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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

8Guy Carpenter

Basic Components of CAT Models

Hazard Module

Engineering Module

Actuarial Module

(Hurricane: Meteorological Info)

Portfolio

(Damagability of assets at risk)

(Financial implications )

9Guy Carpenter

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

19Guy Carpenter

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

25Guy Carpenter

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

34Guy Carpenter

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

35Guy Carpenter

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

37Guy Carpenter

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 ?

41Guy Carpenter

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

42Guy Carpenter

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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