A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 1 Discussion Paper Presentation

March 8, 2007 Slide 1

A New Exposure Base for Vehicle Service Contracts – Miles Driven

CAS Ratemaking Seminar – Atlanta 2007

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




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




Typical Cash Flow of Premium

Retail Price

Dealer Markup

Remitted to Adminstrator

Agency Commission

Adminstrator Fee

“CLP” Premium

Remaining Warranty Reserve

Warranty Reserve




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”




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.




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.




Pure Premium Method - Contract Count

New Domestic 7/84 Term

In-Force Contracts

Policy Policy Age

Year 12 24 36 48 60 72 84

2002 200 194 191 187 179

2003 600 583 557 542

2004 1,200 1,176 1,145

2005 1,500 1,455

2006 1,000

Total 4,500 3,409 1,893 729 179




Pure Premium Method – Pure Premiums

New Domestic7/84 Term

Policy Policy Age

Year 12 24 36 48 60 72 84

2002 2.19 21.81 45.89 134.58 160.38

2003 1.16 47.90 58.93 172.62

2004 1.12 41.22 79.98

2005 2.34 63.00

2006 3.00

Average 1.96 43.49 61.60 153.60 160.38

Selected 1.96 43.49 61.60 153.60 160.38




Pure Premium Method – Future Pure Premiums

New Domestic Future Values Trended 2% 7/84 Term

Development

Policy

Year 12 24 36 48 60

2002 2.19 21.81 45.89 134.58 160.38

2003 1.16 47.90 58.93 172.62 163.59

2004 1.12 41.22 79.98 156.67 166.86

2005 2.34 63.00 62.83 159.81 170.20

2006 3.00 44.35 64.09 163.00 173.60




Estimating the Total CostsNew Domestic Future Values Trended 2%

7/84 Term

Future Earnings Total

Policy Reported Losses Factor Estimated Future

Year Losses Contracts @60months @60months Losses Losses

2002 67,389 179 0 0.78 86,396 19,007

2003 154,921 542 88,589 0.78 312,191 157,271

2004 141,418 1,145 370,447 0.78 656,237 514,819

2005 95,195 1,455 571,639 0.78 854,915 759,720

2006 3,004 1,000 663,318 0.78 854,259 851,255

461,926 1,693,992 2,763,998 2,302,072




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




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




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




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




An ExampleExposure

8,400 12,000 14,400 18,000 22,800 AverageYear

1 252 360 432 540 684 454 2 252 360 432 540 9,708 2,258 3 252 360 7,200 17,460 22,116 9,478 4 8,148 11,640 13,968 17,460 3,492 10,942 5 8,148 11,640 13,968 - - 6,751 6 8,148 11,640 - - - 3,958

Total 25,200 36,000 36,000 36,000 36,000 33,840

Adjusted Exposed Miles per year




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




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)




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




Calculating the Claim Rate

• Impact of Cancellations

• Claims Administration

• Pricing the Book

Documents

A New Exposure Base for Vehicle Service Contracts – Miles Driven CAS Ratemaking Seminar – Atlanta 2007 March 8, 2007Slide 1 Discussion Paper Presentation