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Optimization of National
Flood Insurance Premiums
Using Bayesian Hierarchical Modeling
Journal (TBA)
Work-in-progress
Abstract (Last Update: September 1, 2024)
Abstract (Last Update: September 1, 2024)
Abstract (Last Update: Sep. 01, 2024)
Estimating potential damage from natural disasters is challenging due to their sporadic nature, changing climatic conditions, and geographic variability. These factors complicate the assessment of insurance premiums to protect assets. This paper uses a Bayesian hierarchical model to evaluate optimal flood insurance premiums, incorporating data from a decade of NASA satellite imagery and flood risk compared to actual insurance claims and costs. The findings have two implications. First, extreme catastrophic events, such as hurricanes, cause significant losses but are often underestimated in risk assessments because of their rarity. Second, in areas with specific characteristics, such as flood-prone and tourist areas, policyholders exhibit behavioral responses that lead to adverse selection, with higher costs because their expected returns from insurance exceed the premiums paid. The results underscore the critical role of spatial variation in the pricing of insurance premiums, highlighting the need for improved modeling to enhance disaster response and recovery.
Estimating potential damage from natural disasters is challenging due to their sporadic nature, changing climatic conditions, and geographic variability. These factors complicate the assessment of insurance premiums to protect assets. This paper uses a Bayesian hierarchical model to evaluate optimal flood insurance premiums, incorporating data from a decade of NASA satellite imagery and flood risk compared to actual insurance claims and costs. The findings have two implications. First, extreme catastrophic events, such as hurricanes, cause significant losses but are often underestimated in risk assessments because of their rarity. Second, in areas with specific characteristics, such as flood-prone and tourist areas, policyholders exhibit behavioral responses that lead to adverse selection, with higher costs because their expected returns from insurance exceed the premiums paid. The results underscore the critical role of spatial variation in the pricing of insurance premiums, highlighting the need for improved modeling to enhance disaster response and recovery.
Estimating potential damage from natural disasters is challenging due to their sporadic nature, changing climatic conditions, and geographic variability. These factors complicate the assessment of insurance premiums to protect assets. This paper uses a Bayesian hierarchical model to evaluate optimal flood insurance premiums, incorporating data from a decade of NASA satellite imagery and flood risk compared to actual insurance claims and costs. The findings have two implications. First, extreme catastrophic events, such as hurricanes, cause significant losses but are often underestimated in risk assessments because of their rarity. Second, in areas with specific characteristics, such as flood-prone and tourist areas, policyholders exhibit behavioral responses that lead to adverse selection, with higher costs because their expected returns from insurance exceed the premiums paid. The results underscore the critical role of spatial variation in the pricing of insurance premiums, highlighting the need for improved modeling to enhance disaster response and recovery.
Selected Figures & Tables
Selected Figures & Tables
Selected Figures & Tables
Figures 1.
Impact of Rainfall from Hurricane Sandy on October 28, 2012: Datasource from the National Oceanic and Atmospheric Administration (NOAA)
Figures 1.
Impact of Rainfall from Hurricane Sandy on October 28, 2012: Datasource from the National Oceanic and Atmospheric Administration (NOAA)
Figures 1.
Impact of Rainfall from Hurricane Sandy on October 28, 2012: Datasource from the National Oceanic and Atmospheric Administration (NOAA)



Figure 1 shows the actual path and impact of Hurricane Sandy as of 11 a.m. on October 28, 2012. This image serves as an example to validate NASA's precipitation level datasets (shown in Figures 2a and 2b). The source of the image is the National Oceanic and Atmospheric Administration (NOAA), available at https://www.nhc.noaa.gov/archive/2012/graphics/al18/loop_5W.shtml. Accessed on May 7, 2024.
Figure 1 shows the actual path and impact of Hurricane Sandy as of 11 a.m. on October 28, 2012. This image serves as an example to validate NASA's precipitation level datasets (shown in Figures 2a and 2b). The source of the image is the National Oceanic and Atmospheric Administration (NOAA), available at https://www.nhc.noaa.gov/archive/2012/graphics/al18/loop_5W.shtml. Accessed on May 7, 2024.
Figure 1 shows the actual path and impact of Hurricane Sandy as of 11 a.m. on October 28, 2012. This image serves as an example to validate NASA's precipitation level datasets (shown in Figures 2a and 2b). The source of the image is the National Oceanic and Atmospheric Administration (NOAA), available at https://www.nhc.noaa.gov/archive/2012/graphics/al18/loop_5W.shtml. Accessed on May 7, 2024.
Figures 2a, 2b, and 2c.
NASA Precipitation Analysis for Hurricane Sandy (Data Validity Check; Week of October 28, 2012)
Figures 2a, 2b, and 2c.
NASA Precipitation Analysis for Hurricane Sandy (Data Validity Check; Week of October 28, 2012)
Figures 2a, 2b, and 2c.
NASA Precipitation Analysis for Hurricane Sandy (Data Validity Check; Week of October 28, 2012)

Figure 2a. Weekly Precipitation Level
Figure 2a. Weekly Precipitation Level
Figure 2a. Weekly Precipitation Level

Figure 2b. Weekly Precipitation with Actual Damage Claims
Figure 2b. Weekly Precipitation with Actual Damage Claims
Figure 2b. Weekly Precipitation with Actual Damage Claims
Note: Figure 2a shows NASA's precipitation level data for the entire U.S. map for the week of October 28, 2012. This figure illustrates the accuracy of NASA's precipitation records by comparing it with Figure 1 (route of Hurricane Sandy from NOAA). Figure 2c shows the overlaid actual NFIP insurance claims during the period, highlighted in red shading at the zip code level.
Note: Figure 2a shows NASA's precipitation level data for the entire U.S. map for the week of October 28, 2012. This figure illustrates the accuracy of NASA's precipitation records by comparing it with Figure 1 (route of Hurricane Sandy from NOAA). Figure 2c shows the overlaid actual NFIP insurance claims during the period, highlighted in red shading at the zip code level.
Note: Figure 2a shows NASA's precipitation level data for the entire U.S. map for the week of October 28, 2012. This figure illustrates the accuracy of NASA's precipitation records by comparing it with Figure 1 (route of Hurricane Sandy from NOAA). Figure 2c shows the overlaid actual NFIP insurance claims during the period, highlighted in red shading at the zip code level.
Figures 3a.
Trends in Actual Claims, Policy Costs, and Insurance Premiums (2009-2021)
Figures 3a.
Trends in Actual Claims, Policy Costs, and Insurance Premiums (2009-2021)
Figures 3a.
Trends in Actual Claims, Policy Costs, and Insurance Premiums (2009-2021)

Note: Figure 3a shows the historical NFIP claims data from the Federal Emergency Management Agency (FEMA). The red line shows actual losses, the green line shows NFIP policy costs, and the blue line shows insurance premiums.
Note: Figure 3a shows the historical NFIP claims data from the Federal Emergency Management Agency (FEMA). The red line shows actual losses, the green line shows NFIP policy costs, and the blue line shows insurance premiums.
Note: Figure 3a shows the historical NFIP claims data from the Federal Emergency Management Agency (FEMA). The red line shows actual losses, the green line shows NFIP policy costs, and the blue line shows insurance premiums.
Figures 4a, 4b, and 4c.
Trends in Actual Claims, Policy Costs, and Insurance Premiums by Geography (2009-2021)
Figures 4a, 4b, and 4c.
Trends in Actual Claims, Policy Costs, and Insurance Premiums by Geography (2009-2021)
Figures 4a, 4b, and 4c.
Trends in Actual Claims, Policy Costs, and Insurance Premiums by Geography (2009-2021)

Figure 4a. Actual Claims
Figure 4a. Actual Claims
Figure 4a. Actual Claims

Figure 4b. Policy Cost
Figure 4b. Policy Cost
Figure 4b. Policy Cost

Figure 4c. Insurance Premium
Figure 4c. Insurance Premium
Figure 4c. Insurance Premium
Note: Figures 4a, 4b, and 4c show the geographic distribution of actual claims (Figure 4a), policy costs (Figure 4b), and insurance premiums (Figure 4c) by zip code level between 2009 and 2021.
Note: Figures 4a, 4b, and 4c show the geographic distribution of actual claims (Figure 4a), policy costs (Figure 4b), and insurance premiums (Figure 4c) by zip code level between 2009 and 2021.
Note: Figures 4a, 4b, and 4c show the geographic distribution of actual claims (Figure 4a), policy costs (Figure 4b), and insurance premiums (Figure 4c) by zip code level between 2009 and 2021.
Figures 5a and 5b.
National Flood Insurance Program (NFIP) Claims and An Example of How to Calculate Distances of Flood-Prone Areas Relative to Zipcode Centroids
Figures 5a and 5b.
National Flood Insurance Program (NFIP) Claims and An Example of How to Calculate Distances of Flood-Prone Areas Relative to Zipcode Centroids
Figures 5a and 5b.
National Flood Insurance Program (NFIP) Claims and An Example of How to Calculate Distances of Flood-Prone Areas Relative to Zipcode Centroids

Figure 5a. NFIP Claims (Green) and Zipcode Centroids (Yellow)
Figure 5a. NFIP Claims (Green) and Zipcode Centroids (Yellow)
Figure 5a. NFIP Claims (Green) and Zipcode Centroids (Yellow)

Figure 5b. NFIP Claims (Green) and Zipcode Centroids (Yellow) in District of Columbia, Maryland, and Virginia Area
Figure 5b. NFIP Claims (Green) and Zipcode Centroids (Yellow) in District of Columbia, Maryland, and Virginia Area
Figure 5b. NFIP Claims (Green) and Zipcode Centroids (Yellow) in District of Columbia, Maryland, and Virginia Area
Note: Figure 5a shows the historical NFIP claim records from the Federal Emergency Management Agency (FEMA) (shown as green dots) along with the method used to calculate the distances between the areas claiming damages and the central point of each zipcode (shown as yellow dots). Note that the FEMA's data points are approximations, suggesting that a more precise unit of analysis would be at least at the census tract level and ideally at the zipcode level. This approach to calculating distances helps minimize the spillover effects that can affect risk premium calculations. Figure 5b provides a detailed analysis focused on the District of Columbia, Maryland, and Virginia area, allowing for a closer examination of the data within these regions.
Note: Figure 5a shows the historical NFIP claim records from the Federal Emergency Management Agency (FEMA) (shown as green dots) along with the method used to calculate the distances between the areas claiming damages and the central point of each zipcode (shown as yellow dots). Note that the FEMA's data points are approximations, suggesting that a more precise unit of analysis would be at least at the census tract level and ideally at the zipcode level. This approach to calculating distances helps minimize the spillover effects that can affect risk premium calculations. Figure 5b provides a detailed analysis focused on the District of Columbia, Maryland, and Virginia area, allowing for a closer examination of the data within these regions.
Note: Figure 5a shows the historical NFIP claim records from the Federal Emergency Management Agency (FEMA) (shown as green dots) along with the method used to calculate the distances between the areas claiming damages and the central point of each zipcode (shown as yellow dots). Note that the FEMA's data points are approximations, suggesting that a more precise unit of analysis would be at least at the census tract level and ideally at the zipcode level. This approach to calculating distances helps minimize the spillover effects that can affect risk premium calculations. Figure 5b provides a detailed analysis focused on the District of Columbia, Maryland, and Virginia area, allowing for a closer examination of the data within these regions.
Figure 6.
FEMA's National Risk Index: Assessing Flooding Risks
Figure 6.
FEMA's National Risk Index: Assessing Flooding Risks
Figure 6.
FEMA's National Risk Index: Assessing Flooding Risks

Note: Figure 6 presents a visualization of flood risk according to FEMA's National Risk Index, which provides data at the zip code level. This study uses the index as a basis for prior beliefs about flood risk. In addition, I integrate findings from previous literature reviews on national flood insurance premiums and use them as meta-analytic priors to enrich our understanding of the topic.
Note: Figure 6 presents a visualization of flood risk according to FEMA's National Risk Index, which provides data at the zip code level. This study uses the index as a basis for prior beliefs about flood risk. In addition, I integrate findings from previous literature reviews on national flood insurance premiums and use them as meta-analytic priors to enrich our understanding of the topic.
Note: Figure 6 presents a visualization of flood risk according to FEMA's National Risk Index, which provides data at the zip code level. This study uses the index as a basis for prior beliefs about flood risk. In addition, I integrate findings from previous literature reviews on national flood insurance premiums and use them as meta-analytic priors to enrich our understanding of the topic.
Table 1.
Summary Statistics (Table 1)
Table 1.
Summary Statistics (Table 1)
Table 1.
Summary Statistics (Table 1)

Note: To be added.
Note: To be added.
Note: To be added.
Conclusion
Conclusion
Conclusion
Work-in-progress.
Work-in-progress.
Work-in-progress.

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