Incorporating Catastrophe Models Incorporating Catastrophe Models in Property Ratemakingin Property Ratemaking

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Jeffrey F. McCarty, FCAS, MAAAState Farm Fire and Casualty Company

2000 Seminar on RatemakingMarch 9-10, 2000

San Diego, California

Use of Models in Property Insurance Use of Models in Property Insurance RatemakingRatemaking

General Information Why Use Hurricane Models Modeling Overview Rate Review Analysis Current Issues

OutlineOutline

1 AIY is $1,000 exposures earned in one calendar year

Proper exposure base for catastrophe ratemaking Direct compliment with catastrophe modeling

output Other available data can be used instead (e.g. in-

force, written, etc.)

Amount of Insurance YearsAmount of Insurance Years(AIY)(AIY)

Use of Models in Property Insurance Use of Models in Property Insurance RatemakingRatemaking

Earthquake

Non-Wind Catastrophes

Non-Hurricane, Wind Catastrophes

Hurricane Catastrophes

Uncertainty Provision/Risk Margin

Calculation of the Hurricane Calculation of the Hurricane ProvisionProvision

Previous Method (1989-1996) Used Historical Companywide Losses Statewide provisions determined using relative exposure to loss Provision by territory determined using output from computer simulation model

Current Method (1997-Present) Exclusive use of computer simulation models

Concerns with Use of Historical Concerns with Use of Historical Loss DataLoss Data

Limited Hurricane ActivityLimited Hurricane Activity Frequency and Severity of hurricane activity Frequency and Severity of hurricane activity

has not been constant over time.has not been constant over time. Geographical pattern and physical Geographical pattern and physical

characteristics of the historical record do characteristics of the historical record do not not reflect the full range of possible hurricane reflect the full range of possible hurricane

events.events.

Concerns with Use of Historical Concerns with Use of Historical Loss Data (Cont.)Loss Data (Cont.)

Limited Reflection of Current ConditionsLimited Reflection of Current Conditions Changes in ExposureChanges in Exposure Changes in Policy Conditions and CoveragesChanges in Policy Conditions and Coverages Changes in Company Loss Settlement ProceduresChanges in Company Loss Settlement Procedures Changes in Company Marketing/Underwriting Changes in Company Marketing/Underwriting Increased emphasis on Building Code changes and Increased emphasis on Building Code changes and

enforcement activity.enforcement activity.

Limited Credibility by TerritoryLimited Credibility by Territory

Hurricane Computer Simulation Hurricane Computer Simulation ModelsModels

Address concerns with use of historical experience Simulate full range of possible hurricane events each with associated

probabilities of occurrence. Use of Company’s current exposure information.

Input Considerations ZIP Code versus Geo-Code of exposure location Application of hurricane deductibles Limits by sub-coverage Use of current versus projected exposure distribution

Hurricane Hazard ModelHurricane Hazard Model

Hazard Analysis

Vulnerability Assessment

Financial Assessment

Hurricane Hazard ModelHurricane Hazard Model

Hazard Analysis Hazard Analysis --

Storm ParametersStorm Parameters Central pressure Radius & maximum winds Forward speed Fill rate Storm track Landfall

Site ParametersSite Parameters Distance to the coast Terrain elevation Topology

Ultimate outcome is hurricane wind speed.

Hurricane Hazard ModelHurricane Hazard Model

VulnerabilityVulnerabilityAssessment Assessment -- Ultimate outcome is an estimated

amount of damage for a particular type of building.

Structural CharacteristicsStructural CharacteristicsConstructionNumber of storiesOccupancyRoof type

Hurricane Hazard ModelHurricane Hazard Model

Measures the relative vulnerability of a structure to the different levels of intensity of a Hurricane.

For a given intensity and type of structure, damage is expressed as a probability distribution of damage ratios.

These mean damage ratios express the relative cost of repair for a given structure with respect to its replacement cost.

They are developed separately for building, contents, additional living expense and business interruption.

Damage FunctionDamage Function

Hurricane Hazard ModelHurricane Hazard Model

Financial Assessment Financial Assessment -- Resulting desired output.

Insurance Company Data InputsInsurance Company Data InputsLine of business/policy formProperty location - Geo-Code or ZIP CodeInsured values - Coverage A, B, C, DProperty replacement costDeductibleType of constructionNumber of storiesOccupancyYear of construction

Hurricane Model OutputHurricane Model Output

Annual Average Losses and higher moments

Annual Occurrence and Aggregate Loss Distributions

Probable Maximum Loss Scenarios

Effects of higher Deductibles & Coverage changes

Loss Estimates for specific events

“What If” type analysis

Largest Loss Reports

Hurricane Model OutputHurricane Model OutputAdditional ConsiderationsAdditional Considerations

Demand Surge

Loss Adjustment Expenses

Other Causes of Loss Loss Assessment Flood

Incorporating Hurricane Model Output into Incorporating Hurricane Model Output into Property RatemakingProperty Ratemaking

Loss Ratio MethodologyLoss Ratio Methodology

Calculate Hurricane average annual loss provision/AIY from model output

Add a provision for loss adjustment expense Add a provision for uncertainty (risk provision) using

higher moments of the model output Convert to a Hurricane Loss Ratio using Earned

Premium/AIY factor Add Hurricane Loss Ratio to Non-Hurricane Loss and

Expense Ratio for Total Catastrophe Loss Ratio Same method for Statewide and Territory Indications

Hurricane Provision by TerritoryHurricane Provision by TerritoryExampleExample

Incorporating Hurricane Model Output into Incorporating Hurricane Model Output into Property RatemakingProperty Ratemaking

Hurricane Model HurricaneHurricane Average Annual Input Modeled ProvisionTerritory Loss from Model AIY Hurr$/AIY Incl. LAE

A 1,500,000$ 400,000$ 3.7500$ 4.0125$ B 2,500,000 1,000,000 2.5000 2.6750 C 2,000,000 1,500,000 1.3333 1.4266

Statewide 6,000,000$ 2,900,000$ 2.0690$ 2.2138$

Incorporating Hurricane Model Output into Incorporating Hurricane Model Output into Property RatemakingProperty Ratemaking

Provision for Uncertainty/Risk ProvisionProvision for Uncertainty/Risk Provision

Reflect Relative Risk Use Standard Deviation of modeled hurricane losses as

measure of relative risk among states/territories

Determine minimum/maximum profit

Off-balance to target companywide/statewide profit Selected uncertainty provision related to hurricane

exposure Incorporate into Loss Ratio or Pure Premium Method

Statewide Provision for UncertaintyStatewide Provision for UncertaintyExampleExample

Incorporating Hurricane Model Output into Incorporating Hurricane Model Output into Property RatemakingProperty Ratemaking

Statewide CompanywideModeled Hurricane Variance 8.5550 1.5750

Standard Deviation 2.9249 1.2550 Relative Risk Factor Indicated 2.3306 1.0000

Selected 1.7510 Statewide Indicated Change + 5.0%

Selected Provision for Uncertainty 1.1000

Territory Provision for UncertaintyTerritory Provision for UncertaintyExampleExample

Incorporating Hurricane Model Output into Incorporating Hurricane Model Output into Property RatemakingProperty Ratemaking

Modeled SelectedHurricane Hurricane Standard Indicated Selected Provision forTerritory Variance Deviation Relativity Relativity Uncertainty

A 575.00 23.98 8.1983 1.0000 0.1000 B 77.00 8.78 3.0001 1.0000 0.1000 C 2.00 1.41 0.4835 1.0000 0.1000

Statewide 8.56 2.92 1.0000 0.1000

Hurricane Provision by TerritoryHurricane Provision by TerritoryIncluding Provision for UncertaintyIncluding Provision for Uncertainty

ExampleExample

Incorporating Hurricane Model Output into Incorporating Hurricane Model Output into Property RatemakingProperty Ratemaking

Hurricane Selected TotalHurricane Provision Provision for HurricaneTerritory Incl. LAE Uncertainty Provision

A 4.0125$ 0.1000 4.4138$ B 2.6750 0.1000 2.9425 C 1.4266 0.1000 1.5693

Statewide 2.2138$ 0.1000 2.4352$

Calculation of Total Catastrophe Loss RatioCalculation of Total Catastrophe Loss RatioExampleExample

Incorporating Hurricane Model Output into Incorporating Hurricane Model Output into Property RatemakingProperty Ratemaking

Total LatestHurricane Non-Hurricane Catastrophe Year Catastrophe

Zone Provision Provision Provision EP/AIY Loss Ratio10 4.4138$ 0.5000$ 4.9138$ 12.00 40.9%20 2.9425 0.5000 3.4425 10.00 34.4%30 2.9425 0.5000 3.4425 8.50 40.5%40 1.5693 0.5000 2.0693 7.00 29.6%50 1.5693 0.5000 2.0693 6.50 31.8%

Statewide 2.4352$ 0.5000$ 2.9352$ 8.30 35.4%

Indicated Rate Level ChangeIndicated Rate Level ChangeExampleExample

Incorporating Hurricane Model Output into Incorporating Hurricane Model Output into Property RatemakingProperty Ratemaking

Credibility Wtd. Total IndicatedNon-Catastrophe Catastrophe Formula Off-Balance Rate Level

Zone Loss & FE Ratio Loss Ratio Loss Ratio Relativity Change10 51.0% 40.9% 91.9% 1.2226 28.4%20 41.5% 34.4% 75.9% 1.0098 6.0%30 33.5% 40.5% 74.0% 0.9845 3.4%40 36.0% 29.6% 65.6% 0.8727 -8.4%50 44.5% 31.8% 76.3% 1.0151 6.6%

Statewide 41.3% 35.4% 76.7% 1.0000 5.0%

Modeling uncertainty

Variability between modelers’ results Florida Commission on Hurricane Loss Projection

Methodology - (5) models accepted Use of multiple models in ratemaking

Regulatory Acceptance Before/After an event Proprietary/”Black-Box” concerns

Actuarial Standards Board Exposure Draft

Separate Hurricane Rating/Class Plan

Current IssuesCurrent Issues

Separate Non-Hurricane and Hurricane Separate Non-Hurricane and Hurricane RatingRating

Florida Statutory Requirement

Interim Approach - Hurricane Factors

Separate Hurricane and Non-Hurricane Ratemaking Non-Hurricane - use Loss Ratio Method Hurricane - use Pure Premium Method Separate Class Plan with appropriate classifications Clearly identifies cost of hurricane coverage Identifies cost differences for Loss Mitigation efforts Incorporate different expense and profit provisions