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Cat Ratemaking
22nd May 2008
Jillian Williams
CAE, Spring 2008
2Guy Carpenter
Overview
Price and Events
What is a Cat Model?
Why use a Cat Model?
Commercial Cat Models
Data Cat Models Need
Uncertainty
Output and Uses
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Price and Events
4Guy Carpenter
Comparison of Number of Events and Loss to ROL
Hurricane Andrew
WTC
Hurricane Katrina
What is a Cat Model
6Guy Carpenter
Encompass algorithms and expert systems that allow clients to quantify damage and financial losses from specific perils. The models are built upon detailed databases describing highly localised variations in hazard characteristics, as well as databases capturing property inventory, building stock and insurance exposure.
Uses probability and statistics to quantify and model the randomness of catastrophic events
Uses portfolio information or market share data to quantify exposure to the events
What is a Cat Model?
7Guy Carpenter
Aggregate Distribution
Where are the Insured values Geographical Distribution
Hazards Floods, Storms, Earthquakes, What processes control their magnitude How often (frequency) How bad (severity)
Vulnerability
Maximum Damage ratios Building codes/types
How models are built
Back
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Basic Components of CAT Models
Hazard Module
Engineering Module
Actuarial Module
(Hurricane: Meteorological Info)
Portfolio
(Damagability of assets at risk)
(Financial implications )
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Hazard Module
Estimates location, characteristics & likelihood of a natural
catastrophe
Estimates site intensity – For Earthquake: Ground Motion– For Hurricane: Windspeed– For Tornado/Hail: Windspeed & Hail Impact Energy– For Flood: Depth
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Length ofFault Rupture
Fault
Earthquake (Magnitude)
Earthquake-GeneratedEnergy (Waves)
Fault/seismic source zone location
Magnitude
Focal Depth
Attenuation
Local soil conditions
Hazard Parameters: Earthquake
Ground Motion
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1d1
d3
d2
WV
VA
NC
GA
FL
AL
SC
Radius of max. winds
• Frequency of hurricanes
• Landfall location• Central pressure• Radius of maximum winds• Forward speed• Track angle• Maximum wind speed• Terrain roughness• Filling rate after landfall
Forwardspeed
Hazard Parameters: Hurricane
Site Windspeed
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Tornado• Track area• Tornado intensity
Hail• Hailstones per minute• Hailstone size
Hazard Parameters: Tornado/Hail
Hail Impact Energy & Windspeed
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• Depth• Velocity• Duration
Factors
• Seawater/Freshwater• Sediment Loads• Sewage and other Pollutants• Impervious Area (Flash)• Slope
Hazard Parameters: Flood
Intensity
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Engineering Module
• Estimates physical damage to portfolio• Vulnerability Function (Damage given site
intensity for structural type)
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Financial Module
Net of Cat $5m
Net of Per Risk $10m
Net of Facultative $20m
Gross (Less Deductibles) $25m
Damage (Ground Up) $30m
Insurance & reinsurance
structures are applied to loss
distribution
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Hazard Module
– Parameters similar
– Distributions & relationships vary across models
Engineering Module
– Classifications of structures
– Functional forms of vulnerability curves
Actuarial Module
– Portfolio exposure data interpreted differently
Variation Among Models
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Modeled and Non-Modeled Perils
Total CatastrophicTotal Catastrophic RiskRisk
PrimaryHurricaneEarthquakeTornado/Hail
Non-ModeledRiotWinter Freeze
Secondary/CollateralSprinkler LeakageFire FollowingSea Surge
Not including Terrorism or
Worker Comp
Why use a Cat Model
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Historical Loss Experience
Catastrophe are by definition:– Infrequent – insufficient number of events in historical records for
needed credibility– Severe – generate huge losses and unusual claim settlement
conditions
Historical data available is difficult to normalise to today’s conditions– Incomplete data on number and values of insured properties– Rapid changes in recent decades
Population and distribution Replacement values of properties Policy conditions
Correlation
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Historical Loss Experience
Commercial Cat Models
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Models Vendors
EQECAT
Risk Management Solutions
Applied Insurance Research
All can claim, but none can substantiate that they are “better”
Models are proprietary
None is consistently more accurate in actual events
No independent study has been definitive
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Available Models All Region and All Perils
Number of Perils1237
Data Cat Models Need
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Data Requirements
Hazard Module– Cresta Zone, FSA, postal code, street address, latitude/longitude
Engineering Module– Construction & occupancy– Age, height, roof shape, etc.
Financial Module– TIV– Limits and values by coverage– Deductibles– Reinsurance
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Data Resolution
Aggregated DataAggregated DataDetailed DataDetailed Data
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Data needs
Insurable valueInsurable value
LimitLimit
DeductibleDeductible
Total sum insuredTotal sum insured
LOCATIONLOCATION
They will only work well with good data
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Uncertainty
29Guy Carpenter
Types of Uncertainty
Primary (Aleatory) Uncertainty– Uncertainty of which, if any, event will occur
Secondary (Epistemic) Uncertainty
– Given that an event has occurred, the uncertainty in the amount of
loss
– Distribution of possible outcomes, rather than expected outcome
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Major Sources of Uncertainty
HAZARD Module
Limited historical data on hurricane
– 220 hurricanes in past 100 years
– Only 2 SSI 5 events
Unreliable data quality for old records
Lack of understanding of physical chaotic phenomena underlying hurricane behavior
Unknown elements may not be recognized e.g. El Nino & La Nina,
ENGINEERING Module
Limited data on claims for catastrophic events
Unreliable data quality for old records
– New types of losses - eg computers
Lack of understanding of structural behavior under severe loads
FINANCIAL Module
Estimates loss after application of financial structures.
Portfolio exposure data is interpreted differently - limits versus values-at-risk
Insurance and reinsurance structures are applied to loss distribution differently:
– Site-level loss– Policy-level loss
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Uncertainty Associated with Client
Risks that are in the pipeline
Miscoding of exposure details– including unknown locations– type of construction– how deductible applies
Post event regulatory environment
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Results will vary
0
200,000,000
400,000,000
600,000,000
800,000,000
1,000,000,000
1,200,000,000
1,400,000,000
1,600,000,000
1,800,000,000
0 100 200 300 400 500 600
AIR Res
EQECAT Res
RMS Res
Back
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Quantifying Cat Model Uncertainty
Depending upon point on EP curve, model could be off by a factor of 2.0 to
3.5 times
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You need to recognize uncertainty….
250
year
PM
L w
ith
2.0
x
Model 1 Model 2 Model 3
$20m
$10m
$40m
$30m
$15m
$60m
$50m
$25m
$100m
$25m
$40m
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Comparing Model Results
New Versions– All models constantly being “tweaked”– Changes are not uniform across regions, perils, construction codes,
etc.
Sensitivity– Slight changes and shifts in exposure can produce dramatic changes
in loss estimates– Change in loss may not be equal to exposure change
Output and Uses
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Definition
– Annual probability of exceeding a certain level of loss at least once.
Occurrence Exceeding Probability (OEP)
– Maximum loss in a year
– Drives reinsurance limit
Aggregate Exceeding Probability (AEP)
– Sum of losses in a year
– Mulitple net retentions
Exceeding Probability (EP) Curve
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Other Results
Average Annual Losses
– By line of business
– By geographic area
Deterministic Losses
– User defined event
– Historical event
Such as Hurricane Katrina
Loss $1m to $2mLoss $2m to $5mLoss $5m to $10mLoss $10m to $15mLoss greater that $15m
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How Are Models Used?
Macro
Insurance firms– Loss potential– Business strategies
Reinsurance – Design and evaluation– Program pricing
Regulatory– Ability to respond
Claims– Early warning
Micro
Insurance firms– Underwriting process– Rate development – Loss drivers– Portfolio management
Reinsurance – Decompose account
Claims– High priority loss drivers
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Model Applications – Product Line ManagementAverage Annual Loss – Top Ten Zip Codes
Zip code State AAL31328 GA 7,74729928 SC 5,03631411 GA 4,95131410 GA 4,67929935 SC 4,49329920 SC 4,31529438 SC 4,25011976 NY 4,01029902 SC 3,91629926 SC 3,660
Commercial
Does the premium earned support the
risk assumed ?
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Model Applications – Individual Risk UnderwritingAverage Annual Loss – Top Ten
Annual Property Premium % of Premium
$65,000 16.1%
$15,000 57.1%
$24,000 33.1%
$45,000 14.3%
$49,000 12.5%
$9,000 59.4%
$75,000 6.8%
$17,000 30.0%
$90,000 5.4%
$19,000 16.3%
Policy Number Average Annual Loss
CLP 2965 $10,480
CLP 3967 $8,566
CLP 5111 $7,938
BOP 2905 $6,450
CLP 7786 $6,109
BOP 2890 $5,345
EDP 2789 $5,103
CLP 2121 $5,099
BOP 3088 $4,890
CLP 8634 $3,094
Potential Red Flag
Potential Red Flag
Potential Red Flag
Catastrophe Load
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Model ApplicationsReinsurance 101 – Standard Deviation Load Pricing
Attachment Limit % PlacedDeposit Premium
ROLMean Loss
by LayerStandard Deviation
Standard Deviation
Load$3,000,000 $2,000,000 100.0% $700,000 35% $500,000 $571,429 35%$5,000,000 $5,000,000 100.0% $1,300,000 26% $950,000 $972,222 36%
$10,000,000 $10,000,000 100.0% $1,700,000 17% $1,200,000 $1,250,000 40%$17,000,000 $3,700,000 22% $2,650,000
Standard Deviation Load
=
1,700,000 – 1,200,000
1,250,000 = 40%
Rate on Line = Premium / Limit
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