1. John Kerper, FSA, MAAA JHK Company
9/15/2018
Reserving for Automobile Warranty and Other Long Duration Contracts Gap & Residual Value Casualty Loss Reserve Seminar
John Kerper, FSA, MAAA
JHK Company

2. 9/15/2018
Purpose
Introduce Gap and Residual Value coverages and the methods of estimating unearned premium reserve for these coverages.

3. Topics of Discussion Description of Coverages Sellers Underwriters
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Topics of Discussion
Description of Coverages
Sellers
Underwriters
UEP Reserve for Residual Value
UEP Reserve for Gap

4. Description of Coverages
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Description of Coverages

5. Description of Coverages
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Description of Coverages
Excess of loan balance over book value:
Purchase price above book value
Low, zero or negative down payment
Loan amortization vs. vehicle depreciation
Optimistic residual values
After-market extras
Financed insurance coverages

6. Description of Coverages
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Description of Coverages
Covered Events
Gap - total loss of vehicle (e.g. theft or collision)
Residual Value - maturity of loan

7. Description of Coverages
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Description of Coverages
Common Additional Benefits - Gap
auto insurance deductible
1 or 2 delinquent payments
New car purchase bonus

8. 9/15/2018
Sellers
Auto dealers
Financing source
Auto insurer

9. Underwriters Service Contract or Credit Insurer Auto Insurer
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Underwriters
Service Contract or Credit Insurer
Auto Insurer
Bank / Finance Company (Debt Cancellation)

10. UEP Reserve for Residual Value
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UEP Reserve for Residual Value
No refund value
Timing of losses known
Probability of loss unknown at inception
Base reserve on assumed combined ratio
As business matures, adjust combined ratio assumption
No refund value - doesn't make sense to allow refund when claim can occur only at maturity and probability of claim / no-claim is better known as maturity approaches
Timing of losses known - exposure concentrated at loan maturity
Probability of claim unknown at inception (except to extent residual is high or low compared to market - ALG; better known as time passes); could perform historical study on development of actual market values compared to ALG projections
At issue, in absence of reliable data, could assume x% combined ratio and earn premium accordingly
Adjust projected combined ratio as business matures - can compare current value projections with those embedded in business to develop probable losses in portfolio. Use to project probable losses

11. UEP Reserve for Gap Refund Value (Rule of 78, Pro-Rata) Other tests
9/15/2018
UEP Reserve for Gap
Refund Value (Rule of 78, Pro-Rata)
Other tests
Refund Value – usually reserve due to heavy front-end exposure not recognized in usual methods (R78 & Pro-Rata)
Claim emergence pattern and present value calculations required, but generally will not determine reserve unless premium is inadequate

12. 9/15/2018
UEP Reserve for Gap
Estimating Exposure for each month

13. UEP Reserve for Gap Estimating Exposure for each month - example
9/15/2018
UEP Reserve for Gap
Estimating Exposure for each month - example

14. 9/15/2018
UEP Reserve for Gap

15. 9/15/2018
UEP Reserve for Gap

16. UEP Reserve for Gap Estimating Probability of Loss (frequency)
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UEP Reserve for Gap
Estimating Probability of Loss (frequency)
Experience under existing book of gap contracts
Separate determination of severity (based on exposure) and frequency.
Total loss data from auto insurance statistics
Estimating Probability of Loss (frequency)
1. Experience under existing book of gap contracts
1.1. Separate determination of severity (based on exposure) and frequency. Use frequency, but adjust severity based on relative exposure. Should not assume composite claim pattern (severity x frequency) from existing book will hold true for projections because underlying loan practices may change (fully amortizing vs. lease or balloons, loan term lengthening / shortening, new/used mix, etc) and lead to change in exposure (severity)
2. Use total loss data from auto insurance statistics to estimate frequency

17. 9/15/2018
Conclusion
UEP Reserve for Residual Value is a guess at inception and must be adjusted as residual values develop
UEP Reserve for Gap is generally determined by refund value
Other tests can reveal inadequate pricing or longer exposure period