John Hellyer, Tom Perkins, Ryan Lee, Hannah Bloomfield, Josie Lau, Stephen Close, Paul Harrington, Shane Lachman, David Humphrey
In 2022 a series of storms (Dudley, Eunice and Franklin) have caused a variety of hazards in the UK and across northwest Europe, resulting in £2.5-4.2 billion in insured losses. It dramatically illustrates the potential risks of a “perfect storm” that involves interrelated risks occurring simultaneously that combine to exacerbate the overall effect. Recent scientific research reinforces the evidence that high winds and inland flooding occur on a regular basis. By better modeling how this relationship might increase capital risk for insurers, we can argue more firmly that the insurers’ model assumptions should take into account key dependencies between risks. 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 adequate.
introduction
UK insurers use simulated weather extremes to report their rates, manage their risk buildup, and determine how much capital they need to operate from an economic and regulatory point of view. Historically, for the sake of simplicity, the major natural threat patterns were often modeled separately. However, different types of adverse scenarios can be associated and occur together. If the correlations are too weak in the insurance company model, this can lead to a capital shortage, thus weakening the financial protection of policyholders.
Our work here builds on exploratory work in 2021. It captures some of the UK’s most spectacular and devastating winter weather, reinforcing the evidence that it is important not to neglect the co-existence of extremely wet and windy conditions. However, this is only one of the many correlations that may be underrepresented in many insurance company models, both critically and globally.
Winter storms tend to occur simultaneously with inland floods in many time frames
The two hazards most affected in the UK are high winds (including storms) and inland flooding. Over a nine-day period, Storms Dudley, Eunice, and Franklin delivered a combination of damaging winds, inland flooding, snowfall, and rain-induced landslides. Was this an exception or something to be expected? To shed new light on this question, Bloomfield et al. (2023) measured wind and flood dependencies using consistent methods on a set of datasets, which included 240 years of UK Met Office climate projections and historical loss data. They used a range of correlation time frames (days to seasons) and modeled river flows rather than just precipitation. The main finding is an approximately 70% association between the hazards of extreme winds and inland flooding (Chart 1).
Graph 1: Wintertime correlation plots between floods and high winds in Great Britain (GB) and Western Europe
Notes: Adapted from our recent scientific study.
(a) Correlation level in Great Britain between wind and precipitation hazards (purple), and between wind and river flow (yellow) in the October–March season. Error ranges are at 95% confidence.
(b) to illustrate a broader context, map the correlation in a seasonal time frame across Europe, between historical winds and river flows; Explore this further in an online tool.
When reading this chart, it is important to realize that heavy rain does not necessarily result in a dangerously high flow in a river, which in turn does not always turn into a flood. In panel (a), historically (2006–18) observed losses on the railway network in Great Britain are used as a proofreading of climate projection results. It is reassuring that the historical loss relationships (black line) are similar to those for river flow and wind (yellow lines).
The impact on the solvency requirements of insurers has been determined more robustly
It is one thing to specify that windstorm events tend to coincide with inland flooding. Determining the potential financial impact chosen for an insurer is another matter. Taking entire years, we researched how the level of capital required to remain solvent was affected. Our baseline is a typical trading situation where risks are assumed to be independent. We used UK risk and loss aggregates from two Verisk disaster models, one for inland flooding and the other for wind and storm surge. Take-home letters are listed after the next two paragraphs, and are intended for more technical readers.
First, considering the entire UK market, the choice of method used to join independent flood and wind damage event groups was examined. To correlate the total annual risk severity, copulas (two types of t-copulas, Gaussian and Gumbel) and a rank-switching algorithm common in (re)insurance were implemented. Graph 2 shows their impact on joint losses, which were quantified over a 1-in-200-year return period using the Aggregate Exceeding Probability (AEP) measure. Correlation of 70% is likely to be the most favorable (Chart 1), increasing net reinsurance by 10% to 12%. The height is boosted by 1% to 2% with a Gumbel copula, which firmly binds the extremes. Alternatively, it is reduced to 7%-10% by a lower correlation (40%), or equivalently to 8%-10% if the ratio of wind losses to floods exceeds 3:1 (typically c. 2:1).
In a second analysis, the impact on capital was assessed for four selected firms. The outputs are shown in Table A. The Gaussian coppola is taken as the ‘best estimate’ because it lies in the middle of the range (Graph 2) and fits the W-location joint distribution of risk agents in Hellyer and Dixon (2020). The companies are a representative sample of large companies exposed to natural disasters. In cases of raising the AEP the impact of the solvency capital requirement (SCR) by 2% to 4%, depending on factors such as how diversified the company is (eg with a man-made disaster), it can reasonably be increased to 6%-10% in a stress test of increases From the relative impact of natural disasters in order to fully explain the group of companies in the market.
Chart 2: Indicative effect of the association between flood and wind risk on annual losses for the entire UK market over a 1 in 200 year return period
Notes: Box charts show the distribution created by five types of correlation (eg copula). In practice, event reinsurance is applied with reinsurance once, attaching 1.5 times expected annual loss, and exhausting the 1-in-100-year payout period event loss. It is defined and applied to the set of common events, but before considering correlation, and before the annual aggregation of losses. Gaussian is ‘best’ because it fits the W-location data of Hillier and Dixon (2020), presented in Graph 1b from our previous article.
In summary, two main statements can be drawn from this work, which includes c. 20 million years of statistical simulation:
- The impact on 1-in-200-year combined net collection losses (AEP) has been estimated to be 10%-12% (Chart 2).
- This net rise in AEP causes a 2%-4% impact on the corporate tax reduction rate, and can be as high as 6%-10% depending on the company’s diversification and reinsurance (Table A).
Table A: Indicative Impact on Corporate Venture Capital (top) and Appetite (bottom)
Notes: For the capital, rows 1–3 show the AEP rise from the wind inundation correlation propagating in the effect on the internal model’s SCR. Four large retail insurers (a–d) illustrate the range of selective downsampling effects that may arise, with grade 4 stress testing accounting for the least diversified firms. The bottom two rows relate to risk appetite.
We expanded our initial analysis by including a larger group of companies, longer simulations, and better constrained scientific input. However, the main rise in AEP (~10%) is similar. As such, with strong results for the various choices and implementation details, we believe that a basis for carefully and carefully integrating flood wind reliance into regulatory tools (such as GIST and CBES) and policy has been further solidified.
Broader implications for risk management and insurance premiums
In addition to solvency considerations, failure to recognize interrelationships may be detrimental to corporate risk management. Illustratively, consider a company that writes wind and floods in the UK with risk appetite set such that the capital surplus is able to withstand 1 in 10 years of disasters. Combined losses are assumed to occur every 10 years in a non-correlation view in fact occur every nine years, with a 5%-8% increase in combined AEP (Table A). Given the typical flood-to-wind ratio (c. 2:1), the maximum AEP rise is 13%-17% at a 1-in-50 return period, the impact may actually increase the frequency of the 1-in-10-year hazard threshold set for everyone natural disasters. The total AEP is sure to be greater, so management may think they still have enough room to expand their book when they don’t. At the very least, it might be wise to practice your light touch to scope out this possibility.
Looking more broadly, we mark an interesting recent research paper. This also takes into account risk associations, but by adjusting the scenario used in the CBES Biennial Exploration Scenarios, to give insight into broader implications (eg on necessary future premiums). In other words, the ramifications of co-occurring risks are not limited to the thin segments of interest we have selected for this blog.
results and future work
Our main insight from this work is that we can now argue more firmly that model assumptions for insurers and reinsurers must take into account key dependencies to allow firms to maintain sufficient capital for solvency requirements, premiums, and to accurately reflect their appetite for risk.
The second conclusion is that neither uncertainty (eg in science) nor variance (eg between firms) are sufficient reasons to ignore this thesis. Thus, in line with climate and weather-related risks more broadly, we advocate for capacity building in both regulators and the broader industry. The market should respond to emerging information about the risk correlation, while not overreacting. In addition, there are potential systemic risks if many companies rely on third-party risk models that ignore correlations (i.e. model uncertainty). Therefore, we particularly highlight a CBES finding, that it is good practice for insurers to identify the limitations of any third-party models used. Are key links recorded? If not, what modifications can handle the selection? Or what methods should be developed for insurance companies to do this? However, note that the overall risk may be reduced by anti-phase risk (Hillier et al (2020)), which may provide an opportunity to actively diversify risk. What constitutes a proportional response, to provide indoor and outdoor comfort, will vary by company.
Looking ahead, Bloomfield et al (2023) tentatively identify a three-fold increase in days with very severe and windless flooding in the UK by 2060-80. Results like these justify efforts to understand these hazards and to jointly model them for future climates. An important benefit of funding scientific research on risk is the potential for more effective use of private and public funds for material risk mitigation initiatives in the future.
John Hillier works at Loughborough University, Tom Perkins, Ryan Lee, Stefan Klaus and Paul Harrington work in the bank’s insurance department, Hannah Bloomfield works at Newcastle University, Josie Lau and David Humphrey work in the bank’s insurance policy department, and Shane Lachman work in frisk.
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