time Charter contract price of $16,424 in March 2025, the carbon policy shock translates to approximately a +20% stress shock on the index.

6.2. Physical Risk (Congestion Modelling)

The climate stress test scenario for the Baltic freight index futures contract is an extreme weather disaster affecting the shipping routes that make up the Baltic index. Generally, large vessels on the water are highly resilient to swells caused by hurricanes/typhoons. Even if a vessel is damaged at port by pounding waves, the damage is often insured. The real climate risk is the hazard that pounding waves may damage an enroute port making it inaccessible and causing congestion and delays in laytime for loading/unloading cargo. Verschuur et al. (2023) found that 94.8% of global ports are exposed to more than one natural hazard; 86% are exposed to more than three hazards—primarily cyclone wind, pluvial flooding and fluvial flooding. The top 50 most at-risk ports globally (out of 1340 ports studied) are from ports in Asia, particularly located in the Greater China region, ports in the Gulf of Mexico, and ports in Western Europe. Verschuur et al. (2020) analyzed port disruptions arising from natural disasters and reported a median disruption duration of six days, with a 95th percentile of 22.2 days before operations were restored. As the ISDA physical risk scenario does not specify the underlying hazard type, we assume for stress-testing purposes that a severe climate disaster damages a port along a shipping route, resulting in a disruption lasting 22 days, consistent with this upper-tail benchmark.

For existing contracts (or fixtures) the charterer will pay demurrage, a daily penalty for additional days due to the delay. The total voyage cost will inflate because of longer waiting time at sea, demurrage and a potential reroute to another port. A reroute or port substitution might not be a practical solution because of the lack of hinterland connections, specialized equipment for loading (e.g., rails for Iron ore) and contractual restrictions.

For new charter contracts, it is well documented that port congestion can increase freight and charter rates by reducing the effective supply of available vessels. Michail and Melas (2025) studied the relationship between Asian port congestion and containership freight rates using a Bayesian Vector Autoregression (B-VAR) framework. Their results show that a 4% shock to Asian port congestion leads to an immediate increase of approximately 2% in freight rates, with the effect peaking at around 5% after about 8 months. The study uses the Clarksons Port Congestion Index, developed by Clarksons Research, which measures the proportion of global fleet capacity either in port or waiting at anchorage.

For the purposes of this paper, only the short-term immediate effect is relevant because the stress-testing horizon considered is 1–2 days. Therefore, the immediate 2% freight rate response to a 4% congestion shock implies an approximate short-term passthrough rate g of 50%. Since no equivalent short-horizon econometric estimate is available for dry bulk freight markets, the framework assumes that the bulk carrier segment exhibits a similar short-term passthrough relationship to the containership segment. This should be interpreted as a simplifying stress-testing assumption rather than a precise econometric estimate.

Separately, the congestion level for Asian Capesize bulk carriers is estimated at approximately 24%, based on Clarkson Plc financial disclosures (June 2023), with congestion levels having declined below their pre-COVID average, as illustrated in Figure 5. To test the robustness of the assumption, a sensitivity analysis is conducted using alternative passthrough rates of 10%, 30%, 50%, 70%, and 90%. The baseline assumption remains g = 50%, based on the short-horizon response estimated by Michail and Melas (2025).

Table 6. Sensitivity analysis of congestion passthrough rate.

Port Closure Scenario	g = 10%	g = 30%	g = 50% Baseline	g = 70%	g = 90%
Amsterdam/Antwerp/ Rotterdam/Hamburg	+0.28%	+0.84%	+1.40%	+1.96%	+2.52%
Qingdao	+0.61%	+1.83%	+3.05%	+4.27%	+5.49%
South Korea: Pohang/Yeosu/Busan	+0.20%	+0.60%	+1.00%	+1.40%	+1.80%
Japan: Kobe/Nagoya	+0.20%	+0.60%	+1.00%	+1.40%	+1.80%

shows that the estimated impact on the Capesize Five-Route index scales approximately linearly with the passthrough rate. For the Qingdao port closure scenario, the index impact ranges from about +0.6% under a 10% passthrough assumption to about +5.5% under a 90% assumption. The main conclusion remains unchanged: while single-port disruptions can materially affect individual routes, the diversified Capesize Five-Route index remains relatively resilient due to route and port diversification.

Consider a single round voyage route “A → B → A”. For illustration, take Route C5: “Qingdao → West Australia → Qingdao”. Qingdao is destination A, while West Australia is destination B. Often the Baltic Exchange may define a destination port as a range. For example, West Australia (destination B) can include any three ports: Port Hedland, Dampier, and Cape Lambert, as shown in Figure 6.

When analyzing a single route in isolation, we assume it experiences the same level of congestion, denoted by $\kappa$, as the Asia Port Congestion Index. This is a simplifying assumption for our practical application; in reality a port can service many routes. Hence, the shipping network can be very complex to model. In effect, we have assumed this single route (with nodes A and B) is a closed system, and the system will have a combined congestion of $\kappa$. We assume the number of vessels sailing towards B is the same as the number of vessels departing from it; in a state of equilibrium this is necessarily true. The number of vessels sailing will be $(1-\kappa )$, and approaching one of the two ports will be $(1-\kappa )/2$.

Thus, if destination B (West Australia) is closed for 22 days (where the round voyage takes $T_i$ = 38 days), then the increase in congestion to destination B will be

$$\mathrm{A}\to \mathrm{B}\to \mathrm{A}:{∆}_i={\displaystyle \frac{1-\kappa }{2}}min\left({\displaystyle \frac{22}{0.5T_i}},1\right)$$

(8)

Suppose the recent Asia Port Congestion Index is $\kappa$ = 0.24; then ${∆}_i$ = 38%.

In effect, we assumed the number of vessels sailing towards B will contribute to the congestion, and we scale this down by the portion of vessels that would arrive at B in 22 days (before the port recovers) out of the one-way travel time of 0.5 $T$. Suppose destination B is defined by Baltic Exchange as a range of $N$ ports ($N$ = 3 in the case of West Australia in route $i$ = C5); then the number of vessels enroute to one single port (of the three) will be a third of that enroute to B. We had assumed that realistically only one port can be damaged by climate disaster at any one time. Assuming an immediate passthrough rate of g = 50% for Route C5, the daily charter rates of new contracts would be expected to rise by ${∆}_i$·g/N = +6.3% immediately.

If port A ($N$ = 1, i.e., Qingdao) is closed instead, the daily charter rates of new contracts would be expected to rise by ${∆}_i$·g/1 = +19% immediately.

In the second type of configuration, “A → B → C”, the redelivery port is not the same as the delivery port. For illustration, take C16: revised backhaul, North China-South Japan range → Australia, Indonesia, US West Coast, South Africa or Brazil → Skaw-Passero range. The system of destinations A, B and C will have a combined congestion of c. We assume the number of vessels coming to any port is the same as the number of vessels outgoing from that port in the equilibrium state. The number of vessels sailing will be $(1-\kappa )$ and approaching one of the three destinations will be $(1-\kappa )$/3. Note that vessels leaving destination C will eventually find their way back to A; in a state of equilibrium this is necessarily true.

Thus, if node C is closed for 22 days (where the trip A to C takes $T_i$ = 50 days) then the increase in congestion to node C will be

$$\mathrm{A}\to \mathrm{B}\to \mathrm{C}:{∆}_i={\displaystyle \frac{1-\kappa }{3}}min\left({\displaystyle \frac{22}{0.5T_i}},1\right)$$

(9)

Suppose the Asia Congestion Index is $\kappa$ = 0.24; then ${∆}_i$ = 22%.

For destination C, the ports are Amsterdam, Antwerp, Rotterdam, Hamburg, Djen-Djen, and El Dekheila; thus N = 6. Assuming again an immediate passthrough rate of g = 50% for Route-C16, the daily charter rates of new contracts are expected to rise by ${∆}_i$∙g/N = +1.9% immediately. This is very small compared to the usual price fluctuations in the freight markets, suggesting that when a route system has many port nodes, its charter rates can be quite robust to any single port closure.

Table 7. Definition of routes featured in the Capesize Five-Route Time Charter index.

Index Weight	Routes	Description of Route	Delivery Ports	Passthrough or Loading Ports	Redelivery Ports
0.25	C8_14: Gibraltar/ Hamburg transatlantic round voyage	Delivery Gibraltar– Hamburg range, laydays/cancelling 3/10 days from index date, 1 transatlantic round voyage, of 30/45 days, redelivery Gibraltar–Hamburg range. Basis: Baltic capesize vessel. Total commission: 5%.	Amsterdam/ Antwerp/ Rotterdam/Hamburg	Columbia–Puerto Bolivar/Puerto Drummond	Redelivery same as delivery
				Brazil–Tubarao/ Ponta Da Madeira
				East Coast Canada–Seven Islands/Port Cartier/Pointe Noire
0.125	C9_14: Continent/ Mediterranean trip China–Japan trip	Delivery Amsterdam– Rotterdam–Antwerp range or passing Passero, laydays/cancelling 3/10 days from index date, redelivery China–Japan range, duration about 65 days. Basis: Baltic capesize vessel. Total commission: 5%.	Amsterdam/ Antwerp/ Rotterdam/Hamburg	East Coast Canada–Seven Islands/Port Cartier/Pointe Noire	China–Qingdao/ Rizhao/ Lianyungang/ Caofeidian
				Norway–Narvik	South Korea– Pohang/Yeosu/Busan
					Japan–Kobe/Nagoya
0.25	C10_14: China–Japan transpacific round voyage	Delivery China–Japan range, laydays/cancelling 3/10 days from index date, redelivery China–Japan range, duration 30–40 days. Basis: Baltic capesize vessel. Total commission: 5%.	China–Qingdao/ Rizhao/ Lianyungang/ Caofeidian	West Australia–Dampier/ Port Walcott/ Port Hedland/ Stanley Point	Redelivery ports same as delivery
			South Korea– Pohang/Yeosu/Busan	East Australia– Newcastle/ Abbot Point/ Gladstone
			Japan–Kobe/Nagoya
0.25	C14: China–Brazil round voyage	Delivery Qingdao 15–25 days after sailing Qingdao, round voyage via Brazil or West Africa, redelivery China–Japan range, duration 80–90 days. Basis: Baltic capesize vessel. Total commission: 5%.	Qingdao	Brazil–Tubarao/Sudeste/Itaguai/CSN	China–Qingdao/ Rizhao/ Lianyungang/ Caofeidian
				West Africa–Freetown/Kamsar/Pepel	South Korea–Pohang/Yeosu/Busan
					Japan–Kobe/Nagoya
0.125	C16: Revised backhaul	Delivery North China–South Japan range, 3–10 days from index date for a trip via Australia, Indonesia, US West Coast, South Africa or Brazil, redelivery UK-Cont-Med within Skaw–Passero range, duration to be adjusted to 65 days. Basis: Baltic capesize vessel. Total commission: 5%.		Australia–Haypoint/ Newcastle
			China–Qingdao/ Rizhao/ Lianyungang/ Caofeidian	Indonesia–Taboneo/ Samarinda/Tanjong Bara	Amsterdam/ Antwerp/ Rotterdam/Hamburg
			South Korea– Pohang/Yeosu/Busan	US West Coast–Long Beach	Djen-Djen/El Dekheila
			Japan–Kobe/Nagoya	South Africa–Saldanha Bay/Richards Bay Coal Terminal
				Brazil–Tubarao/ Ponta Ubu

shows the routes of the Capesize Five-Route Time Charter index published by Baltic, which is the focus of this study given its futures and FFA have the highest trading activity. Furthermore, the index emphasizes Asia-related routes due to the region’s dominance in dry bulk commodity imports and exports, i.e., only Route C8 does not include Chinese ports. The ports listed in the table are considered primary ports by assessors.

Table 8. Impact on daily charter rates for Capesize Five-Route Time Charter index due to closure of one of the most connected ports.

Routes	Index Weight	Voyage Days	Amsterdam/Antwerp/Rotterdam/Hamburg	Qingdao	South Korea–Pohang/Yeosu/Busan	Japan–Kobe/Nagoya
C8_14: Gibraltar/Hamburg transatlantic round voyage	0.25	55	3.80%
C9_14: Continental/Mediterranean trip China–Japan	0.125	68	2.00%	0.90%	0.90%	0.90%
C10_14: China–Japan transpacific round voyage	0.25	37		2.10%	2.10%	2.10%
C14: China–Brazil round voyage	0.25	93		9.00%	1.00%	1.00%
C16: Revised backhaul	0.125	49	1.90%	1.30%	1.30%	1.30%
Impact on index			1.40%	3.05%	1.00%	1.00%

shows the calculation of the price impact on individual routes and on the index as a weighted sum, arising from the closure of the four most connected destinations in the system. Qingdao is by far the most connected port due to its role as a hub for iron ore imports from Brazil, Australia and South Africa into China and East Asia. The 22-day closure of the Port of Qingdao will cause a 9% price shock to C14 charter rates and a 3% impact on the overall index. This result suggests that the shipping indices (and their derivative products) are very robust to climate change risk because of the diversification effects of multiple routes and ports involved. A single port closure due to extreme weather disaster will cause limited shock to indexed freight rates, even though the impact on individual routes, such as C5, can be material.

Stress testing generally requires only a ball-park estimation of shocks. Thus, we have adopted a simplified approach using regional data. A more precise approach would use congestion data of each port, for example, from data providers such as portcast.io. Such data is compiled using satellite-based vessels tracking. This could allow a model to calculate the passthrough rates for combinations of ports and routes. Such a network model is left for future research.

7. Intensity of Climate Stress Scenarios

Using the transmission channel framework, we derive a set of market shocks over a one-day trading horizon under three climate scenarios in

Table 9. Climate stress test scenarios and shocks.

Methodology	Asset	1. Physical Risk Scenario	2. Transition Risk Tier 1	3. Transition Risk Tier 2
Scaling method (using Country Climate Index)	Japan equities	−5%	−5%
	China equities	−8%	−5%
	India equities	−9%		−6%
	Singapore equities	−8%		−7%
	Taiwan region equities	−8%		−4%
Inference (using Broken Arrow Stress Test)	INR against USD	Appreciate by 5%	Appreciate by 5%
	JPY against USD	+0%	0%
	CNH against USD	Appreciate by 1%	Appreciate by 1.5%
	Thermal and coking coal	−10%	−10%
	Iron ore, all grades	−1%	−11%
	Marine oil	+0%	−11%
	Paraxylene	+0%	−9%
	Rubber	+0%	+5%
	Lithium	−1%	+2%
	Milk powder	+0%	−1%
Carbon cost direct calculation	Capesize CW 5-route	+3%	+20%
	Panamax PW 5-route	+3%	+12.4%
	Panamax PV 4-route	+3%	+22.7%
	Supramax SW 10-route	+3%	+6.6%

:

(i)

A global extreme weather catastrophe (physical risk);

(ii)

A coordinated policy response by climate-ready countries (transition risk, first wave);

(iii)

A delayed policy response by other countries (transition risk, second wave).

A key question is how intense these shocks are compared to historical financial crises. To quantify intensity, we use Mahalanobis distance, which measures the deviation of a shock vector from the historical return distribution while accounting for cross-asset correlations. Unlike Euclidean distance, it adjusts for differences in volatility and dependence, providing a scale-invariant measure of stress severity.

To gauge the intensity of these climate stress events we compare them with historical events from the period from January 1998 to October 2024 using Mahalanobis distance6 to score each event. We illustrate this in Figure 7 by refencing two pairs of key assets and plotting the contour lines of Mahalanobis distance. We can quantify how much a particular scenario deviates from historical norms, considering the correlations between assets. This metric offers a scale-invariant measure of stress intensity for the three climate scenarios under study. All points on the same contour line will have the same Mahalanobis distances from the centroid of the joint distribution. If point A has twice the Mahalanobis distance compared to point B, then event A will be twice as severe as event B. Note that the metric does not inform the probability of A versus B.

Mahalanobis distance is contingent upon the selection of assets, and consequently, it may vary across different financial institutions due to portfolio differences.

Table 10. Mahalanobis distance of climate stress scenarios.

Stress Scenario	Mahalanobis Distance
Global_Financial_Crisis_Oct_2008	19.25
ISDA_Climate_Transition_Risk_First_Wave	19.02
Asian_Crisis_Jan_1998	15.24
ISDA_Climate_Physical_Risk	13.63
Carry_Trade_Unwinding_Aug_2024	12.54
China_Stock_Market_Stress_Jul_2015	12.08
COVID_19_Pandemic_Mar 2020	11.88
ISDA_Climate_Transition_Risk_Second_Wave	9.99

presents the relative intensities of all stress test scenarios derived from a portfolio of 20 assets considered in this study. Mahalanobis distance can be interpreted as a relative measure of stress intensity rather than an absolute measure of loss. A scenario with a Mahalanobis distance comparable to that of the Global Financial Crisis (GFC) indicates that the joint movement of asset prices is of similar magnitude in a multivariate sense. This does not imply identical economic drivers or asset-level impacts, but rather that the overall deviation from normal market conditions is comparable in scale.

However, it is important to note that the Mahalanobis measure is based solely on unit asset shocks and does not account for position concentration. A more refined approach would incorporate the actual portfolio composition. In such a case, one would anticipate that portfolios with a larger allocation to “brown” assets and assets highly sensitive to green transition would be more susceptible to climate stress losses.

8. Further Discussion: Portfolio Aggregation of Climate Risks

This paper proposes a three-component framework for modelling the transmission of climate risks into market risk, establishing a mapping between selected climate scenarios and corresponding asset-level price shocks. This mapping is inherently one-to-many, as a single climate scenario may generate shocks across multiple asset classes. For diversified portfolios comprising securities and loans, this creates non-trivial aggregation challenges, particularly given heterogeneous liquidity horizons across asset classes, which range from days for trading books to up to one year for loan portfolios. Stress loss aggregation must therefore be aligned with the relevant risk horizon. For short-horizon portfolios—such as trading books with a two-day horizon—it is inappropriate to aggregate losses from physical and transition risk scenarios. Climate events unfold sequentially: policy responses to major physical disasters typically require days to weeks to materialize, exceeding short-term risk horizons. A combined physical-transition scenario would thus incorrectly assume contemporaneous losses within the same period. In contrast, for longer-horizon portfolios such as loan books, a combined scenario is meaningful and can be applied consistently.

In transition-risk-only scenarios, globally traded assets (e.g., commodities) are assumed to react immediately to unexpected carbon policy announcements. However, given fragmented global climate regulation, synchronous carbon tax implementation across countries within a few days is unlikely. For country-specific assets such as equities and bonds, policy transmission depends on domestic legal and institutional readiness. We therefore model transition shocks in two waves: an immediate response for countries with operational emissions trading systems, and a delayed response for others, resulting in two distinct sets of transition-related stress losses.

Physical climate risks, by contrast, are assumed to affect countries idiosyncratically due to geographical separation. As a result, short-term physical risk losses across countries are not aggregated. Aggregation becomes feasible only over longer risk horizons, such as those relevant for loan portfolios. For intermediate horizons, a tailored aggregation approach is required.