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
CAS Ratemaking Seminar – Atlanta 2007
Slide 1
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
CAS Ratemaking Seminar – Atlanta 2007
Slide 2
A New Exposure Base for Vehicle
Service Contracts – Miles Driven
Typical Cash Flow of Premium
Remitted to
Adminstrator
Retail Price
Agency
Commission
Dealer
Markup
March 8, 2007
Adminstrator
Fee
“CLP”
Premium
Warranty
Reserve
Remaining
Warranty
Reserve
CAS Ratemaking Seminar – Atlanta 2007
Slide 3
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
CAS Ratemaking Seminar – Atlanta 2007
Slide 4
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
CAS Ratemaking Seminar – Atlanta 2007
Slide 5
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
CAS Ratemaking Seminar – Atlanta 2007
Slide 6
A New Exposure Base for Vehicle
Service Contracts – Miles Driven
Pure Premium Method - Contract Count
New Domestic
7/84 Term
In-Force Contracts
Policy
Year
Policy Age
12
24
36
48
60
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
March 8, 2007
4,500
3,409
1,893
729
72
84
179
CAS Ratemaking Seminar – Atlanta 2007
Slide 7
A New Exposure Base for Vehicle
Service Contracts – Miles Driven
Pure Premium Method – Pure Premiums
7/84
Term
New Domestic
Policy
Policy Age
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
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
CAS Ratemaking Seminar – Atlanta 2007
72
84
Slide 8
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
March 8, 2007
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
CAS Ratemaking Seminar – Atlanta 2007
Slide 9
A New Exposure Base for Vehicle
Service Contracts – Miles Driven
Estimating the Total Costs
New Domestic
Future Values Trended 2%
7/84 Term
Policy
Reported
Year
Losses
Contracts
2002
67,389
179
2003
154,921
542
2004
141,418
2005
2006
Earnings
Total
Losses
Factor
Estimated
Future
@60months
@60months
Losses
Losses
0.78
86,396
19,007
88,589
0.78
312,191
157,271
1,145
370,447
0.78
656,237
514,819
95,195
1,455
571,639
0.78
854,915
759,720
3,004
1,000
663,318
0.78
854,259
851,255
2,763,998
2,302,072
461,926
March 8, 2007
Future
0
1,693,992
CAS Ratemaking Seminar – Atlanta 2007
Slide 10
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
CAS Ratemaking Seminar – Atlanta 2007
Slide 11
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
CAS Ratemaking Seminar – Atlanta 2007
Slide 12
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
CAS Ratemaking Seminar – Atlanta 2007
Slide 13
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
CAS Ratemaking Seminar – Atlanta 2007
Slide 14
A New Exposure Base for Vehicle
Service Contracts – Miles Driven
An Example
Adjusted Exposed Miles per year
8,400
12,000 14,400 18,000 22,800
Exposure
Average
Year
1
2
3
4
5
6
252
252
252
8,148
8,148
8,148
360
360
360
11,640
11,640
11,640
432
432
7,200
13,968
13,968
-
540
540
17,460
17,460
-
684
9,708
22,116
3,492
-
454
2,258
9,478
10,942
6,751
3,958
Total
25,200
36,000
36,000
36,000
36,000
33,840
March 8, 2007
CAS Ratemaking Seminar – Atlanta 2007
Slide 15
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
CAS Ratemaking Seminar – Atlanta 2007
Slide 16
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
CAS Ratemaking Seminar – Atlanta 2007
Slide 17
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
CAS Ratemaking Seminar – Atlanta 2007
Slide 18
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
CAS Ratemaking Seminar – Atlanta 2007
Slide 19