22nd May 2008
Cat Ratemaking
Jillian Williams
CAE, Spring 2008
www.guycarp.com
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
Comparison of Number of Events and Loss to ROL
Hurricane Andrew
Hurricane Katrina
WTC
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What is a Cat Model
What is a Cat Model?
 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
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How models are built
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
Back
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Basic Components of CAT Models
Hazard Module
Engineering Module
(Hurricane:
Meteorological Info)
(Damagability of
assets at risk)
Portfolio
Actuarial Module
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(Financial
implications )
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Hazard Module
 Estimates location, characteristics & likelihood of a natural
catastrophe
 Estimates site intensity
– For Earthquake:
– For Hurricane:
– For Tornado/Hail:
– For Flood:
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Ground Motion
Windspeed
Windspeed & Hail Impact Energy
Depth
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Hazard Parameters: Earthquake
Earthquake-Generated
Energy (Waves)
Length of
Fault Rupture
Earthquake (Magnitude)
 Fault/seismic
source zone
location
 Magnitude
 Focal Depth
 Attenuation
 Local soil
conditions
Fault
Ground Motion
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Hazard Parameters: Hurricane
• Frequency of hurricanes
WV
•
•
•
•
•
•
•
•
VA
NC
SC
d3
AL
GA
d2
1
d1
FL
Landfall location
Central pressure
Radius of maximum winds
Forward speed
Track angle
Maximum wind speed
Terrain roughness
Filling rate after landfall
Radius of
max. winds
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Forward
speed
Site Windspeed
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Hazard Parameters: Tornado/Hail
Tornado
• Track area
• Tornado intensity
Hail
• Hailstones per minute
• Hailstone size
Hail Impact Energy & Windspeed
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Hazard Parameters: Flood
• Depth
• Velocity
• Duration
•
•
•
•
•
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Intensity
Factors
Seawater/Freshwater
Sediment Loads
Sewage and other Pollutants
Impervious Area (Flash)
Slope
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Engineering Module
• Estimates physical damage to portfolio
• Vulnerability Function (Damage given site
intensity for structural type)
Damage Ratio
100%
80%
60%
40%
20%
0%
70
90
110
130
150
Wind Speed
Const 1
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Const 2
Const 3
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Financial Module
$30m
Damage (Ground Up)
$25m
Gross (Less Deductibles)
Net of Facultative
Insurance &
reinsurance
structures are
applied to loss
distribution
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Net of Per Risk
Net of Cat
$20m
$10m
$5m
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Variation Among Models

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
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Modeled and Non-Modeled Perils
Primary
Non-Modeled
Riot
Winter Freeze
Hurricane
Earthquake
Tornado/Hail
Total Catastrophic
Risk
Not including
Terrorism or
Worker Comp
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Secondary/Collateral
Sprinkler Leakage
Fire Following
Sea Surge
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Why use a Cat Model
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
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Commercial Cat Models
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 Perils
1
2
3
7
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Data Cat Models Need
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
Detailed Data
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Aggregated Data
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Data needs
Total sum insured
Insurable value
Limit
Deductible
LOCATION
They will only work well with good data
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Uncertainty
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
ENGINEERING Module
FINANCIAL Module
 Limited historical data on
 Limited data on claims for
 Estimates loss after
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
catastrophic events
 Unreliable data quality for old
records
– New types of losses - eg
computers
 Lack of understanding of
structural behavior under
severe loads
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
be recognized e.g. El Nino &
La Nina,
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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
1,800,000,000
AIR Res
EQECAT Res
RMS Res
1,600,000,000
1,400,000,000
1,200,000,000
1,000,000,000
800,000,000
600,000,000
400,000,000
200,000,000
0
0
100
200
300
400
500
600
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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250 year PML with 2.0x
You need to recognize uncertainty….
$100m
$60m
$40m
$50m
$30m
$20m
$25m
$10m
Model 1
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$40m
$25m
$15m
Model 2
Model 3
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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
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Output and Uses
Exceeding Probability (EP) Curve

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
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Other Results
 Average Annual Losses
– By line of business
– By geographic area
 Deterministic Losses
– User defined event
– Historical event
Loss $1m to $2m
Loss $2m to $5m
Loss $5m to $10m
Loss $10m to $15m
Loss greater that $15m
 Such as Hurricane Katrina
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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
Micro
 Insurance firms
– Underwriting process
– Rate development
– Loss drivers
– Portfolio management
 Reinsurance
– Decompose account
 Claims
– High priority loss drivers
 Claims
– Early warning
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Model Applications – Product Line Management
Average Annual Loss – Top Ten Zip Codes
Commercial
Zip code
State
31328
GA
29928
SC
31411
GA
premium
31410 Does theGA
earned support the
29935
SC
risk assumed
?
29920
SC
29438
SC
11976
NY
29902
SC
29926
SC
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AAL
7,747
5,036
4,951
4,679
4,493
4,315
4,250
4,010
3,916
3,660
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Model Applications – Individual Risk Underwriting
Average Annual Loss – Top Ten
Policy Number
Average Annual Loss
Annual Property Premium
Catastrophe
Load
% of
Premium
$10,480
$65,000
16.1%
$8,566
$15,000
57.1%
CLP 5111
$7,938
$24,000
33.1%
BOP 2905
$6,450
$45,000
14.3%
$6,109
$49,000
12.5%
$5,345
$9,000
59.4%
$5,103
$75,000
6.8%
$5,099
$17,000
30.0%
$4,890
$90,000
5.4%
$3,094
$19,000
16.3%
CLP 2965
CLP 3967
CLP 7786
BOP 2890
Potential
Red Flag
Potential
Red Flag
EDP 2789
CLP 2121
BOP 3088
CLP 8634
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Potential
Red Flag
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Model Applications
Reinsurance 101 – Standard Deviation Load Pricing
Attachment
$3,000,000
$5,000,000
$10,000,000
Limit
$2,000,000
$5,000,000
$10,000,000
$17,000,000
% Placed
100.0%
100.0%
100.0%
Rate on Line = Premium / Limit
Deposit
Premium
ROL
Mean Loss
by Layer
$700,000
$1,300,000
$1,700,000
$3,700,000
35%
26%
17%
22%
$500,000
$950,000
$1,200,000
$2,650,000
Standard
Deviation
Load
$571,429
35%
$972,222
36%
$1,250,000
40%
Standard
Deviation
Standard Deviation Load
=
1,700,000 – 1,200,000
= 40%
1,250,000
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