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Vehicle Service Contracts

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									                            A New Exposure Base for Vehicle
                            Service Contracts – Miles Driven


 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

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

 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


March 8, 2007                                                  Slide 2
                   CAS Ratemaking Seminar – Atlanta 2007
                                 A New Exposure Base for Vehicle
                                 Service Contracts – Miles Driven

 Typical Cash Flow of Premium

   Retail Price                             Remitted to
                                           Adminstrator




                    Agency          Adminstrator                Warranty
                  Commission           Fee                      Reserve




       Dealer                                           Remaining
                            “CLP”
       Markup                                            Warranty
                           Premium
                                                         Reserve


March 8, 2007                                                              Slide 3
                        CAS Ratemaking Seminar – Atlanta 2007
                              A New Exposure Base for Vehicle
                              Service Contracts – Miles Driven

 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”



March 8, 2007                                                    Slide 4
                     CAS Ratemaking Seminar – Atlanta 2007
                          A New Exposure Base for Vehicle
                          Service Contracts – Miles Driven


 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.


March 8, 2007                                                Slide 5
                 CAS Ratemaking Seminar – Atlanta 2007
                         A New Exposure Base for Vehicle
                         Service Contracts – Miles Driven


 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.


March 8, 2007                                               Slide 6
                CAS Ratemaking Seminar – Atlanta 2007
                                          A New Exposure Base for Vehicle
                                          Service Contracts – Miles Driven

 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

March 8, 2007                                                                  Slide 7
                                 CAS Ratemaking Seminar – Atlanta 2007
                                       A New Exposure Base for Vehicle
                                       Service Contracts – Miles Driven

 Pure Premium Method – Pure Premiums
                       7/84
New Domestic           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
March 8, 2007                                                              Slide 8
                              CAS Ratemaking Seminar – Atlanta 2007
                                      A New Exposure Base for Vehicle
                                      Service Contracts – Miles Driven

 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

March 8, 2007                                                                         Slide 9
                             CAS Ratemaking Seminar – Atlanta 2007
                                                A New Exposure Base for Vehicle
                                                Service Contracts – Miles Driven


 Estimating the Total Costs
New 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



March 8, 2007                                                                                                Slide 10
                                      CAS Ratemaking Seminar – Atlanta 2007
                         A New Exposure Base for Vehicle
                         Service Contracts – Miles Driven

 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



March 8, 2007                                               Slide 11
                CAS Ratemaking Seminar – Atlanta 2007
                           A New Exposure Base for Vehicle
                           Service Contracts – Miles Driven


 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




March 8, 2007                                                 Slide 12
                  CAS Ratemaking Seminar – Atlanta 2007
                                    A New Exposure Base for Vehicle
                                    Service Contracts – Miles Driven


 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


March 8, 2007                                                              Slide 13
                           CAS Ratemaking Seminar – Atlanta 2007
                                  A New Exposure Base for Vehicle
                                  Service Contracts – Miles Driven


 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
March 8, 2007                                                        Slide 14
                         CAS Ratemaking Seminar – Atlanta 2007
                                     A New Exposure Base for Vehicle
                                     Service Contracts – Miles Driven


 An Example
                      Adjusted Exposed Miles per year                 Exposure
                8,400   12,000 14,400 18,000 22,800                   Average
 Year
    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



March 8, 2007                                                                    Slide 15
                            CAS Ratemaking Seminar – Atlanta 2007
                                A New Exposure Base for Vehicle
                                Service Contracts – Miles Driven


 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
March 8, 2007                                                      Slide 16
                       CAS Ratemaking Seminar – Atlanta 2007
                                  A New Exposure Base for Vehicle
                                  Service Contracts – Miles Driven


 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)

March 8, 2007                                                          Slide 17
                         CAS Ratemaking Seminar – Atlanta 2007
                                A New Exposure Base for Vehicle
                                Service Contracts – Miles Driven


 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

March 8, 2007                                                      Slide 18
                       CAS Ratemaking Seminar – Atlanta 2007
                          A New Exposure Base for Vehicle
                          Service Contracts – Miles Driven


 Calculating the Claim Rate
 • Impact of Cancellations

 • Claims Administration

 • Pricing the Book




March 8, 2007                                                Slide 19
                 CAS Ratemaking Seminar – Atlanta 2007

								
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