swiss reexposure rating chris svendsgaard z 1 exposure rating chris svendsgaard, fcas, cpcu, maaa...
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Swiss Re Exposure Rating Chris Svendsgaard Z
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Exposure Rating
Chris Svendsgaard, FCAS, CPCU, MAAA
Swiss Re
Swiss Re Exposure Rating Chris Svendsgaard Z
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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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Applications of exposure rating
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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Applications of exposure rating
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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Applications of exposure rating
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
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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