Swiss ReExposure Rating Chris Svendsgaard Z 1 Exposure Rating Chris Svendsgaard, FCAS, CPCU, MAAA Swiss Re

Swiss Re Exposure Rating Chris Svendsgaard Z

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Exposure Rating

Chris Svendsgaard, FCAS, CPCU, MAAA

Swiss Re


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Outline

• Definition of exposure rating

• Applications of exposure rating

• Steps in exposure rating


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Definition of Exposure Rating

• Use exposure information to price a reinsurance risk

– Don’t use risk’s loss information


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Applications of exposure rating

1. Casualty excess of loss treaties

2. Casualty excess of loss facultative certificates

3. Property per risk excess of loss treaties

4. Property per risk facultative certificates

5. Property catastrophe programs


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1. Casualty excess of loss treaties

2. Casualty excess of loss facultative certificates

– These two are rated similarly.

– Differences

– Treaty starts with subject premium, cert starts with exposures

– Treaty is mix of policy limits, increased limits tables


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3. Property per risk excess of loss treaties

4. Property per risk facultative certificates

– Rated similarly--Differences:

– Treaty starts with subject premium, cert starts with exposures

– Treaty is mix of occupancies, has more total insured values

– Certs are exposure-rated only, usually

– Certs usually cover more perils


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5. Property catastrophe programs

– Extensive exposure information

– Engineering/meteorological/geophysical models

– Not covered in this talk


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Basic Reinsurance Pricing Concept

• Calculate expected losses and expenses in layer

• Discount for the time value of money

• Load the expected losses for internal expenses, commission, brokerage, and risk

• Express as a percentage of premium, if necessary


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Basic Formula

Loss in layer =

Premium x Expected Loss Ratio x Excess Layer Factor

= (Premium x Expected Loss Ratio) x Excess Layer Factor

= (Expected Primary Loss & ALAE) x Excess Layer Factor


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Exposure Rating Concepts

Policy Reinsurance

Deductible

Policy Limit Retention

Reinsurance Limit


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Exposure Rating Concepts

Policy Reinsurance

Deductible

Policy Limit Retention

Reinsurance LimitExposes Layer

Graphic Design by Piet Mondrian


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Concepts: Example

• Deductible = 100 Policy Limit = 1,000,000

• Retention = 250,000 R. Limit = 750,000

Ground-up Primary Reinsurance Loss Payment Payment 250,001 249,901 0 250,101 250,001 1 500,000 499,900 249,900 1,000,000 999,900 749,900 1,000,100 1,000,000 750,000 5,000,000 1,000,000 750,000


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General Equation

ELF =

Expected losses & ALAE for exposed layer

Expected losses & ALAE for primary policy


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General Equation

ELF =

Cost at Reinsurance Top - Cost at Reinsurance Bottom

Cost at Policy Top - Cost at Policy Bottom

Cost at Top = Cost of claims limited to “Top” , etc.

R. Top = Highest ground-up claim amount where R. pays = Min (Deductible + Pol. Limit, Ded. + Retention + R. Limit) usually

P. Top = Policy Limit + Deductible

P. Bottom = Deductible


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Cost

Retained Part

Cost function


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General Equation (wrong version)

ELF =

ILF(Ded+RT+LIM) - ILF(Ded+RT)

ILF(Ded+PL) - ILF(Ded)

Where:

LIM = Reinsurance Limit RT = Retention

Ded = Deductible PL = Policy Limit


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Problems with ILFs

• ILFs are meant for all costs, not just losses + ALAE

• Using ISO ILFs:

– ISO Risk Load gets in

– ULAE creeps in

– Aggregate limits distort values (depending on which ILFs you use)

– ALAE drops out (because is loaded 100% in basic limit)

– Reinsurance treatment of ALAE not reflected


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A Solution

• Use Limited Expected Value function for “Cost” function

• Adjust separately for ALAE


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Limited Expected Value

• Average limited severity

K

KFKdxxxf

KLEV

0)](1[)(

)(


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Limit LEV(Deductible) 100 99

(Deductible + Retention) 250,100 8,200

(Deductible + Policy Limit) 1,000,100 12,300

ELF = (12,300 - 8,200) / (12,300 - 99) = 4,100 / 12,201 = 34%

Sample ELF Calculation


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ISO ILF Definition

• By Table

– Prem/Ops

– 1, 2, 3 x State Group

– Products

– A, B, C

– C. Auto

– Wt Class x State Group


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ISO ILF Definition

• Ratio of

– Costs at policy limit sold

– Costs at basic limit


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ISO ILF Definition

• Costs (expressed per occurrence)

– Expected Losses, limited by policy per-occurrence limit

– Expected ALAE (same for all limits)

– ULAE (fixe % of sum of loss + ALAE)

– Risk Load (increases with policy limit)


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Property Cost Function

• “Scales”

– Often by peril

– Fire, Wind, EQ

– Lloyd’s/Salzmann/Y (Swiss Re)/Ludwig (Hartford)

– PSOLD (ISO)


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100%

100%

Property Scale


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Property Scale

• USUALLY

– x axis is Retention/Total Insured Value

– y axis is Limited Expected Value(Ret)/Expected Value

– These are for the severity distribution

• Sometimes people use “EML” instead of TIV

Documents

Swiss ReExposure Rating Chris Svendsgaard Z 1 Exposure Rating Chris Svendsgaard, FCAS, CPCU, MAAA Swiss Re