1. Chris Svendsgaard, FCAS, CPCU, MAAA Swiss Re
Exposure Rating
Chris Svendsgaard, FCAS, CPCU, MAAA
Swiss Re

2. Outline
Definition of exposure rating
Applications of exposure rating
Steps in exposure rating

3. Definition of Exposure Rating
Use exposure information to price a reinsurance risk
Don’t use risk’s loss information

4. 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

5. 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

6. 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

7. Applications of exposure rating
5. Property catastrophe programs
Extensive exposure information
Engineering/meteorological/geophysical models
Not covered in this talk

8. 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

9. 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

10. Policy Reinsurance Exposure Rating Concepts Reinsurance Limit
Policy Limit
Retention
Deductible

11. Policy Reinsurance Exposure Rating Concepts Exposes Layer
Reinsurance Limit
Policy Limit
Retention
Graphic Design by Piet Mondrian
Deductible

12. Deductible = 100 Policy Limit = 1,000,000
Concepts: Example
Deductible = Policy Limit = 1,000,000
Retention = 250,000 R. Limit = 750,000
Ground-up Primary Reinsurance Loss Payment Payment
250, ,
250, ,
500, , ,900
1,000, , ,900
1,000, ,000, ,000
5,000, ,000, ,000

13. General Equation
ELF =
Expected losses & ALAE for exposed layer
Expected losses & ALAE for primary policy

14. Cost at Reinsurance Top - Cost at Reinsurance Bottom
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

15. Cost function
Cost
Retained Part

16. 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

17. ILFs are meant for all costs, not just losses + ALAE Using ISO ILFs:
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

18. A Solution
Use Limited Expected Value function for “Cost” function
Adjust separately for ALAE

19. Limited Expected Value
Average limited severity

20. Sample ELF Calculation

21. ISO ILF Definition By Table Prem/Ops Products C. Auto
1, 2, 3 x State Group
Products
A, B, C
C. Auto
Wt Class x State Group

22. ISO ILF Definition Ratio of Costs at policy limit sold
Costs at basic limit

23. Costs (expressed per occurrence)
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)

24. Property Cost Function
“Scales”
Often by peril
Fire, Wind, EQ
Lloyd’s/Salzmann/Y (Swiss Re)/Ludwig (Hartford)
PSOLD (ISO)

25. Property Scale
100%
100%

26. Sometimes people use “EML” instead of TIV
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