Downward Counterfactual Analysis in Insurance Tropical Cyclone Models: A Miami Case Study

Abstract

The insurance industry uses catastrophe models to assess and manage the risk from natural disasters such as tropical cyclones, floods, and wildfires. However, despite being designed to consider a credible range of future events, catastrophe models are ultimately calibrated on historical experience. This means that unexpected things can happen, either because risks that were overlooked or deemed immaterial turn out to be meaningful, or because black swans occur that scientists and insurers were not yet aware of. When faced with these types of extreme uncertainty, insurers can use downward counterfactual analysis to explore how historical events could have had more severe consequences (and help identify previously unknown or overlooked risks). In this chapter, we present a methodology for insurers to operationalise downward counterfactuals using tropical cyclone catastrophe models. The methodology is applied to three recent major hurricanes that were near misses for Miami—Matthew (2016), Irma (2017), and Dorian (2019). The results reveal downward counterfactuals that produce insured losses many times greater than what transpired, at up to 300x greater for Matthew, 25x for Irma, and 250x for Dorian. We argue that it is increasingly important for insurers to examine such near-miss events in a changing climate, particularly in disaster prone regions, like Miami, that might not have seen a large loss in recent years. By operationalising downward counterfactuals, insurers can increase risk awareness, stress-test risk management frameworks, and inform decision-making.

9.1 Introduction

Risk management practices, such as those in the insurance industry, are often strongly shaped by historical events. For example, in the 1980s and 1990s, insurers were surprised when a series of large natural disasters struck the United States, Europe, and Japan in close succession (tropical cyclones Hugo in 1989, Mireille in 1991, and Andrew in 1992; European windstorms 87J in 1987 and Daria in 1990; and the Kobe earthquake in 1995). The outcome was several reinsurance firms filing for bankruptcy and an increased demand for detailed physically-based catastrophe models for managing the risk from natural disasters (Grossi and Kunreuther 2005; Jones et al. 2017). Today, catastrophe models form an integral component of insurance risk management frameworks in a number of countries and are frequently updated to reflect lessons learnt from new disasters.

However, past experience does not always fully prepare us for the future. Despite being designed to consider a credible range of future events, catastrophe models are ultimately calibrated on historical experience (Lin et al. 2020). This means that unexpected things can happen, either because black swans (unpredictable or unforeseen events) occur that scientists and insurers were not yet aware of (Taleb 2007), or because risks that were overlooked or deemed immaterial turn out to be meaningful. For example, Hurricane Katrina made landfall in New Orleans in 2005, resulting in US$65 billion (2005 dollars) in insurance claims, making it the most expensive natural catastrophe for the global insurance industry to date (Swiss Re 2020). The severity of the disaster was in a large part due to a storm surge of up to 20 ft, which led to the failure of levees and flooding of 80% of the city (Knabb et al. 2005). This event was not a black swan—the historical record contains several instances of levee failures (e.g. Dunbar et al. 1999). But catastrophe models used at the time overlooked the risk as they did not consider the prospect of levee failure. The possibility of significant flood damage in New Orleans (and the subsequent displacement of the city’s inhabitants) had therefore not been considered by most insurers.

When faced with these types of extreme uncertainty, insurers can use counterfactual analysis to explore alternative histories (e.g. Woo et al. 2017; Woo 2018, 2019; Lin et al. 2020). In particular, downward counterfactual thinking provides a framework for considering how historical events could have had more severe consequences, with a view to identifying disasters (such as Katrina) before they occur. For example, an insurance firm may investigate how near-miss weather events—which are only footnotes in the historical record—could have led to large economic losses had they turned out slightly differently. A multitude of disasters is theoretically possible because history represents just a single realisation of the underlying climatic variability; alternative realisations could have led to different outcomes and different ex-post decisions being made. In this way, lateral thinking using downward counterfactuals can help with the identification of previously unknown or overlooked risks, which are not fully visible in the historical record, and may not be adequately represented in existing catastrophe models.

One application of downward counterfactual thinking that has yet to be fully explored by the insurance industry is climate change. The current generation of insurance catastrophe models are built and calibrated with historical hazard and loss data, so they reflect the recent past rather than the present or future (Golnaraghi et al. 2018). Given this limitation, insurers have turned to scenario analysis—often using probabilistic climate model projections—to explore how future changes in the frequency and/or severity of extreme weather events could impact financial losses (e.g. PRA 2019; CISL 2020; Rye et al. 2021). However, uncertainties in predicting future weather extremes at the regional scale mean that such scenarios often hinder rather than support decision-making (e.g. Fiedler et al. 2021). Downward counterfactual thinking can provide insurers with an alternative approach that focuses on individual events without being burdened by the uncertainties that come with weather and climate prediction. Thinking in terms of events is beneficial because it is more in-line with how humans are known to perceive and respond to risk (Shepherd et al. 2018). The practicality of an event-oriented approach for climate change decision-making has been demonstrated through event attribution studies, which aim to assess the effect of climate change on individual historical catastrophes (e.g. Schwab et al. 2017). But unlike downward counterfactuals, attribution investigations tend to focus on high-impact historical events such as Hurricane Harvey in 2017 (Van Oldenborgh et al. 2017), while low-impact or near-miss events are largely ignored.

We argue that in a changing climate it is increasingly important for insurers to examine near-miss events and contemplate what could have been. Focus should be placed on areas that are particularly prone to disasters, such as Miami, but might not have seen a large loss in recent years so may now have a different risk profile due to factors such as urban growth and sea level rise. As a result, people may not be fully aware of the potential risk, since we know from behavioural science that humans have cognitive biases that mean they tend to emphasise the importance of historical experience (or the lack thereof) in estimating future events (Kahneman 2011). Although catastrophe models simulate a wide range of natural disasters, the emphasis is mostly placed on loss probabilities rather than on specific event outcomes, which means cognitive biases can still exist despite the use of these models. It should be noted that deterministic catastrophe scenarios are often used in the insurance industry for regulatory stress-testing (e.g. Lloyd’s Realistic Disaster Scenarios, see Sect. 7.3), but these focus on a limited number of hypothetical events and are not directly related to historical disasters in the same way that downward counterfactuals are.

In this chapter we consider Miami, Florida, as a case study because the region has not seen a major hurricane landfall since Andrew in 1992. The Miami metropolitan area has experienced substantial urban development over the last 30 years, and with much of the land near sea level, there are concerns for Miami’s resilience under a changing climate (e.g. Tompkins and Deconcini 2014). Insurance claims for Andrew in 1992 totalled US$15.5 billion and a reoccurrence of the storm today would result in an insured loss in the region of US$50-60 billion (Swiss Re 2020). We present a methodology for insurers to operationalise downward counterfactual analysis using tropical cyclone catastrophe models. This is demonstrated for three recent major hurricanes—Matthew (2016), Irma (2017), and Dorian (2019)—which were all, at one point in time, forecast to strike Miami and produce significant economic damages. Fortunately, the actual storm tracks were more favourable to Miami, which escaped the worst outcomes. We do not attempt to quantify the role of climate change in these events—that is best left to event attribution scientists (Allen 2003). Instead, our aim is to demonstrate how insurers can use downward counterfactual analysis as a tool for managing risk in a changing climate, especially in situations where cognitive biases may exist.

For insurers to operationalise counterfactual analysis, a pragmatic solution is required that facilitates decision-making. For this reason, we adopt a ‘storyline’ approach (Shepherd et al. 2018) which focuses on understanding event outcomes, not event likelihoods. A storyline can be defined as “a physically self-consistent unfolding of past events, or of plausible future events” (Shepherd et al. 2018). Storylines can be viewed as conditional scenarios that aim to understand the consequences of an event or situation, assuming it has occurred. For example, after identifying a downward counterfactual for Hurricane Matthew, a storyline could be developed to consider the business implications of the event (e.g. solvency) and identify risk management actions that could improve future resilience. The overall outcome is a set of deterministic scenarios (storylines) that can be used by insurers to increase risk awareness, stress-test risk management frameworks, and inform decision-making.

9.2 Catastrophe Modelling

A “natural catastrophe” can be broadly defined as an extreme event resulting from a natural process—such as a tropical cyclone or earthquake—that exceeds the capability of those affected to manage the consequences. Catastrophe models are tools designed for the insurance industry (but also increasingly used in other domains such as the public sector) to quantify the financial risks arising from such events (Jones et al. 2017). They simulate the frequency, severity, and location of natural disasters over a specified time period—usually 100,000 years—with each modelled year representing a possible realisation of “next year”. This is achieved by considering the interactions between four core components (Fig. 9.1):

• Exposure. The primary input to a catastrophe model is information on the assets (exposure) being insured. The data typically comprise detail on the location, type, and physical characteristics—such as construction and year built—of each asset, along with information about the insurance terms and conditions such as deductibles.

• Hazard. The hazard module comprises a stochastic “event set” (e.g. Hall and Jewson 2007), which represents a wide range of plausible events, from small events which have minimal impacts to major disasters that cause widespread damage over entire regions. For each event, a hazard footprint is created, which provides information on the intensity (e.g. flood depth or wind speed) at each point within the affected area.

• Vulnerability. Vulnerability models (known as vulnerability curves) are used to convert between hazard intensity and physical damage (e.g. Khanduri and Morrow 2003). These curves are often built using historical claims data, engineering principles, and expert judgement. In most catastrophe models, damageability varies depending on exposure characteristics such as construction type, occupancy, and year of construction.

• Financial Loss. A financial engine is used to translate physical damage into a monetary loss. This accounts for the value of insured assets as well as any insurance terms and conditions. The primary output of a catastrophe model is an exceedance probability (EP) curve, which provides the insurers with the annual probability of exceeding certain levels of loss (Fig. 9.2).

Catastrophe models simulate a wide range of physically plausible events that have not been observed in history, which enables insurers to undertake a comprehensive analysis of the risks they face from natural disasters. However, an over-reliance on models can lead to gaps in the assessment of risk. This is because surprise events can occur that are not adequately represented in catastrophe models (e.g. Hurricane Katrina), or represented in the models but dismissed as unlikely due to cognitive biases that place more weight on historical experience (Kahneman 2011; Shepherd et al. 2018).

Fig. 9.1

The main components, inputs and outputs of a catastrophe model

Fig. 9.2

A schematic of an exceedance probability curve, which is the primary output of a catastrophe model and provides an annual probability of exceeding certain levels of loss

9.3 Counterfactual Disaster Risk Analysis

A counterfactual is a “what if” exercise designed to explore hypothetical alternatives to historical events by modifying them in some way (Woo et al. 2017). For example, “what if national governments had acted sooner to stop the spread of the COVID-19 global pandemic?” (Born et al. 2021). This is an example of upward counterfactual thinking, which considers how things could have turned out for the better with the benefit of hindsight. But according to experts in psychology, it is much less common to consider the antithetical scenario that involves downward counterfactual thinking to explore how an outcome could have had more severe consequences (Roese 1997)—“in what ways could the pandemic have been made worse?” This is because mitigating actions are often only taken in direct response to disasters that have actually occurred, rather than in response to what might have been (Shepherd et al. 2018).

Insurers often adjust risk management practices after large natural disasters. For instance, in 2011, extensive flooding in Thailand shut down manufacturing production, impacting global supply chains and resulting in US$12 billion in insured losses at the time (Lloyd’s 2012). This event led to many insurance firms improving their management of flood exposures outside of the United States and Europe, which were generally not modelled (and often poorly monitored) at the time. The advantage of downward counterfactual thinking is that it can improve resilience by providing foresight on risks that fall outside of realm of current expectations. Similar meteorological conditions that led to the 2011 Thai floods had occurred before in 1995, and therefore, a downward counterfactual analysis could have foreseen the risk (Woo et al. 2017).

Downward counterfactual analysis is ultimately a lateral thinking exercise (De Bono 1977) that involves exploring the phase space of a disaster—the ‘space’ in which all possible outcomes are represented, with each outcome corresponding to a unique point in the phase space. Searching the disaster phase space for counterfactuals can be considered analogous to traditional numerical methods used to find the minimum or maximum of an objective function (e.g. Nelder and Mead 1965). This involves producing a trajectory of system perturbations along a downward path of increasing impact relative to the original historical event (Woo 2019, 2021). The search is terminated when further iterations no longer lead to new events with worse outcomes, or the computational requirements are prohibitive. Figure 9.3 shows a schematic of the phase space of a disaster. In this simple example, the historic disaster is shown by an asterisk, and the characteristics of the disaster that can be varied are the landfall location (distance along the coast, x-axis) and hurricane intensity (y-axis). If the historic event were to make landfall at the same intensity but closer to an area of high population density (moved rightwards towards the dashed line in the centre of this figure), the resulting loss severity could be higher. Similarly, if the hurricane intensity were to increase but the landfall location remained the same (moved upwards in this figure), the loss could also increase.

Fig. 9.3

A schematic of the phase space of a historical disaster, where perturbations of the characteristics can lead to more or less severe consequences. The dashed line represents a landfall on a major population centre

Exploring the phase space of a natural disaster and quantifying the financial impacts of each outcome can be a time-consuming exercise. For this reason, Lin et al. (2020) have proposed a guiding framework that sets out the conditions of the search (Table 9.1). The framework involves identifying a past event which may or may not have caused catastrophic damage, and then perturbing some of the event parameters to explore small changes that could result in worse consequences. Perturbations can be applied to a wide range of different parameters such as geography, hazard, exposure, compound risks, and socio-economic conditions. The more parameters that are perturbed, the larger the search space, and the greater the resources required for the downward thinking exercise. The search continues until one or more pre-defined end-of-search criteria are reached. Both the parameter perturbations and end-of-search criteria should be defined such that the final set of scenarios are physically plausible.

Table 9.1 The six step framework for identifying downward counterfactual events as defined by Lin et al. (2020) that is used as a basis for the counterfactual analysis presented in this chapter

9.4 Matthew, Irma, and Dorian

We explore unrealised downward counterfactuals for three recent hurricanes—Matthew (2016), Irma (2017), and Dorian (2019). These storms provide an interesting case study because historical wind swathes show that Miami was spared hurricane strength winds in all three events (Fig. 9.4). Table 9.2 shows the insured losses incurred from each of the three events; note that while these events (particularly Irma) produced significant insured losses in the United States, for the purposes of our study they are physical near-misses for Miami. It is not hard to conceive of counterfactual realisations in which all three storms had worse outcomes from small changes to the hurricanes’ paths. Given the lack of recent large loss experience in Miami, as well as the expected impacts of climate change on sea levels (e.g. Wdowinski et al. 2016) and hurricane activity (e.g. Knutson et al. 2020), a downward counterfactual analysis is warranted to raise awareness of potential future hurricane losses and stress test risk management frameworks.

Fig. 9.4

The hurricane tracks of Matthew, Irma and Dorian and their Saffir Simpson categories at six-hourly timesteps along the track. Also shown are the estimated hurricane-force wind swathes (1-minute sustained windspeeds of over 74 mph). Data from the National Hurricane Center (NOAA NHC 2021). Basemap © OpenStreetMap contributors

Table 9.2 United States nominal gross industry insured losses from Matthew, Irma and Dorian as documented by Aon Benfield. Note that insured loss estimates are also available from other sources (e.g. Property Claims Services) but these are not available in the public domain and so are not included in this study

9.4.1 Matthew

Hurricane Matthew originated from a tropical wave off the west coast of Africa that developed into a tropical storm east of the Lesser Antilles on 28th September 2016. The system underwent rapid intensification and reached Category 5 strength by 1st October at the lowest latitude ever recorded in the Atlantic Basin. Matthew made landfall in Haiti, Cuba, and the northern Bahamas as a Category 4 hurricane (see Fig. 9.5). Although some forecasts predicted that Matthew would make landfall in Miami, the storm instead remained offshore and moved northwards, parallel to the eastern coast of Florida, before making a final landfall in South Carolina at Category 1 strength (NOAA 2016). Whilst the strong winds associated with the bypassing track of Matthew caused some damage on the east coast of Florida and led to a mainland United states insured loss of around US$4 billion (Table 9.2), the effects were minimal compared to the potential impact of a landfall in Miami if the hurricane eye had crossed the coastline.

Fig. 9.5

The actual tracks of Matthew, Irma and Dorian. Data from the National Hurricane Center. (NOAA NHC 2021)

9.4.2 Irma

The following year, Irma formed from a tropical wave near Cape Verde on 30th August 2017. Irma rapidly reached a peak intensity of Category 5 strength only two days after genesis; this rate of intensification is rare and only achieved by about 1 in 30 Atlantic tropical cyclones and was not well captured in the early forecasts (NOAA 2017). Irma underwent a second period of rapid intensification as it moved towards Barbuda and made landfall there on 6th September (see Fig. 9.5). Irma made further landfalls between 6th and 9th September whilst traversing westward through the Caribbean islands. The forward speed of Irma then decreased and the hurricane turned northwards, which was captured in many forecasts. However, Irma moved further west of many of the predicted tracks which delayed the northward turn toward Florida and avoided a landfall or close bypass in Miami. Irma made further landfalls in the Florida Keys at Category 4 strength and in southwestern Florida at Category 3 strength, both of which are relatively sparsely populated compared to Miami (NOAA 2017). The overall insured loss to the mainland United States from Hurricane Irma was around US$25 billion (Table 9.2). As Irma was the only hurricane of the three to make landfall in Florida, the insured losses for this storm are significantly higher than those for Matthew and Dorian.

9.4.3 Dorian

Two years later, Dorian developed into a tropical storm on 24th August 2019 and reached hurricane strength on 27th August while moving over the U.S. Virgin Islands. Between 28^th and 30^th August, many forecasts predicted that the hurricane eye would pass directly over Miami; a state of emergency was declared for the whole of Florida on 29th August. Dorian underwent a period of rapid intensification on around 31st August and reached Category 5 strength before continuing on a westward trajectory and making a first landfall in the Bahamas on 1st September as the strongest hurricane in modern records to make landfall here. Although Dorian was still moving towards Miami-Dade County after landfall in the Bahamas, it changed direction sharply, and the eye of the storm remained around 100 miles from the Florida coastline as it traversed northwards (see Fig. 9.5). As a result, Florida experienced tropical storm force winds but remained relatively unscathed compared to the potential impacts of a direct landfall. Dorian later made landfall in North Carolina, which experienced Category 1 strength winds over land (NOAA 2019) and total United States insured losses reached around US$1 billion (Table 9.2).

9.5 Methodology

We use the six-step framework outlined in Lin et al. (2020) (Table 9.1) to demonstrate how insurers can operationalise downward counterfactual analysis by using tropical cyclone catastrophe models. This is achieved by first utilising operational ensemble weather forecasts to define a disaster phase space from which counterfactuals can be drawn (Steps 1–2). A Dynamic Time Warping (DTW) similarity algorithm (Berndt and Clifford 1994) is then employed to select a subset of stochastic storm tracks from a catastrophe model which have similar properties to those within the phase space (Steps 3–4). Finally, the catastrophe model is used to quantify the insured loss impact of each stochastic (counterfactual) event that has been identified (Step 5). To ensure computational efficiency, the search stops once a pre-defined number of downward counterfactuals have been identified (Step 6). The advantage of this approach is that it can be easily incorporated into existing insurance risk-management frameworks—which often involve the use of catastrophe models—to provide a set of downward counterfactuals in near real-time. Note that most catastrophe models are proprietary and cannot be edited by end-users, hence the need to select similar stochastic tracks from the catastrophe model, rather than using the operational ensemble forecast tracks directly.

Version 17 of the RMS North Atlantic Hurricane model (RMS 2021) is used to illustrate the methodology, although any stochastic tropical cyclone catastrophe model could be used. The RMS model is one of several models that have been approved by the Florida Commission on Hurricane Loss Projection Methodology (FCHLPM), which aims to protect homeowners and insurers by setting standards to rigorously evaluate model methodologies. This includes specifications on the historical “Base Hurricane Storm Set” that hurricane catastrophe models must be calibrated and validated against in order to be approved by the FCHLPM. The RMS model comprises tens of thousands of physically plausible stochastic storm tracks that make landfall in or bypass the coastlines of the Gulf of Mexico, Florida, and United States Eastern Seaboard. For each event, the model simulates the financial impacts of wind and storm surge damage (using the RMS recommended default model settings), as well as post-event loss amplification (PLA), which includes factors such as demand surge and claims inflation. Damage resulting from precipitation-induced flooding is not included.

As detailed earlier, we use a ‘storyline’ approach to evaluate the downward counterfactuals that are identified using the RMS model (Shepherd et al. 2018). Each counterfactual is considered a physically plausible and self-consistent future event. We do not assign a priori probabilities to the scenarios; instead, emphasis is placed on the event outcomes and the implications for the insurance industry (or individual insurer). The benefit of a storyline approach is that it presents risk in an event-oriented way, which is how most people perceive and respond to risk (Shepherd et al. 2018). This improves risk awareness and facilitates decision-making without being burdened by the uncertainties that come with weather and climate prediction.

9.5.1 Step 1: Identify Past Events

The first step is to identity one or more historical events of interest (in our case Matthew, Irma, and Dorian). The observed parameters of each event—such as the storm intensity or landfall location—provide the starting point for the downward counterfactual search. The search also requires an observed outcome against which the unrealised counterfactual outcomes can be compared. For this, we use the reported gross industry insured loss of each historical event (Table 9.2).

9.5.2 Step 2: Define Disaster phase space parameters

As detailed by Lin et al. (2020), acceptable event perturbations should be defined upfront to ensure that: (1) the resultant downward counterfactuals are physically plausible; and (2) the search is computationally feasible. For Matthew, Irma, and Dorian, the disaster phase space is constrained using two criteria:

• Storm track. One of the best ways of defining the disaster phase space for a windstorm is to use ensemble weather forecasts. This is because the ensemble members represent a set of physically realistic perturbations to the historical event given the underlying atmospheric conditions. For Matthew, Irma, and Dorian we use operational ensemble weather forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF) and the Global Ensemble Forecast System (GEFS). The data were downloaded from NCAR/UCAR Research Data Archive (THORPEX 2021). For each historical event there are 51 ensemble members available from ECMWF and 21 from GEFS, and the location of the centre of the hurricane is provided at six-hourly timesteps (Table 9.3). Forecasts initialised between three and four days prior to a potential landfall are used to define the disaster phase space to ensure a sufficient range of realistic storm tracks.

• Landfall intensity. Since the focus of a downward counterfactual search is to identify more severe events, the phase space is restricted to only include RMS stochastic tracks that make landfall somewhere in the United States at Category 3 or above (111mph+ sustained winds). This is physically realistic because all three events were major hurricanes on their approach to the United States.

Finally, prior to commencing the search, it is important to apply expert judgement to remove any outlier forecast ensemble members that may produce erroneous matches with the catastrophe model storm tracks. Out of the three historical events considered in this study, only one ensemble member for Hurricane Matthew is removed, which is shown in Fig. 9.6. This track was excluded from the phase space to prevent unrealistic matches with catastrophe model tracks that pass into the Gulf of Mexico.

Table 9.3 Forecast data sources used in the counterfactual analysis

Fig. 9.6

The outlying Hurricane Matthew ECMWF forecast track that is removed from the analysis (dark blue) because it causes unrealistic counterfactual events to be selected. Also shown is the actual Hurricane Matthew track (light blue)

9.5.3 Step 3: Define End-of-Search Criteria

The search for counterfactual events is completed in this example once 70 stochastic tracks per hurricane are selected from the catastrophe model. This number is chosen as it produces a wide range of outcomes that reflect the variety in forecast tracks (72 ensemble members), while ensuring that the search is computationally feasible. Selecting significantly more than 70 tracks would provide a wider range of outcomes, but this would also lead to counterfactual events that are not as good matches to the forecast tracks.

9.5.4 Step 4: Search the Disaster Phase Space

An iterative search algorithm is used to identify physically plausible counterfactuals within the RMS stochastic model. For each forecast ensemble member, the search algorithm loops through all stochastic events in the RMS model and calculates the dynamic time warping distance between each pair of tracks. DTW is a commonly used algorithm for quantifying the similarity between two temporal sequences which may vary in speed (Berndt and Clifford 1994). The sequences are “warped” non-linearly in the time dimension, and the Euclidean distances between pairs of data points are calculated. The optimal match is the one that has the lowest total Euclidean distance.

For computational efficiency and to ensure good matches in the area of interest, the stochastic tracks are first clipped to a bounding box two degrees wider than the extent of all the forecast tracks in the east, west, and south directions. To the north, the bounding box is set to 45 degrees north to avoid the matching algorithm placing undue emphasis on the portion of the track that cannot cause damage in the mainland United States. Stochastic tracks that enter and exit the bounding box more than once are omitted, as these tracks often produce erroneously good DTW scores, matching well within the box, but deviating significantly from the forecast ensemble outside the box (e.g. looping into the Gulf of Mexico).

The 70 stochastic tracks with the best match to the set of forecast tracks (i.e., lowest DTW distances) are selected per hurricane. It is possible for a stochastic track to appear more than once in the top 70 if it produces the lowest DTW match for two or more forecasts. Therefore, if duplicate stochastic storms appear in the top 70, these are removed, and additional storms are included until 70 unique tracks have been identified. Figure 9.7 shows the resultant selected stochastic tracks for the three historical events.

Fig. 9.7

The ECMWF and GEFS ensemble members (dark blue) and selected RMS stochastic tracks (light blue) for Dorian, Irma and Matthew

It should be noted that in Lin et al. (2020)’s framework, the phase space search involves identifying a set of counterfactual events that form a ‘chain’, each one a perturbation of the previous event. However, in our study we apply the framework independently to each forecast ensemble member. This results in the identification of a set of counterfactuals that are related (each ensemble member is a perturbation of the forecast initial conditions), but the events themselves are not explicit perturbations of one another.

9.5.5 Step 5: Compare to the Historic Consequence

For each of the selected stochastic tracks shown in Fig. 9.7, the modelled gross industry losses are calculated using the RMS model. The actual insured losses for each event (Table 9.2) are used for comparison to the modelled counterfactual event losses. As all events have occurred recently, reported losses are not on-levelled to account for factors such as inflation, as the uncertainties in the reported numbers will be larger than the differences due to real-term monetary value adjustment over such a short time frame. In contrast to Lin et al. (2020)’s framework, the algorithm presented here is not prevented from returning upward counterfactuals, in which the counterfactual outcome is more favourable than the historical outcome.

9.5.6 Step 6: Criteria to Continue or End Counterfactual Search

The downward counterfactual search is terminated when the end-of-search criteria defined in Step 3 have been met. As noted above, this is when the best 70 DTW matches have been identified. In the unlikely event that 70 matches cannot be found, the search will end once the algorithm has iterated over all forecast ensemble members and each catastrophe model stochastic event track.

9.6 Results

9.6.1 Individual Scenarios

The results of the downward counterfactual searches for Matthew (a), Irma (b), and Dorian (c) are presented in a series of scatter plots in Fig. 9.8. Each light blue point represents a separate counterfactual scenario, which are plotted in ascending order of loss (y-axis). The x-axis represents the counterfactual loss normalised by the reported event loss (Table 9.2), which is also shown on each plot as a dark blue point. In accordance with a storyline approach, each counterfactual is considered a physically plausible outcome without assigning likelihoods. Note that the normalised gross industry losses produced by the RMS model reflect average industry practices (including insurance take-up rates and terms and conditions, such as deductibles). As detailed in Sect. 9.5, modelled losses also include post-event loss amplification which accounts for factors such as economic demand surge and claims inflation.

Fig. 9.8

Counterfactual scenarios for (a) Matthew, (b) Irma and (c) Dorian. Each light blue point represents the loss associated with an RMS stochastic track; the top 70 tracks with the lowest DTW distance are shown. The losses are normalised by the historical reported loss (x-axis) and ordered according to increasing event severity (y-axis). Subplot (d) shows the range of losses from all possible combinations of the three hurricane losses. The reported loss is shown in dark blue

In total, 68, 61, and 70 downward counterfactuals are identified for Matthew, Irma, and Dorian, respectively. As noted above, we do not explicitly prevent the algorithm from returning upward counterfactuals. For example, in the case of Irma, nine upward counterfactuals are identified, which produce lower losses than the original event. The large number of downward counterfactual scenarios that were identified highlights that all three historical events could have produced significantly worse outcomes had they turned out slightly differently. In the worst-case counterfactuals, insured losses are nearly 300 times the reported loss for Hurricane Matthew, 25 times higher for Hurricane Irma, and over 250 times higher for Hurricane Dorian. Note that the reported insured loss for Irma (US$25 billion, Table 9.2) is an order of magnitude larger than the reported losses for Matthew and Dorian. This explains why the normalised worst-case scenario of Irma is an order of magnitude lower than the other two events.

Figure 9.9 shows the tracks of the five worst downward counterfactuals for each hurricane, with the single worst outcome highlighted in dark blue. All of the worst-case scenarios involve significant wind and storm surge damage to the Miami metropolitan region, which has a population of over six million inhabitants (United States Census Bureau 2019). The worst-case counterfactuals for Irma and Matthew also transit much of the eastern coast of Florida, causing damage in the heavily populated cities of Orlando and Jacksonville. Also note that for both Dorian and Irma, some of the worst five outcomes impact the city of Tampa on the western coast of Florida, and many of the events make landfall a second time in states north of Florida—all of which contributes to the cumulative damage and loss for these events.

Fig. 9.9

The top five downward counterfactuals by gross industry loss for each historical hurricane (light blue) and the top overall loss event (dark blue). The location of the City of Miami is marked in red

9.6.2 Combined Scenarios

Figure 9.8d shows all possible counterfactual combinations for the three historical events. In total, 361,934 possible loss combinations are identified, the largest of which is the sum of the three worst-case outcomes for each individual storm. This shows that the combined loss for all three hurricanes could have been up to 70 times larger than was observed. Overall, 22% of the combinations had losses that were 10 times greater than the combined historical loss, and 2% had losses that were 25 times greater (as noted earlier, these outcomes represent storylines, not likelihoods). Many of the worst-case outcomes involve three direct hits on Miami which, while unlikely, was possible given the atmospheric conditions at the time of each event. It should be caveated that this analysis assumes that each event is independent, meaning that full economic and societal recovery occurs between each landfall. In reality, if three hurricanes were to impact Florida over a short period of time, each storm could create antecedent conditions that may affect subsequent events. For example, the loss from a given storm could be amplified if the local economy was under strain from a previous event, leading to inflated labour, material, and alternative accommodation costs.

9.6.3 Climate Change

Under climate change, the intensity of some hurricanes is likely to increase (e.g. Knutson et al. 2020). Therefore, it is possible that hurricanes similar to Matthew, Irma, and Dorian may make landfall in Florida with a higher intensity than occurred historically. To explore the impact of storm severity on insured losses, Table 9.4 shows the mean counterfactual loss normalised by the reported loss across each major hurricane category (3, 4 and 5). As can be seen, the loss increases significantly with increasing hurricane category. For Matthew, Category 3 counterfactuals cause average losses of seven times the reported loss, whilst Category 5 counterfactuals cause average losses of 110 times the actual loss. For Irma, the factors are less extreme, with counterfactuals on average causing up to 6 times more loss for Category 5 storms. For Dorian, the mean counterfactual loss is 25 times larger than the actual loss for Category 3 counterfactuals, and 126 times the actual loss for Category 5 counterfactuals. This is not unexpected since stronger storms are known to cause greater damage; however, it does raise awareness of how increasing storm severity due to climate change could affect insured losses. Note that this is only one example; climate change could affect tropical cyclones in several ways other than wind severity, such as precipitation intensity, forward speed, or event frequency. These are all factors that could be considered in further research (see Sect. 9.7.4).

Table 9.4 Modelled industry mean gross loss normalised by the reported loss for each historic storm per hurricane category across the 70 selected stochastic events. The numbers represent how many times greater the modelled mean loss is than the reported loss

9.7 Discussion

Our analysis has shown that Matthew, Irma, and Dorian could have, in many scenarios, had much worse outcomes for the United States. This in itself is not unexpected—catastrophe models have been used by the insurance industry for more than three decades to manage the risk from physically plausible disasters that have not yet occurred. However, behavioural science tells us that most humans have problems perceiving risk that falls outside historical experience (availability bias) or occurred a long time ago (recency bias), even when quantitative information—such as from catastrophe models—is available (Shepherd et al. 2018). Downward counterfactual thinking can overcome this problem by highlighting situations in which risks have become distorted by near misses or good fortune, such as in Miami (Woo et al. 2017; Woo 2019). We have presented a methodology building on the work of Lin et al. (2020) that allows insurers to explore such downward counterfactuals using tropical cyclone catastrophe models. Our approach has three key benefits for insurers, each of which will now be discussed in the context of our Miami case study: (1) increased risk awareness; (2) operationalised counterfactuals within risk management frameworks; and (3) improved decision-making in the face of extreme uncertainty, including climate change.

9.7.1 Risk Awareness

What if Matthew, Irma, and Dorian had all hit Miami? This is a scenario that was possible given the underlying atmospheric conditions at the time of each event. Yet for most insurers this is not something to which they would have given much contemplation; a similar set of events has not occurred in living memory and is therefore considered unlikely. However, as argued by Woo et al. (2017), in order to avoid future surprises, it is important for insurers to consider the potential implications of unlikely, but possible, disasters. This is particularly true in a changing world, where urbanisation, economic growth, and climate change are constantly altering the risk profile. Using downward counterfactual analysis to focus on event (storyline) outcomes, rather than probabilities, helps raise awareness by providing tangible information to decision-makers (Shepherd et al. 2018). For example, consider a storyline in which the combined loss from Matthew, Irma, and Dorian was 33 times larger (which was possible according to our analysis in Fig. 9.8d). This would have resulted in insurance claims of around US$1 trillion. Average annual insured losses from global tropical cyclones for the period 2000–2018 have been around US$20 billion (Aon Benfield 2018). A loss in excess of US$1 trillion would have therefore put significant strain on the insurance industry, and likely the global economy (Mahalingham et al. 2018). This illustrates the importance of raising awareness in situations where there is a known risk, but the last major disaster (Hurricane Andrew) was a long time ago and therefore cognitive biases may exist.

In addition to direct financial impacts, downward counterfactuals can also be used to contemplate the wider implications for the insurance industry. For example, in 2004 and 2005, unusually warm sea surface temperatures in the North Atlantic produced a record number of hurricanes, which led to several large, insured losses from Hurricanes Katrina, Wilma, and Ivan (Virmani and Weisberg 2006). As a direct reaction to this, catastrophe model vendors introduced alternative “near-term” views of risk in order to quantify expected losses during more active seasons (e.g. Jewson et al. 2009). The 2004/5 hurricane seasons also led to wide-ranging changes to insurance policies, including an increase in premiums and more stringent underwriting practices, such as higher deductibles and sub-limits (Guy Carpenter 2014). It is likely that far worse disruption would occur following a cumulative US$1 trillion loss over the space of just a few years. This could include the Floridian government stepping in to legislate to protect home and business owners, as occurred in California following the 2017/18 wildfires when the State Senate ruled that insurers must grant up to 36 months of additional living expenses and offer to renew policies for up to two years (Senate Bill 894 2018).

Similarly, counterfactuals can be used to consider the impact on the perception of climate change risk, both within the insurance industry and among the general public. For example, following Hurricane Irma in 2017 there was significant media attention on the extent to which climate change had contributed to the severity of the event (e.g. Carbon Brief 2017). Subsequent scientific investigations have found that while there is evidence that the precipitation from Irma contained a climate change signal, the wind hazard did not (Patricola and Wehner 2018). If Matthew, Irma, and Dorian had all hit Miami in close succession, the media reaction would almost certainly have been far greater (regardless of the role of climate change in the losses). Contemplating the implications of changing public perceptions around climate change risk following such a large set of disasters might be considered by some to be a leap into the unknown. However, it is not too difficult to envision a situation in which climate change is pushed to the forefront of insurance and government agendas, leading to greater regulation, changing insurance products and risk pricing, more investment in research, and an increased focus on mitigation and adaption.

9.7.2 Operationalisation

Following a natural disaster, most insurance companies will have an “event response” process to produce an early loss estimate, which is shared with key stakeholders both internally (e.g. business planning) and externally (e.g. regulators, rating agencies, markets). The magnitude of the event will usually determine the level of event response, with large disasters (e.g. a major hurricane landfall in the United States) receiving the most attention. The lessons learnt following a large disaster—for example from claims data—will often feed into risk management activities, such as the validation and adjustment of catastrophe models (Jones et al. 2017). However, this ex-post process is very much an upward counterfactual thought exercise that focuses on the worst events. Near-misses are often ignored, both during the event response and the post-event analysis.

The operationalisation of counterfactual analysis could therefore provide significant value to insurers by brining downward scenarios into risk management and decision-making frameworks. While the methodology presented in this chapter uses historical weather forecasts, it could easily be extended to include real-time data as an event unfolds. This would enable downward counterfactuals to be included in event response processes. For example, in addition to asking the question “what is our best guess of the loss for this event?”, insurers can also ask “could the loss be worse?”, thereby enabling real-time stress-testing of portfolios. This also facilitates post-event analysis, where counterfactuals could be used to validate and adjust catastrophe models for lessons learnt. It is worth noting that operationalisation is only possible because catastrophes contain a wide range of physically plausible events and are already integrated into existing insurance risk management frameworks. Without catastrophe models, the process would be far more arduous to undertake in real-time.

9.7.3 Decision-Making

Downward counterfactuals that focus on event outcomes can improve insurance decision-making by providing conditional statements that lead to tangible business impacts (Shepherd et al. 2018). This is opposed to probabilistic statements that cover a wide range of scenarios and are therefore less discernible. Focusing on specific events can help insurers identify vulnerabilities and develop risk-mitigating business strategies (Woo et al. 2017). For example, consider the question: “If Matthew, Irma, and Dorian had all hit Miami as major hurricanes, how would this have affected capitalisation?”. This provides a specific scenario in which capital can be stress-tested and mitigating actions taken if weaknesses are found. This is the opposite of an upward counterfactual approach, which only considers reacting after a disaster has occurred (by which point it might be too late).

Deterministic scenarios are already widely used in the insurance industry for decision-making and regulatory purposes. For example, following the large natural catastrophes of the 1980s and 1990s, Lloyd’s of London introduced Realistic Disaster Scenarios (RDSs), which are designed to stress-test insurance portfolios to plausible high-loss events of low probability (e.g. Lloyd’s 2021). Downward counterfactuals could therefore easily be integrated into existing insurance decision frameworks. A distinction should of course be made between existing deterministic scenarios (which are often hypothetical) and counterfactuals (which are grounded in history).

An event-orientated approach to decision-making is particularly useful in situations of extreme uncertainty, where an event may not have occurred in living memory and is therefore hard to imagine, even for subject matter experts. Climate change is a good example of this—even those that are familiar with the science often struggle to make decisions because it is difficult to conceptualise what the future will look like (Weber 2006). Given the short observational record and changing socio-economic/demographic factors over time, it is often difficult to attribute loss trends to climate change (e.g. Hoeppe 2016). Therefore, using near-misses to “fill-in” history can add significant value in a changing climate, particularly for cities like Miami that have not experience a large disaster in several decades.

9.7.4 Caveats and Further Research

The results presented in this study are conditional both on the reported historical losses (Table 9.2) and the RMS catastrophe model. The reported losses may include sources of loss that are not simulated by the catastrophe model. For example, loss adjustment expenses (associated with investigating and settling insurance claims) are included in the reported loss numbers, but not in the RMS model. This does not undermine our findings for Matthew, Irma, and Dorian, since any uncertainty in the reported losses is lower than the magnitude of range in downward counterfactuals, but it should be borne in mind when interpreting the results. It should also be noted that whilst RMS simulate a wide range of physically plausible hurricanes, it is possible that events (e.g. black swans) or sources of loss exist that are not represented in the catastrophe model.

The work presented here could be extended by widening the disaster phase space to consider events that fall outside the realm of the catastrophe model. This could be achieved by considering extreme outcomes under the present-day climate (e.g. compound events, Woo 2021) or by incorporating aspects of future climate change not currently represented in the model (e.g. sea level rise). The methodology could also be applied to different catastrophe model vendors, as well as different perils (e.g. flooding) and geographic regions. Another area of further research would be to investigate the sensitivity of the results to additional parameters that have an impact on potential damage such as the translational speed, intensity along the track and tidal state at landfall. Obtaining these details would require close collaboration with catastrophe model vendors, as this information is not provided to users as standard in the models.

9.8 Conclusions

We have presented a methodology for insurers to operationalise downward counterfactual analysis using tropical cyclone catastrophe models. Downward counterfactuals provide insurers with a way of exploring how historical events could have turned out for the worse. We combine this with a ‘storyline’ approach, which focuses on describing and understanding specific event outcomes, rather than prescribing likelihoods. The methodology was applied to three recent major hurricanes that were near misses for Miami—Matthew (2016), Irma (2017), and Dorian (2019). The results revealed downward counterfactuals that produced insured losses many times greater than what transpired—Matthew (300x), Irma (25x), Dorian (250x), and up to 70x for all three combined. Downward counterfactuals are an important tool that should be used by insurers to complement catastrophe models. They provide a set of deterministic scenarios that can be used to increase risk awareness, stress-test risk management frameworks and inform decision-making. This is particularly true in situations where cognitive biases may exist due to a lack of recent loss experience, such as in Miami, and therefore people may not be fully aware of the potential risk due to factors such as urban growth and climate change. This work will also have applications outside of the insurance industry and will therefore be of interest all readers concerned with tropical cyclone risk in a changing climate.

9.9 Competing Interests

C.J.R. and J.A.B. are employees of MS Amlin — a global speciality insurer and reinsurer that is part of the MS&AD Insurance Group. C.J.R. and J.A.B. have contributed to this chapter in their own capacity; any views expressed in this chapter are their own and not those of MS Amlin or MS&AD. The THORPEX dataset was used for non-commercial research purposes only.