GLMs in Personal Lines Pricing

1
GLMs in Personal Lines Pricing
MAF Fall Meeting September 26, 2002

• Claudine Modlin, FCAS
• Watson Wyatt Insurance Financial Services Inc.
• www.watsonwyatt.com/pretium

2
Agenda

• Overview of GLMs in the rating process
• GLMs in practice
• data
• diagnostics
• interactions
• Territory analysis
• How to get started

3
Agenda

• Overview of GLMs in the rating process
• GLMs in practice
• data
• diagnostics
• interactions
• Territory analysis
• How to get started

4
Objective
Age
Sex
Vehicle
Premium
Rate Scheme
Area
Claim
Limit
5
Modeling the cost of claims
6
Modeling the cost of claims
x
Freq
BI
Cost 1
Amt


x
Freq
PD
Cost 2
Amt


x
Freq
MED
Cost 3
Amt


x
Freq
COL
Cost 4
Amt


x
Freq
OTC
Cost 5
Amt


7
Modeling the cost of claims

• Rating factors
• Statistical techniques

8
Example auto rating factors

• Standard factors
• Age
• Sex
• Marital status
• Number years licensed
• Claim experience
• Territory
• Usage
• Mileage
• Limits
• Deductibles
• Make/Model of vehicle
• Violations
• Credit
• Multi-line
• Multi-car
• Safety devices
• Theft devices

• External data
• geodemographic data
• geophysical data
• Data from other products
• banking data
• other insurance data

9
The failings of one way analysis
2
2.5
10
Example correlation
11
Generalized linear models

• EY m g-1(X.b x)
• VarY f.V(m) / w
• Consider all factors simultaneously
• Allow for nature of random process
• Robust and transparent
• EU industry standard

12
Why GLMs over other methods

• One-way and two-way analyses
• Distorted by correlations, no diagnostics
• Iteratively standardized one-ways
• No diagnostics, no faster than GLMs, less
  flexibility for allowance of random process, not
  always tractable solution
• Neural networks
• Not transparent, hard to interpret, can be
  unstable with new types of policy, easy to
  over/under fit
• Cluster analyses / "segmenting"
• Suitable for marketing but less appropriate for
  assessing continuous risk does not fit with
  rating structures
• Data mining
• General term for all of the above but can often
  be merely one-way or two-way analyses on subsets
  of data

13
Example of GLM output (real UK data)
0.25
180
0.2
160
0.15
0.1
140
0.05
0
120
0
-4
-5
-0.05
100
Log of multiplier
Exposure (policy years)
-0.1
-15
80
-17
-0.15
-19
-20
-0.2
60
-0.25
40
-0.3
-0.35
20
-0.4
-0.45
0
1
2
3
4
5
6
7
Factor
Exposure
Approx 2 SE from estimate
GLM estimate
14
Example of GLM output (real UK data)
22
0.25
180
0.2
160
0.15
10
0.1
7
140
6
0.05
0
0
120
0
-4
-5
-0.05
100
Log of multiplier
Exposure (policy years)
-0.1
-15
-16
80
-17
-0.15
-19
-19
-20
-0.2
60
-0.25
40
-0.3
-0.35
20
-0.4
-0.45
0
1
2
3
4
5
6
7
Factor
Exposure
Oneway relativities
Approx 2 SE from estimate
GLM estimate
15
Modeling the cost of claims
x
Freq
BI
Cost 1
Amt


x
Freq
PD
Cost 2
Amt


x
Freq
MED
Cost 3
Amt


x
Freq
COL
Cost 4
Amt


x
Freq
OTC
Cost 5
Amt


16
The premium rating process
17
The premium rating process
18
Factor effect analysis
19
Factor effect analysis
20
Factor effect analysis
21
Impact analysis
22
Impact analysis
23
Impact analysis
24
Impact analysis
25
Impact analysis
26
The premium rating process
Freq
TPBI
x
Cost 1
Amt

Competitor
Amt

Freq
TPPD
x
Cost 2

Current Rates
Freq
AD
x
Cost 3
Amt


Model
Freq
FT
x
Cost 4
Amt


Amt

Freq
WS
x
Cost 5

Expense loadings
Profit loadings
Risk
Compare
Model
27
Competitive position

• Survey market
• rate filings
• quotation systems
• question policyholder
• mystery shopping
• Investigate competitors' structures

• Apply "cheapest" tariff to own portfolio
• Use in retention / new business model

28
The premium rating process
Freq
TPBI
x
Cost 1
Amt

Competitor

Freq
TPPD
x
Cost 2

Amt
Current Rates
Freq

AD
x
Cost 3

Amt
Model
Amt

Freq
FT
x
Cost 4

Freq
WS
x
Cost 5
Amt


Expense loadings
Profit loadings
Risk
Lapse/take-up
Compare
Model
Model
29
Modeling retention

• Model
• - rating factors - other products held
• - payment method - change in coverage
• - discount expectation plus
• - source - change in premium
• - claims history - competitiveness

30
Retention model - Policyholder age
31
Retention model - Change in premium
32
New business modelCompetitiveness of premium
33
Customer lifetime value
34
Price elasticity
35
The premium rating process
Freq
TPBI
x
Cost 1

Amt
Competitor
Freq
TPPD

Amt

x
Cost 2
Current Rates


Freq
AD
x
Cost 3
Amt
Model
Freq
FT
x
Cost 4

Amt

Freq
WS
x
Cost 5


Amt
Expense loadings
Profit loadings
Risk
Lapse/take-up
Compare
Model
Model
New
Model
Rates
office
36
Agenda

• Overview of GLMs in the rating process
• GLMs in practice
• data
• diagnostics
• interactions
• Territory analysis
• How to get started

37
Data required

• Linked policy claims data
• Record one insured risk (eg car) for one policy
  period or portion of policy period for which risk
  has not changed
• Fields
• explanatory variables - rating, underwriting,
  marketing, external
• stats - earned exposure, incurred claim count,
  incurred loss, earned premium (optional)
• Minimum of 100,000 earned exposures

38
Data considerations

• Reflect cancellation/endorsement
• Include time lag to reduce effect of IBNR
• Include dummy variables to standardize for
  geography (if countrywide study) and time
• Display rating factors applicable at time of
  exposure, categorized on current basis

39
Model iteration diagnostics

• Standard errors of parameter estimates
• F-tests / c2 tests on deviances (with ranks)
• Consistency over time
• Common sense

40
Standard errors ofparameter estimates
41
Deviances
42
Consistency over time
43
Common sense

• Does it make sense given correlations?
• Are ordered categorical variables well behaved?
• Can you believe it?
• Can underwriters believe it?
• Consider results for frequency and amounts at the
  same time
• Consider results for each claim type at the same
  time

44
Interactions
45
Interactions
46
Interactions
47
Interactions
?
?
48
Agenda

• Overview of GLMs in the rating process
• GLMs in practice
• data
• diagnostics
• interactions
• Territory analysis
• How to get started

49
Geographic rating

• Territory is one of the main drivers of cost
• Considerable variety in how insurers rate for
  territory
• One insurer will have limited exposure in any one
  area

50
Spatial smoothing

• Fit GLM (excluding current territories)
• Map "residual" risk by "region"
• Make this residual risk more predictive
• Categorize into territories to derive appropriate
  loadings

51
Residual risk
High residual
Low residual
52
A model form

• ri Z.ri ( 1 - Z ) . neighboring experience
• where
• ri smoothed residual risk
• ri unsmoothed residual risk

53
Definitions of "neighboring"
54
Example results
Unsmoothed residuals
Smoothed residuals
55
Finding the parametersEffect of smoothed vs
unsmoothed residual zone
Zone based on smoothed residuals
Zone based on unsmoothed residuals
56
Agenda

• Overview of GLMs in the rating process
• GLMs in practice
• data
• diagnostics
• interactions
• Territory analysis
• How to get started

57
How can I start?

• Programming from scratch
• Software applications
• tailored to personal lines
• easy to navigate
• fast, even on PC
• clear output
• cost is often less than the annual compensation
  of one actuary

58
GLMs in Personal Lines Pricing
MAF Fall Meeting September 26, 2002

• Claudine Modlin, FCAS
• Watson Wyatt Insurance Financial Services Inc.
• www.watsonwyatt.com/pretium