Discussion Paper Presentation

1. Discussion Paper Presentation “An Exposure Based Approach to Automobile Warranty Ratemaking and Reserving” Authors:John Kerper, FSA, MAAA Lee M. Bowron, ACAS, MAAA Kerper and Bowron LLC www.kerper-bowron.com Slide 1

2. Vehicle Service Contracts – A Different Animal • Service Contracts are single premium, long term policies • These require special treatment on actuarial opinions • Insurance Company typically receives the premium after payment of expenses • In some cases, not considered insurance • Other times, only a “CLP” premium is remitted • However the legal treatment, establishing the liability and pricing the book are still issues Slide 2

3. Typical Cash Flow of Premium Slide 3

4. Claims Pattern for New Car Vehicle Service Contract • for example, 7 years/84,000 miles with a 3 year/36,000 mile basic and a 5 year/60,000 mile powertrain • Initial period of few claims due to manufacturer’s basic (bumper-to-bumper) warranty • A period of claims during the powertrain only manufacturer’s warranty • An increase in claims when the manufacturer’s warranty expires • A slowing of claims as the coverage “miles out” Slide 4

5. Earnings Curves • Earnings curves are predetermined amounts of earnings for system reports • Earnings curves are not the true earnings since the unearned premium reserve is subject to additional actuarial testing • Rule-of-thumb curves (pro-rata, reverse rule of 78s) should be avoided in most cases. Slide 5

6. Current Actuarial Practice • The most common method is to triangulate pure premiums at various evaluations • Pure premiums are then trended to the evaluation date • Tail factors are usually defaulted to earning curve assumptions. Slide 6

7. Pure Premium Method - Contract Count Slide 7

8. Pure Premium Method – Pure Premiums Slide 8

9. Pure Premium Method – Future Pure Premiums Slide 9

10. Estimating the Total Costs Slide 10

11. Issues with Pure Premium Method • Data may not be available in the tail • Older data may not be appropriate • Subdividing data will likely decrease credibility • Sensitive to outlier data points Slide 11

12. An Alternative Approach • Instead of claims as a function of time, claims as a function of miles driven • Claims = Miles Driven * Cost per mile * trend factor Slide 12

13. Estimating Miles Driven • Miles driven during a vehicle service contract can be modeled from observed events • Claims • Cancellations • Distributional approach to model the variability in the book • Segment observations into quintiles by average miles driven per month • triangulate the data and project to ultimate the average miles driven per year Slide 13

14. An Example - Assumptions • Coverage term – 6 years / 72,000 miles • Manufacturer warranty – 3 years / 36,000 miles • Basic and powertrain • Average miles driven per month by quintile • 8,400 • 12,000 • 14,400 • 18,000 • 22,800 • 3% of claims during manufacturer warranty Slide 14

15. An Example Slide 15

16. Calculating the Cost per Mile • Calculate average historical rate • Develop relativities to adjust for contract / vehicle factors • Type and term of coverage • Deductible • Initial mileage of vehicle when contract purchased • Classification of vehicle (should reflect expected claims) • Type of business Slide 16

17. Calculating the Cost per Mile • Techniques • Minimum bias • Iterative approach starting with all relativities at 1, adjusting factors for variable with greatest variance (to expedite convergence) • (mostly) independent variables required • GLM • Tweedie distribution with parameter at or near 1 (1 is same as minimum bias) Slide 17

18. Trending the Miles • Miles should be trended for the increase in costs due to inflation and “wear-and-tear” • There is also a negative trend factor for: • preexisting conditions (typically on used cars) • decreasing claims consciousness or unreported disposition of vehicle • Apply the trend factor to the estimate of miles driven Slide 18

19. Calculating the Claim Rate • Impact of Cancellations • Claims Administration • Pricing the Book Slide 19