Generating Useful Climate Scenarios For Financial Risk Assessment 

Blogpost series on scenarios for assessing financial risk, see part 1 here.

Lots of discussion has happened around climate disclosure for financial institutions as a mechanism for discussion to begin on whether they are at risk from climate processes, and whether these generate systemic risks for the entire financial system. Following various exercises, banks increasingly do stress test their positions, as do central banks. Physical risks are increasingly recognised as material, and so are transition risks, although to a lesser degree (though not as much and, we think, probably vastly underestimated). Scenarios have been identified as useful for more effectively understanding, identifying and discussing climate-related risks. The NGFS has achieved what is arguably the most important contribution by creating climate scenario storylines that have been unanimously adopted across member country central banks.

However, much work remains, and while the importance of using scenarios has been emphasised  and entered the regulatory space, there has been little discussion regarding the content of scenarios. What storylines are useful to look at? Obviously, there is both the potential to help raise awareness of risks, as well as downplay the risks, depending on what we choose to explore in scenarios. For example, a scenario of flood risks presented as the worst-case scenario could be reasonably interpreted as meaning that no floods greater than those described could be expected to occur. If the bar chosen is too low, then the scenarios create moral hazard. We have discussed this moral hazard in a previous blog post. This piece is about working out from clear scientific premises what content scenarios for financial risk assessment must provide, and how to calibrate their frequencies and magnitudes in a scientifically robust way.

Why do economic decision-makers need scenarios?

Scenarios are used by most decision-makers one way or another, whether it is fiscal forecasts, central bank stress tests, or energy demand and supply for the energy sector. We’ve articulated in an AFD working paper why Ministries of Finance and Public Development Banks could benefit from climate risk and policy scenarios. The narrative is that MoFs, under their mandate, have to navigate an increasingly complex and fragmented landscape of public finance, debt sustainability and global financing conditions. This is for a range of reasons, including intensifying climate impacts with events of ever greater magnitude, global geopolitical rifts, global financial instabilities, cross-border risks, debt sprawling with volatile interest rates. Global risks are magnified partly by the increasingly interconnected nature of the global economy. These risks however are relevant to all types of economic and financial decision-makers, including central banks, public development banks, investment banks, funds, pensions and so on.

Extreme climate physical risks are illustrative of a broader landscape of risks relevant to economic decision-makers. Floods, storms, heatwaves, droughts, and other climate change driven disasters increase in frequency and magnitude as the planet warms. A better way to look at it however is to say that their magnitude increases in such a way that they frequently break historical records. It is the tail of physical risks that matter. One way to understand this is to observe that these risks are ‘heavy-tailed’ (frequency distributions that decline with magnitude more slowly than exponential), and that their tail heaviness increases over time. This means in practice that, rather than seeing a yearly cost out of GDP characterized by an expect annual damage, what we see instead is no costs most of the time but an increasing risk of out of proportion disaster. Nothing of note may happen in many years, or, several record-breaking events can occur the same year obliterating the country. Both of these are not implausible, and we have to live with those superimposed possibilities.

Figure 1: Illustration of changes in mean and variance for heavy-tailed distributions for climate disasters, the effect of which moves probability weight into the right tail, and therefore the ‘tail heaviness’ increases. The emergence of tail events is often much more impactful than the changes in mean or variance themselves.

Economists often make a critical mistake with these statistics: a World Bank report said that climate risks impose a cost of 6.5-9% of GDP per year to Pakistan. But when the disaster actually hit, the big flood covered the 30% of the country’s landmass and wiped out 30% of public finances, although it didn’t occur every year. Hard to say whether if we average this over time, it would give 9% per year, but that’s not the point. 9% per year is a misunderstanding of the statistics. The reality is that a flood of such magnitude is entirely possible, and its likelihood will only go up as the planet continues to warm, but it doesn’t mean it will happen every year. Furthermore, the challenges for the sovereign are vastly different between 9% GDP per year and 30% of public finances in one go. Thus, taking an average of climate damages is not helpful to anyone, it is quite misleading.

Why do we get such large disasters at all, when they should be entirely improbable? How is it possible that we break records like that every year, or several times a year? (e.g. the UK got 5 record breaking heatwaves in 2026). Hugely costly disasters are not improbable, they occur essentially because the elements conspire. Compounding multiplies the losses. Problems attract more problems that attract ever more problems. Cascading rapidly escalates. We live in a new era in which there is no ‘normal’ climate, where the likelihood of the climate-related events that conspire become mainstream, and this means that we should expect to see all kinds of extremes from compounding. We need to understand this better.

 

Risk assessment is all about plausible extremes

In some mainstream scenario methodologies, risks are understood as exploring what may happen if various trends are maintained, bringing the evolution of the economy in different directions, which is used to delineate a range of plausible situations. Some may use, for example, utility or cost optimisation scenarios with different contextual inputs incorporating different types of shocks to the economy. This is used to assess whether existing preparedness is adequate. Philosophically, this is a bit circular, as it looks at risk from the perspective of a very tame subset of possibilities, the ones that we already know well, the ones we see if we look at the trends. It explores mostly things that are already well modelled, and plays blissful ignorance over the things that we know less well, like extremes.

However, risk assessment is, by definition, about studying the potential implications of events lying outside of the known path. This is critical, because as we discussed in our previous blog post, being unambitious with the risks included in scenarios and stress test exercises creates real risk for economic decision-makers, which, for example, may lead to adopting inadequate capital buffers. So the question then is, which scientific basis do we have to work out what is plausible in the vast world of extremes? How do we avoid getting lost in the vastness of possibilities? How big is big?

In reality, there really are no excuses for being unambitious with climate risk. In Japan, and other countries lying on the tectonic ring of fire, methodologies are well established for assessing preparedness to earthquakes, they don’t mess around with this. We will henceforth use an earthquake metaphor for all climate risks, something that we call the earthquake law. The frequency-magnitude distribution of earthquakes (the Richter-Gutemberg law) is exceedingly well measured everywhere where it matters. It is quite a simple relationship, it is a straight line on a frequency-magnitude log-log graph over more than 8-10 orders of magnitude, with a slope of -1. Essentially, it means that an earthquake 10 times larger than a reference is 10 times less frequent. If you know exactly how many magnitude 7 earthquakes you’ve had in history, you know fairly well how many magnitude 8 or 9 you can expect. That law doesn’t change over time, and -1 describes what we will call its tail ‘heaviness’.

Do climate disasters behave like earthquakes? The answer is, in many cases, yes (Figure 2, reproduced from the book by Mercure & Pollitt using EM-DAT). The caveat is, it depends on which variables we look at (physical, economic or human), but damages and casualties typically follow their own earthquake law, roughly speaking, a straight line on a log-log graph (it doesn’t matter that much if it is exactly a straight line – it takes a lot of data to measure tails precisely). The difference with earthquakes however is the slope, and the fact that the tail gets heavier over time due to anthropogenic climate change. What we need to know is how fast this is happening. The advantage of looking at the problem from this perspective is that it offers a good way to understand what to expect over time quantitatively. It doesn’t need to be extremely precise to be useful. In fact, the lack of apparent precision is a strength when compared to other climate economic approaches that give the illusion of well quantified damages and risk suggesting false precision.

Figure 2: Density distribution for flood impacts globally (left) in terms of casualties, and (right) in terms of monetary damages, using the EM-DAT database. The slope has changed before and after 2012, chosen as the mid-point of the dataset. This indicates that tails are getting substantially heavier over time.

 

Some notes from complexity science and the stats of rare events

One of the fathers of complexity science, Benoit Mandelbrot (mostly known for fractals), noted back in the 60s something really important that we keep forgetting these days. In finance, we love the so-called ‘central limit theorem’, which tells us that if we add a large number of random variables to one another, we always obtain the standard bell curve. This sort of certainty feels comforting, because it makes us believe that statistical processes always follow bell curves that are bounded on both the upsides and downsides. We then measure things like financial asset price time series and with as few as 50 data points, we fit the bell curve, and abracadabra, we already know how likely tail events are and calculate the value at risk. 10 sigma events cannot happen within the lifetime of the universe. We consider that anything 3-4 standard deviations away from the mean is literally impossible. You can’t beat the central limit theorem.

What Mandelbrot told us back in the 60s is that there are two possible outcomes of the central limit theorem. If all the variables are ‘thin-tailed’, then the outcome is the bell curve, true. But if any single one of the variables is sufficiently heavy-tailed, the sum converges towards a heavy tailed distribution, but not the bell curve anymore. More often than not, it can described by a straight line on a log-log graph. That’s quite a strong finding, because it means it might become hard to find anything that is not heavy-tailed in climate processes (this is also the main argument of Taleb in The Black Swan). And indeed, in the world that we observe, there are relatively few things truly described by the bell curve. And for disasters, the bell curve is a bit of a fallacy, it would mean that ‘the largest event you can expect to see is the largest one you have ever seen’ in the historical record. Absolutely not true in general.

Figure 3: Frequency-magnitude density distribution of delays in the London Tube between early 2020 and end of 2025.

But there is science behind this. Heavy tails arise because of compounding. We’ll use our now famous example of the London Tube (Fig 3, See Chapter 3 in the book by Mercure & Pollitt). Let’s assume that a train, operating on its own in the middle of the night, has a likelihood of arriving on time described by the bell curve, for a range of reasons to do with its own operation. When you put it in a very busy tube system, it is much more likely that it will be disrupted by other trains than being disrupted by its own operational problems. One train delay causes a domino chain of other train delays. All the train delays compound, and it is not rare that one or another tube line is entirely bogged down for hours. With a large dataset of all London Tube delays over five years, we’ve shown that delays follow an earthquake law (up to a cutoff duration of one day), with a tail heaviness that depends on the particular tube line according to how busy it is. In the real messy world, we would be tempted to suggest that risks more or less always cascade into earthquake laws. Whether it is exactly true is not so much the point, but what’s critical is not to underestimate extreme events, which are often the most impactful events,  as may happen with other modelling methods.

A few additional things emerge from this: high magnitude disasters have long-range correlations and systems have memory (Fig 4). By that we mean that things that seem to operate independently, such that we’d consider their risks unrelated, are often not unrelated in situations of disaster. Think of asset prices and financial institutions during the 2008 crash, there seemed to be nowhere to hide. Systems have memory in the sense that when trouble starts, it starts to feed on itself in a vicious cycle: we see clustering. This is also a feature of earthquakes: they always come with aftershocks. The highest chance of an earthquake happening is when you’ve just had one. The chance is not evenly distributed over time.

Figure 4: Water level at a random measurement point on the Otter River, Devon. Seasonality is visible, but zooming in, clustering of high water levels is clearly observed over winters. The density distribution of water levels follows approximately an earthquake law with cutoff.

The last point to borrow from complexity science is that heavy tails don’t have reliable statistical moments. The expected value of a fat-tailed quantity is either infinity, or is infinitely uncertain because the standard deviation is itself infinity. There is, however, an interesting way to explore heavy tails, which is to imagine a business event expecting 1000 attendees, where we want to calculate two quantities as people enter the venue one at a time: (A) the average height of persons in the room; and (B) the average income in the room (Fig 5).

The income distribution in all societies is heavy-tailed with a tail heaviness that varies by country, largely because changes in the wealth of people depends on changes in the wealth of other people, creating cascades, just like train delays in networks (here we used values for the US). But the height of people is very well described by the bell curve, because the height of one person is independent from the height of another. After 500 persons have entered the venue, the average height becomes extremely accurate, and is unlikely to change much even if a very tall person comes in. The expected value for the height of the next person to come in is very clearly defined within uncertainty bounds. The likelihood of seeing a 3m tall person is zero.

But for wealth, it’s very different, after 500 persons come in, we still don’t really know the exact average wealth, as it jumps up every time someone with high net worth comes in, and the standard deviation is not stable. It may appear to be converging, but if we then let 1 million new people in, the standard deviation would keep creeping up without end as the chance of wealthy people coming in rises. For an infinite number of people, the standard deviation would be infinity. The implication is that the expected value for the wealth of the next person coming in is anything between zero and the value of the richest person around, with essentially infinite uncertainty and zero predictive power. This is illustrative of climate driven extremes.

Figure 5: Thought experiment with bell curves and fat tails, imagining the average (A) height and (B) wealth of persons in a room as they come in one at a time.

The analogy with floods is that the magnitude of the next flood is undefined, and so is its standard deviation, making the damage function a fallacy. That’s why “searching” for the correct damage function, or even its functional form, is a hopeless endeavour, there is no correct function to describe economic damages from climate change that is waiting to be “discovered”.

Adopting the right philosophy for climate scenario design: how big is big?

Getting to the practical stuff – in scenario design, it is important to avoid making choices arbitrarily, because arbitrariness is misleading. It means we make up the risks we are assessing, which is circular. What we’ve often seen happen in the sector is a process in which analysts will choose a set of disasters to include (first degree arbitrariness), and then create storylines with those events using magnitudes also chosen, often in discussion with the clients buying the scenarios (second degree arbitrariness). For example, someone designing a scenario of climate-related financial meltdown may decide that the meltdown size scales to 2008, because the paying clients said this would be sensible. Using events bigger than this ‘doesn’t sell’, because nobody thinks it is plausible, or if it happens, the financial analysts would be out of a job anyway, therefore nobody wants to look at that.

Sadly, the statistics very much don’t work that way. Critically, it is not true that we don’t know enough about magnitudes that we would have to ask clients for advice on what they ought to be. And this is of course where all the moral hazard is created: if for-profit clients want something, chances are it is because it is profitable in some way. The question here is then: for a given level of cumulative emissions, should we really calibrate our financial preparedness to the largest event we have ever seen, assuming it is the largest we will ever see? Why should we think that the relative sizes of the next financial crises are unlikely to be larger than 2008? That’s definitely a scientific fallacy, financial crises follow an exact earthquake law, something known for more than 20 years .

In truth, it is actually very easy to calibrate event magnitudes: we can simply use earthquake laws, which are incredibly easy to measure. In our team we have applied earthquake laws to all sorts of things: Trump tariffs on other countries, protests in countries with political turmoil, armed attacks in conflict, exchange rate drops, supply chain breakdowns, S&P500 crashes, commodity price hikes in politically volatile situations, and many more. The question is much more about how stable the tail heaviness is, rather than whether the extremes follow a heavy tail. Extremes pretty much always follow heavy tails. But as the world becomes increasingly unstable, tail heaviness increases everywhere.

So which bit of the fat tail should we use in a specific scenario? Extreme value theory allows us to convert a magnitude into a frequency or a return rate. This means that instead of using an arbitrary choice over the magnitude, or asking the clients to choose the magnitude, we can make a much safer arbitrary choice on the time of recurrence determined by our “risk appetite”. For example, once in 100 years. It’s clear that an event that occurs once in a billion years is barely relevant, and unimportant. An event that occurs monthly will not have a magnitude worth discussing. One in 100, 200, or even 500 years are sufficiently frequent that we may see them happen in a lifetime, and sufficiently powerful to cause a crisis. This carefully chosen value is what expresses risk tolerance. This is standard in risk management across various domains and common practice in the actuarial profession. For example, under regulatory frameworks like the European Union’s Solvency II and the UK’s prudential standards, insurers must hold enough capital to absorb unexpected losses up to a 99.5% Value-at-Risk (VaR) over 12 months, or a 1 in 200 year event. It would be wise, and straightforward, to adopt this approach across the board of climate risks.

This would solve one of the big philosophical debates in the climate space, whether or not to use historical data to identify what can be expected in order to design risk assessment scenarios. Those who say that historical data should not be used, because it is not a reliable guide to the future when disaster frequencies and magnitudes increase, underestimate what can be done with the data. If what one was planning to do with the data was standard linear regressions, and calibrate bell curves to derive damage functions, then indeed, this methodology is trapped by the false adage ‘the largest event you will ever see is the largest event you have ever seen’, a misleading fallacy. Eliminating the assumption of normality solves a lot of problems. The earthquake law, or alternatively, quantile regressions, as demonstrated by Matteo Coronese from Sant’Anna, provide more reliable magnitudes.

It is natural that decision-makers would rather have precise yearly cost numbers for climate change, to weigh against other aspects of policy or company strategy. But those damage functions don’t actually exist in reality. A “correct” function that describes climate driven damage simply does not exist.

What the earthquake frequency-magnitude profile doesn’t solve is the event clustering that we observe. People sometimes think that when you haven’t had an earthquake for a long time, that you are due having one, or waiting for the ‘big one’ to occur. But that’s not a correct interpretation of data (Fig. 3). The likelihood is highest just after events, which actually decreases exponentially afterwards, and is true of more or less all disasters, even socio-economic ones. This operates at all time scales. It’s not actually uncommon to have more than one record breaking flood in a single year, something that under the bell curve would be doubly implausible. In scenarios, should we have one big event, or a series of 10 smaller ones? Or one big followed by lots of aftershocks? The outcomes are all different, and it’s not clear that taking averages of all those possible outcomes is informative.

Conclusion

In short climate-economic risk is distributional rather than adequately represented by an expected annual loss. Severe outcomes arise from the upper tail of hazards and, critically, from nonlinear transmission through exposed and interconnected economic systems. Scenario design should therefore explicitly sample this tail. Instead of choosing event magnitudes subjectively or anchoring them to the largest historical event, scenario designers should specify a transparent risk tolerance or “appetite”, which can be expressed as an exceedance probability or stress level, and use extreme-value, climate and impact evidence to determine the corresponding severity under the relevant future climate state. The crucial object is not simply whether the climate hazard itself has a fat tail, but how tails are generated, amplified and transformed as physical extremes propagate into economic losses and ultimately financial instability.