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CLIMAFIN - Quantify Climate Transition Risk

Updated: Feb 4

 This paper presents CLIMAFIN, an innovative framework designed to inte grate climate risk assessment into financial portfolios, addressing the urgent need for sustainable finance in light of the European Commission’s ”Action Plan on Sustainable Finance.” Through the utilization of Integrated Assess ment Models (IAMs), CLIMAFIN evaluates the impact of climate policy un certainties on investments, focusing on government bonds and equity holdings. It introduces methodologies for calculating Climate Value at Risk (VaR), as sessing potential losses from climate change, and distinguishing between green and brown investment strategies. The tool aims to guide investors, policymak ers, and financial analysts towards making informed decisions in a transition ing economy, emphasizing the importance of proactive, sustainable financial planning to mitigate climate-related financial risks.


The growing interest of European insurers and policymakers in green finance is a direct result of increased awareness and targeted strategies to lessen the financial sector's risk from climate change. This forward-looking approach is not just a passing trend but a necessary answer to worldwide challenges, as highlighted by the European Commission's "Action Plan on Sustainable Finance." This plan, among others, aims to reduce the risks from a disorder move towards a greener economy, introducing a new kind of risk to the financial world: the risk from transitioning to a low-carbon economy.

In this report, we introduce CLIMAFIN, a state-of-the-art tool developed to calculate the financial risks from sudden changes related to climate policies, focusing especially on how they affect the value of investments. This model carefully examines how uncertainties in climate policies impact government bonds and equity holdings. It is based on the idea that investors are generally aware of broad climate and energy goals, yet there's still widespread uncertainty about when and how specific climate policies will be put into action in different countries. Such uncertainty is worsened by unclear future economic paths, particularly those involving changes in how economies produce and adopt energy. These changes ripple through the complex world of market dynamics, affecting the competitiveness and earnings of businesses in both fossil fuel and renewable energy sectors.

We delve into the nature transition risk, explore the complex world of Integrated Assessment Models (IAMs), and dissect the financial basics of stocks and bonds considering changes in climate policy. Nonetheless, in doing so, we must tackle the complex challenges that traditional financial risk methods face when dealing with climate risks, marked by deep uncertainty, unpredictable patterns, and internal factors. With CLIMAFIN, not only is the aim to stress out the potential financial turmoil caused by the transition to a greener economy but also to provide financial experts with a useful tool for navigating the changing energy and policy landscape. Ultimately, what we wish for is to make the financial impact of climate change not just visible but measurable, providing a strong base for making strategic decisions and shaping policies.

Climate Transition Risk

The Network of Central Banks and Supervisors for Greening the Financial System, or NGFS, describes climate transition risks as those linked to adjusting to a greener, less carbon-intensive economy. These risks are about unexpected changes in the value of assets because market players are not fully prepared for or protected against the effects of suddenly aligning with climate goals.

Indeed, It is now widely accepted that achieving a "net-zero-emission" target is inevitable. The discussion, thus, has shifted to determining the right time and method to reach this goal. No matter the strategy, the impact on various economic sectors and the value of financial assets will be substantial. However, planned and gradual steps towards this change could help soften the blow compared to a rapid and unanticipated transition, which would likely hit financial stability much harder.

To illustrate the potential impact, research has shown that losses could be as high as 4 trillion USD for just the energy sector, and when considering the entire economy, this figure could soar to 20 trillion USD.

Specifically, a messy transition could lead to sudden and severe changes in Gross Value Added (GVA)—the measure of the value of goods and services produced—which affects the income of both lenders and borrowers. Thus, it would also force a reevaluation of the likelihood of borrowers not meeting their obligations, affecting both the price difference between government and non-government bonds and the perceived risk of lending, as a consequence.

Furthermore, climate risks possess unique features when compared to more common categories. For one, they are not-linear, meaning they cannot be predicted by looking at past trends and are not evenly distributed. Secondly, they come with deep uncertainty. Because of factors in the natural sciences, predicting the outcomes of global warming involves dealing with rare but significant events whose timing and location are unknown. Specifically, tail events and tipping points are much more recurrent in these situation than in ordinary ones.

Finally, the inherent nature of climate risk is influenced by the uncertainty of policy decisions and how investors think about these risks, leading to a situation where multiple outcomes are possible. As a result, even well-informed investors cannot commit to a single preferred strategy.

In general, the complex nature of these statistical issues means that ordinary financial risk methods do not work, and new approaches need to be developed.

Figure 2 shows the impact of climate change on GDP, distinguishing between three scenarios: no transition, delayed transition and successful transition to Net-zero emission by 2050. Note that, after 2050, transition risk is ruled out of the model.

Integrated Assessment Models

To meet the challenges of climate risk (deep uncertainty, endogeneity, and non-linearity) an innovative kind of modelling must be developed. Several disciplines shall be considered and merged with the objective to build a model able to quantify the economic impact of climate change and policies. It is from this very heterogeneity that the complexity of this approach derives. Linking macroeconomics, sociology, and other social sciences to studies on greenhouse gas opens a Pandora’s box from which a broad range of scenarios escapes.

Figure 3 shows the some climate policy scenarios and the Base one. The columns respectively describes: the shock, the scenario considered, the type of scenario, the extent of the target , the target’s technical details in terms of ppm (concentration of CO2 emitted) and W/m2 (radiative forcing).

Each IAM is unique and combines diverse fields differently: they vary based on the need they answer to, and it would be impossible to fit each into a single category. For example, while some focus on estimating the cost of global warming, others attribute more importance to quantifying future scenarios, providing more detailed information. Still, one factor remains common among the different categories: their primary objective is to provide policymakers with the tools to make the best decisions possible. In fact, rather than predicting the future, IAMs seek accurate estimates of what future outcomes look like.

Equity Contracts

In this section we will focus on the valuation of risk-neutral equity contracts. Not accounting for any climate policy scenario, the value of equity at time , is canonically calculated as the Net Present Value of future dividends. Namely, Considering a constant growth rate g, it is:

Or, put more elegantly,


  • div(b) denotes the dividends under the Base (no-shock) scenario;

  • g(B) is the (constant) growth rate of dividends;

  • r is the cost of capital

Introducing the possibility of a climate policy shock in our valuation means assuming a change in both dividends and growth rate. To be more precise, in carbon-intensive sectors both dividends and growth rate are expected to decrease logically. Whereas, they are likely to rise for green economic activities. The new value shall then simply be the sum of:

- the NPV of dividends before the shocks;

- the NPV of dividends computed after the effect of the policy-shock at , namely div(P)


Sovereign Bonds

Consider a sovereign bond, issued in with maturity . If we assume a probability of default equal to , and, as a consequence, a probability of not defaulting, the bond’s value at maturity shall be:

Given (Recovery Rate) and (Loss given default), respectively the bond’s percentage recover and loss in case of default, the expected value of the security shall then be computed as:

Reached this point, it is straightforward to provide a formula for the sovereign bond price . All is necessary is to discount its expected value, , by the risk free rate (under the risk-neutral measure Q):

Viceversa, vj implicitly defines the yield to maturity for bond j. The bond spread can then be defined as, sj=yj-yf , with

Sovereign Default Probability

Despite being usually perceived as “safe assets”, sovereign bonds too carry credit risk , i.e. the losses to due borrower’s failure to fully repay the loan. This occurs when the borrower’s liabilities exceed its assets. Specifically for sovereign bonds: whenever the debt securities issued (liabilities) surpass the accrued value of tax revenues minus expenditures (assets).

Thus, given an idiosyncratic shock n in time T, a sovereign entity default if:

Introducing a climate policy shock ξ in the model, forces us to expand the default condition to

Or, in terms of teta(the default threshold under scenario P):

(Note that the two shocks are assumed to be independent)

Now, it is possible to define sovereign default probability and its adjustment due to climate policy shock. Intuitively, the default probability, under climate scenario P, is defined as:

Hence, being ΦP(η) the probability distribution of the idiosyncratic shock:

In order to extend our analysis to the adjustment in the default probability, we must take a step back, and consider the impact of small productivity shocks. Indeed, regardless of the implementation of climate policies, such disturbances have a notable effect on the default probability. Once we factor in the influence of climate policies, it becomes apparent that these measures, by affecting productivity, indirectly contribute to shifts in the probability of default.

Therefore, considering θ(P) = θ(B) − ξ(P), the adjustment in default probability due to scenario P is:

Δq(P) = q(P) − q(B)

Then, utilising basic principles of calculus, we reach the final formula

Climate Spread

Climate Spread is the adjustment in the spread a bond, under the Climate Policy Shock Scenario B->P . It quantifies the economic impact that climate policies and the connected risks may have on specific investments or on an whole portfolio. Hence, it shall be computed as:

Δsj = sj (qj (P)) − sj (qj (B))

Where defines the probability of default for trajectory X. Moreover, once we denote the policy shock as ξj , it follows from previous formulas that the Climate Spread is inversely proportional to the latter.

Figure 4 shows the change, in percentage points, of the Long term interest rate, comparing three scenarios: current policies, delayed transition and successful transition to Net-zero emission by 2050

To give a quantitive and graphical perception of the subject-matter, the above graphs come in handy. As data from the NGFS Climate Scenarios report of 2021 clearly depicts, the long term interest rate is bound to increase much more substantially under delayed transition, than with other scenarios.

Climate Value at Risk

Climate VaR measures the maximum potential loss that investors’ portfolio may incur in a given period and with a predetermined confidence level ,CVaR , due to events strictly linked to climate change. Put it more roughly, it measures the maximum financial risk associated to the impact of climate change on investments’ value.

Climate VaR is particularly relevant for investors that tries to understand and mitigate the effect of climate risks on their portfolios. It may comprehend either the to direct physical risks, such as natural disasters; as well as transition risks, namely those stemming from the shift toward a low-carbon economy. Regarding debt securities, the “standard” definition of Value at Risk is value VaR such that

Here,πi and ψi denote , respectively, the portfolio’s rate of return and its probability distribution. Considering a Climate Policy shocks we adjust the formula as follow

In addition, the Climate VaR is:

- inversely proportional to the policy shocks ξj;

- directly proportional to the marginal default probability adjustment Δqj (P) of a bond.

On the other hand, for equity contracts, the definition is similar:

To give some numbers, a research conducted in 2017, have compared the Climate VaR between “green” and “brown” investment strategies, in the 20 European commercial banks most affected by climate risk.

Figures 5 & 6 show the Climate Value at risk (at 5% significance) in equity holdings of the 20 European commercial banks most affected by climate risk. The different colours indicated “green” and “brown” investment strategies. Source: Battiston et al, A Climate stress-test of the financial system , 2016

As the graphs clearly shows, when including Climate Risk into the computation of the Value at Risk, the difference between investment strategies is massive. Since low-carbon investment are incredibly less risky (at least in term of climate risk), we can assume that banks which shifted their stakes from policy-relevant sectors to sustainable ones will witness positive volatility in their assets.


Evidences show that financial markets have been remiss in including climate transition risks into the computation of expected returns. This glaring gap has spurred the development of innovative models capable of accurately quantifying and measuring the unique characteristics of this category of risk.

Navigating the complexities of deep uncertainty, non-linearity, and inherent complexity often appears as a challenge for statisticians, akin to a nightmarish scenario. Yet, it is through the adoption of groundbreaking models, such as Integrated Assessment Models (IAMs), that the tools to free analysts from this analytical issues are found. IAMs, drawing from various disciplines, serve the crucial purpose of providing policymakers with precise estimates of potential future outcomes.

Distinguishing between equity contracts and sovereign bonds, the specifics of pricing models were explored. For equity, the Value at a given time (t), under a climate policy scenario (P) was determined, factoring in dividends (div) , the cost of capital (r), and a constant growth rate (g).

Secondly, sovereign bonds were analyzed. Leading to the conclusion that bond prices should align with the expected value of the bond.

Moving to the study on risk measures, focus closed in on the impact of climate transition risk on productivity, subsequently affecting sovereign probability of default. Here, the adjustment in default probability was introduced as a critical metric.

Successively, Climate Spread was presented as an equally important measure. Defined as the adjustment in the spread a bond, under the Climate Policy Shock Scenario B->P . Its computation take the following form:

Finally, the paramount measure of risk, Climate Value at Risk (CVaR), was unveiled. This metric, applicable to both equity and sovereign contracts, factor in the probability, the value of security under a climate policy scenario, and a new confidence value. It is defined as:

We would like to point out that, drawing from a 2017 study, the profound divergence in CVaR between sustainable and fossil-fuel-intensive investments was underscored, emphasizing the magnitude of the distinction. In conclusion, the comprehensive body of evidence presented in this report echos a call for action in the face of climate change. This imperative necessitates a thoughtful and transparent response, where investors are informed about the expectations set by policymakers. A key revelation is that the evolution toward a new era of finance is inevitable. The choice lies before society: to proactively embrace this evolution and prepare for the future or to close eyes and dismiss it as a mere nightmare. An unequivocal truth remains: this marks only the initial step toward a finance paradigm that is as transformative as it is necessary


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