Catastrophe (CAT) models have become standard tools used by insurers and reinsurers to manage exposures, develop rates, and create risk transfer strategies for extreme event risk. In recent years, advanced flood solutions and catastrophe models have emerged to aid the growing flood insurance market in creating actuarially sound rates. To confirm the robustness and reasonability of CAT model output, users should evaluate their ability to replicate their company’s historical loss experience as well as produce robust estimates of industry insured loss estimates in an unbiased fashion.
Model evaluation poses several challenges, one of which is comparing modeled losses to claims for individual historical events. When making this comparison, the best, although potentially time-consuming, practice is to simulate modeled losses using the portfolio in force at the time of the event. In this way modeled losses reflect the value of money on the day of the event and can be compared to actual losses directly. Most companies use the latest and current portfolio in force to simulate modeled losses across all historical events, in which case the comparison of modeled losses to claims requires claims to be trended to the value as of the portfolio in force.
The trending of losses from past years to bring them to today’s monetary value can be performed in several ways [1,2]. Techniques range from the use of inflation, population growth, and increase in gross domestic product to trend actual losses to the latest monetary values. More recently, methods such as the perpetual inventory method have been used. This method considers annual investment, asset retirement, and price inflation by evaluating the year-by-year estimates of the region’s capital stock using Gross Fixed Capital Investment Index data. Losses can also be trended by looking at the changes in a company’s exposure portfolio over the years at regional scales. The robustness of the trending methodology can be further enhanced by accounting for factors such as changes in the number of insured properties; policy conditions, including deductibles and limits; building vulnerability changes over time; and changes in site characteristics, e.g., local terrain and mitigation techniques employed.
Recently, Verisk released a major update to our flagship U.S. hurricane model, along with a substantially updated U.S. inland flood model. Both models incorporate the same new pluvial component that uses a physically based 2-dimensional (2D) shallow water wave model to simulate pluvial flood risk over the entire contiguous U.S. These two models also incorporate the same new precipitation-induced flood vulnerability framework. Together, these two models provide a comprehensive view of U.S. flood risk—from both tropical and non-tropical sources on and off the floodplain as well as from storm surge. In addition to the industry loss data used in the validation of both these models—including industry insured loss estimates from ISO®’s Property and Casualty Services® (PCS®)—a significant amount of time and effort was dedicated to rendering the publicly available loss data from Federal Emergency Management Agency’s (FEMA) National Flood Insurance Program (NFIP) useful for validation. This article highlights the various steps that Verisk took to transform the publicly available NFIP data for use in validating CAT models.
NFIP Exposure and Claims Data Explained
Verisk used a total of USD 70 billion worth of NFIP claims data spanning four decades. These actual losses, or claims, data at ZIP Code level are available from 1978 through the end of 2018. NFIP exposure data at the ZIP Code level is available from 1994 through their portfolio in force as of 2018 [3]. The exposure data include more than USD 8 trillion worth of total sum insured and USD 22 trillion worth of total coverage values between 1994 and 2018. These data sets include recent years of exposure and loss information that FEMA released in 2019. Figures 1 and 2 summarize NFIP claims paid and exposure change over time. For this validation, only claims paid for building and contents coverage were considered; claims paid due to payment provision, such as increased cost of compliance, were not.


Attributing NFIP’s Daily Claims to Define Events
NFIP claims paid were associated with historical events to assign a flood peril and cause of loss to each claim. The losses included claims from sub-perils covered under both the Verisk U.S. hurricane model (storm surge and hurricane precipitation-induced flooding) and the Verisk U.S. inland flood model (flooding from non-hurricane precipitation) as well as non-modeled perils, such as surge caused by Nor’easters. To determine historical NFIP losses from inland flood and hurricane-related events, Verisk researchers analyzed the claims data for covered loss types, assigned them to flood sub-peril categories, removed storm surge and non-modeled components, and trended the losses by taking NFIP exposure growth and change in inflation into account.
FEMA’s Significant Flood Events database was used to identify events from historical floods, torrential rains, Nor’easters, and tropical storms [4]. The FEMA website reports significant historical flood events—those with more than 1,500 paid claims—and provides the month of occurrence, the total number of claims filed, and the total paid loss associated with each event. The total number of claims were plotted with a date of loss one month prior and one month after the date listed in the report. Once claims within this date range were identified, the geographic extent of the event was delineated based on the clustering of claims data. Verisk assigned claims with a date of loss within this time frame and geographic area to an event for further analysis (Figure 3).

Verisk researchers identified claims associated with historical hurricanes from the Atlantic Hurricane Database (HURDAT) and used data that indicated the date of landfall and area impacted. HURDAT contains the location, minimum pressure, and maximum wind data for historical tropical cyclones at six-hour intervals from storm formation through dissipation. Using HURDAT data, Verisk reconstructed hurricane tracks based on the six-hour hurricane location data. A buffer equal to the extent of tropical storm–force winds at each known location was applied to the track to determine the geographic area that the hurricane was likely to have impacted. Historical NFIP claims that fell within this buffer, had a date of loss from two days prior to landfall through the storm’s dissipation, and opened within one year of the event were assigned to the event. Figure 4 illustrates the process of assigning claims for Hurricane Ivan. For the years post-2012, where location-level claims were not available, Verisk researchers relied on PCS data to identify the NFIP claims associated with tropical storms and hurricanes. From PCS data, impacted states and specified date range information associated with a tropical storm or hurricane were used to label corresponding tropical storm or hurricane NFIP claims, respectively.

Further Attribution of Hurricane Event Losses to Flood and Surge
NFIP claims associated with a hurricane need to be assigned to a cause of loss; claims caused by hurricane storm surge are separate from those caused by hurricane-induced precipitation. Verisk has developed storm surge inundation footprints for most recent major hurricane events. We used these footprints to identify claims associated with the events that were likely caused by storm surge and to distinguish them from claims caused by precipitation from the hurricane as it continued to move over land. With the use of Flood Insurance Risk Study (FIRS) data [6], we were able to find the intersection of the claim location and the storm’s surge footprint. Claims located within the footprint were labeled as hurricane storm surge; all other claims corresponding to the event were identified as hurricane-induced precipitation. If location-level claims were not available and only ZIP Code-level claims were, then the claims in those ZIP Codes that saw surge were attributed in their entirety to surge and the remainder to hurricane precipitation-induced flooding.

Loss Trending Methods, Risk Count– versus Coverage-Based
Having looked at how to attribute event total claims to surge vs. precipitation-induced flooding, we can now explore how to bring these losses from past years to today’s monetary values. Historical losses need to be trended to present loss values by accounting for various factors, including changes in building stock, premium, vulnerability, mitigation, and inflation over time, such that the modeled and industry-reported loss values can be compared. To account for these factors, Verisk researchers developed an exposure growth index based on regional changes in FEMA’s portfolio growth and on annual increases in exposure (“risk count”) from the event loss year to the end of 2019. First, the annual exposure risk count was estimated by ZIP Code and by occupancy for each year from 1994 to 2017. Second, trending factors for a given year-of-interest between 1994 and 2017 (TFx) were estimated by taking the ratio of the 2018 risk count to the given year-of-interest’s (x) risk count and multiplying by an inflation factor, as shown in the following equation:

Where the Inflation factor is defined as the yearly average inflation and median home value change between 2019 and the year-of-interest, as shown in the following equation:

Note that due to lack of detailed exposure data prior to 1994, the FEMA-reported total policy count at the state level was used as a proxy for risk count [5]. This risk count was then used to trend the NFIP loss data between 1978 and 1993 to the equivalent 1994-dollar values. These 1994 values were then trended to 2019 using the equations above.
While Verisk researchers also developed an alternative coverage (total limit)-based loss trending method where NFIP’s yearly total coverage was used by ZIP Code and occupancy to estimate the trending factors, we found that this method was limited, as NFIP coverage changes in the past resulted in a sharp increase in trending factors in certain ZIP Codes. In reality, a property may not suffer a loss of that magnitude in today’s monetary value. To avoid the limitation of coverage-based trending methodology, risk count–based trending was used.
Summary of Trended Loss
Using the calculated trending factors, detailed claims paid are trended to 2019 dollars. Figure 6 shows the comparison between how much the paid claims would be in 2019 dollars for non-hurricane precipitation related events, revealing the severity of high loss-causing years between 1978 and 2018. For example, if similar inland flood events from 1979 were to occur today, the expected losses would be USD 5.105 billion due to the exposure growth in the flooded ZIP Codes. Users of this method should be mindful that for certain events, after multiplying with trending factors, a few ZIP Code-level losses may exceed the total NFIP latest coverage. In these cases, the trending factor for that ZIP Code needs to be readjusted based on the ratio of total 2019 coverage and the original loss. If the factors are still high even after coverage restriction is applied, proxy factors can be estimated based on the spatial analysis of neighboring ZIP Codes that experienced a relatively similar amount of historical loss.

Detailed Loss Validation Using Trended NFIP Loss
The trended NFIP loss data was extensively used to validate the flood loss output from the Verisk U.S. inland flood and hurricane models for both the historical and stochastic catalogs. To obtain a modeled view of insured losses, Verisk developed an exposure data set that replicates NFIP’s portfolio in force as of 2019. NFIP policy conditions by specific lines are applied to every exposure in Verisk’s 2019 U.S. Industry Exposure Database, which is shared by both the U.S. hurricane and inland flood models, and take-up rates are estimated for each line of business based on flood zone and county to develop this NFIP-specific exposure view. As a result of using this state-of-the-art exposure database and newly developed loss trending methodology, the loss validation significantly improves, even at the county level. Figure 7 shows the comparison between modeled and observed losses for the Louisiana flooding in 2016 using the Verisk Inland Flood Model for the United States and for Hurricane Harvey in 2017 using the Verisk Hurricane Model for the United States; both comparisons show robust model validation even at the county level.
Louisiana Flooding 2016

Hurricane Harvey 2017

To validate losses generated from the stochastic catalogs from both models—and specifically average annual loss (AAL)—Verisk’s modeled average annual losses from tropical and non-tropical precipitation are compared with observed NFIP losses from all sources of precipitation for 40 years (Figure 8). The orange bars in the chart are NFIP’s yearly losses paid out in the form of claims for all events. The blue line shows the NFIP aggregate average annual loss from these 40 years of actual loss data and the green line shows the modeled estimate from the U.S. inland flood and hurricane models. Based on this comparison the models were in good agreement with what was observed. Given that the models each have 10,000 years’ worth of events, it is expected that the modeled AAL would be larger than the observed AAL because high-loss events (e.g., events that involve a levee failure that results in extensive inland flooding) are not captured in a limited observed data set, but they are included in the modeled data set.

Managing U.S. Flood Risk
Verisk leveraged detailed high-resolution NFIP data as part of the model validation process for our U.S. inland flood and hurricane models updated in 2020. Our newly developed loss trending methods can help companies improve their own validation processes for our models. The resultant loss benchmark database can be used to validate both flood model frequency and severity, giving you more confidence when using Verisk solutions to manage your flood portfolios. The comprehensive and granular view of flood risk that our models offer can help you produce more robust results at the individual and portfolio levels, thereby enabling you to own your U.S. flood risk.
References
- Weinkle, J., Landsea, C., Collins, D. et al. (2018) Normalized hurricane damage in the continental United States 1900–2017. Nat Sustain 1, 808–813
- Pielke, R. (2018). Tracking progress on the economic costs of disasters under the indicators of the sustainable development goals. Environmental Hazards, 1-6.
- FEMA NFIP redacted claims dataset
- U.S. Department of Homeland Security’s Federal Emergency Management Agency. (2019, December 23). Significant Flood Events. Retrieved from FEMA significant events website.
- U.S. Department of Homeland Security’s Federal Emergency Management Agency. (2020, March 9). Statistics by Calendar Year. Retrieved from FEMA significant events website.
- Federal Emergency Management Agency. (2015). National Flood Insurance Program: Report to Congress on Reinsuring NFIP Insurance Risk and Options for Privatizing the NFIP. U.S. Department of Homeland Security.