John Hillier, Tom Perkins, Ryan Li, Hannah Bloomfield, Josie Lau, Stefan Claus, Paul Harrington, Shane Latchman and David Humphry
In 2022 a sequence of storms (Dudley, Eunice and Franklin) inflicted a variety of hazards on the UK and across Northwest Europe, resulting in £2.5–4.2 billion in insured losses. They dramatically illustrate the potential risk of a ‘perfect storm’ involving correlated hazards that co-occur and combine to exacerbate the total impact. Recent scientific research reinforces the evidence that extreme winds and inland flooding systematically co-occur. By better modelling how this relationship might raise insurers’ capital risk we can more firmly argue that insurers’ model assumptions should account for key dependencies between perils. This will ensure that insurers continue to accurately assess and manage risks in line with their risk appetite, and that capital for solvency purposes remains appropriate.
Introduction
UK insurers use simulated extreme weather events to inform their pricing, manage their accumulation of risk, and decide how much capital they need to operate from both an economic and regulatory viewpoint. Historically, for simplicity, major modes of natural threat were often modelled separately. Yet, different types of adverse scenarios can correlate and occur together. If the correlations are too weak in an insurer’s model, it could lead to under-capitalisation, thereby weakening financial protection for policyholders.
Our work here builds on exploratory work in 2021. It picks on some of the UK’s most spectacular and destructive winter weather, strengthening the evidence that it is important not to neglect the co-occurrence of severely wet and windy conditions. Critically and globally, however, this is but one of numerous correlations that might be under-represented in many insurers’ models.
Wintertime windstorms tend to co-occur with inland flooding on many timeframes
The UK’s two most impactful hazards are extreme wind (including storm surge) and inland flooding. Over nine days, storms Dudley, Eunice and Franklin brought a mixture of damaging winds and inland flooding, snowfall and rain-triggered landslips. Was this an exception, or something to be expected? To shed new light on this question, Bloomfield et al (2023) measured flooding-wind dependency using consistent methods on a range of data sets, which included 240 modelled years of UK Met Office climate projections and historical loss data. They used a spectrum of time frames for correlation (days to seasons) and they modelled river flows rather than just rainfall. The key result is that a correlation of ~70% exists between the hazards of extreme wind and inland flooding (Chart 1).
Chart 1: Plots of wintertime correlation between flooding and extreme wind in Great Britain (GB) and western Europe
Notes: Adapted from our recent scientific study.
(a) The level of correlation in Great Britain between wind hazard and rain (purple), and between wind and river flow (yellow) in the October–March season. Error bands are 95% confidence.
(b) To illustrate a broader context, a map of correlation at a seasonal time frame across Europe, between wind and historical river flows; explore this further in an online tool.
In reading this chart, it is important to recognise that heavy rain does not necessarily result in a dangerously high flow in a river, which in turn does not always convert into flooding. In panel (a) the historically observed losses (2006–18) on Great Britain’s rail network are used as a sense-check on the climate projection results. It is reassuring that the historical loss correlations (black line) are similar to those for river flow and wind (yellow lines).
Impact on insurers’ solvency requirements more robustly established
Identifying that windstorm events tend to co-occur with inland flooding is one thing. Quantifying a selected potential financial impact to an insurer is another. Taking whole years, we investigated how the level of capital required to remain solvent is affected. Our baseline is a typical commercial situation wherein the perils are assumed to be independent. We used totals of hazard and loss for the UK from two Verisk catastrophe models, one for inland flooding and one for wind and storm surge. The take-home messages are listed after the next two paragraphs, which are for more technical readers.
First, looking at the whole UK market, the choice of method used to join the independent flooding and wind damage events sets was examined. To link total annual hazard severities, copulas (two t-copulas, Gaussian, Gumbel) and a rank-swapping algorithm common in (re)insurance were implemented. Chart 2 shows their effect on joint losses, quantified at a 1-in-200 year return period using the Aggregate Exceedance Probability (AEP) measure. 70% correlation is likely most appropriate (Chart 1), which induces a 10%–12% uplift net of reinsurance. The uplift is enhanced by 1%–2% using a Gumbel copula, which more strongly associates extremes. Alternatively, it is reduced to 7%–10% by a lower correlation (40%), or equivalently to 8%–10% if the ratio of wind to flooding losses exceeds 3:1 (typically c. 2:1).
In a second analysis, impact on capital was assessed for four selected firms. Outputs are shown in Table A. A Gaussian copula is taken as a ‘best estimate’ because it is in the middle of the range (Chart 2) and best fits the joint distribution of hazard proxies – Site W in Hillier and Dixon (2020). The firms are a representative sample of significant firms with exposure to natural catastrophes. AEP uplift cases a Solvency Capital Requirement (SCR) impact of 2%–4%, depending upon factors such as how well diversified a firm is (eg with man-made catastrophe), and can be raised plausibly to 6%–10% in a stress test that increases the relative influence of natural catastrophes in order to more fully account for the range of firms in the market.
Chart 2: Indicative impact of a correlation between flooding and wind hazards on annual losses for the whole UK market at a 1-in-200 year return period
Notes: Box plots display the distribution created by five types of correlation (eg copula). Pragmatically, reinsurance is applied to events with 1 reinstatement, attaching at 1.5x annual expected loss, exhausting at a 1-in-100 year return period event loss. These are defined on and applied to the joint set of events, but before correlation is considered, and prior to annual aggregation of losses. Gaussian is ‘best’ as it best fits the data of Site W in Hillier and Dixon (2020), displayed in Chart 1b of our previous article.
In summary, two main statements can be drawn from this work, which involves c. 20 million years of statistical simulation:
- The effect on 1-in-200 year joint net aggregate (AEP) losses is estimated at 10%–12% (Chart 2).
- This net AEP uplift causes an impact of 2%–4% on firms’ SCR, plausibly up to 6%–10% depending on a firm’s diversification and reinsurance (Table A).
Table A: Indicative impact on firms’ risk capital (top) and appetite (bottom)
Notes: For capital, rows 1–3 show the AEP uplift from wind-flooding correlation propagating into impact on an internal model’s SCR. Four large retail insurers (A–D) illustrate a range of SCR impacts that might arise, with row 4 a stress test to account for less diversified firms. The bottom two rows relate to risk appetite.
We extended our initial analysis by including a greater variety of firms, longer simulation runs, and better constrained scientific inputs. Yet, the headline AEP uplift (~10%) is similar. As such, with results robust to various choices and details of implementation, we believe that a basis for cautiously and carefully incorporating flooding-wind dependency into regulatory tools (eg GIST and CBES) and policy is more solidly established.
Wider implications for risk management and premiums
In addition to solvency considerations, failure to recognise correlations might be detrimental to firms’ risk management. Illustratively, consider a firm writing UK wind and flooding with a risk appetite defined such that surplus capital should be able to withstand a 1-in-10 year for catastrophes. Joint losses assumed to occur every 10 years in a view with no correlation in fact occur every nine years, with the 5%–8% uplift in joint AEP (Table A). Since, for a typical flooding to wind ratio (c. 2:1), the maximum AEP uplift is 13%–17% at a 1-in-50 return period, the effect might actually drive up the frequency of a 1-in-10 year risk threshold defined for all natural catastrophes. Certainly, the 1-in-10 year aggregate AEP will be bigger, so management could think they still have enough headroom to expand their book when they do not. At least, a light touch exercise to scope this possibility might be wise.
Looking more widely, we signpost a recent interesting paper. This also considers inter-peril correlation, but by modifying a scenario used in the Climate Biennial Exploratory Scenarios (CBES), to give insights into the wider implications (eg on necessary future premiums). In other words, the ramifications of hazard co-occurrence are not limited to the thin slices of interest we selected in this blog.
Conclusions and future work
Our main insight from this work is that we can now more firmly argue that insurers’ and reinsurers’ model assumptions should account for key dependencies to allow firms to hold sufficient capital for solvency requirements, price premiums, and to accurately reflect their risk appetite.
A second conclusion is that neither uncertainty (eg in science) nor variability (eg between firms) are sufficient reasons to ignore this message. Thus, in line with climate and weather-related risk more widely, we argue for capability building in both regulators and the wider industry. The market should be responsive to emerging information about risk correlations, whilst not over-reacting. Additionally, there is a potential systemic risk if many firms rely on third-party risk models that omit correlations (ie model uncertainty). So, we specifically highlight a CBES finding, namely that it is good practice for insurers to identify limitations of any third-party models used. Are key correlations captured? If not, what adjustments can address the limitation? Or, what methods need to be developed for insurers to do this? This said, note that overall risk might be reduced by perils in anti-phase (Hillier et al (2020)), which may present the opportunity to actively diversify risk. What constitutes a proportionate response, to provide internal and external comfort, will differ by firm.
Looking into the future, Bloomfield et al (2023) tentatively identify a threefold increase in days where very UK severe flooding and wind co-occur by 2060–80. Results like this justify efforts to understand and jointly model such perils in future climates. A significant benefit of funding scientific hazard research is the possibility of more effectively using of private and public funds in future physical risk mitigation initiatives.
John Hillier works at the University of Loughborough, Tom Perkins, Ryan Li, Stefan Claus and Paul Harrington work in the Bank’s Insurance Division, Hannah Bloomfield works at Newcastle University, Josie Lau and David Humphry work in the Bank’s Insurance Policy Division and Shane Latchman works at Verisk.
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