The pricing of a policy are highly
dependent on the characteristics of the individual to whom the policy is sold. The
characteristics could consist of existing conditions (inherent risks) and
claims patterns from the same pool of policy holders. An individual could consist of characteristics
from different pools of data (by age, by location, by gender, etc).
To find the relationship between the various
pools of claims history is the traditional way of looking at series of one-way
tables to determine relativities by rating factor (either focusing on the relative
risk premiums or the relative loss ratios)
SIMPLE CLAIMS FREQUENCY EXAMPLE
Here
is a simple example calculating the relative loss ratio from 2 pools of claims data (Age group & Location).
POPULATION
|
CLAIMS COUNT
|
||||||
AGE GROUP
|
LOCATION
|
AGE GROUP
|
LOCATION
|
||||
NORTH
| EAST | WEST |
NORTH
|
EAST
|
WEST
|
||
1
|
100
|
1200
|
500
|
1
|
1
|
37
|
42
|
2
|
300
|
500
|
400
|
2
|
14
|
73
|
101
|
ACTUAL
FREQUENCY (claims ratio)
|
EXPOSURES
(relativity)
|
||||||
AGE GROUP
|
LOCATION
|
AGE GROUP
|
LOCATION
|
||||
NORTH
| EAST | WEST | NORTH | EAST |
WEST
|
||
1
|
0.010
|
0.031
|
0.084
|
1
|
1.0
|
3.1
|
8.4
|
2
|
0.047
|
0.146
|
0.253
|
2
|
4.7
|
14.6
|
25.3
|
The relative loss exposure shows age group
no. 2 from West should be charged a premium 25 times of age group 1
from North.
This approach assumes
that the average claim value is the same for each class. In addition, the age group no.1 from North is assumed to be the ‘base class’, which
has a relativity of 1.0.
Factors affecting claims experience are
much larger, and this creates problems when deciding on what pricing
differentials to apply between different groups.
ONE-WAY METHOD
The one-way method
computes relativity separately for each value of the car size variable and the
age group variable. Below is an example using the same claims data.
Relativity for Locations
LOCATION
|
CLAIMS COUNT
|
POPULATION
|
FREQUENCY
|
RELATIVITY
|
NORTH
|
15
|
400
|
0.038
|
1.0
|
EAST
|
110
|
1700
|
0.065
|
1.725
|
WEST
|
143
|
900
|
0.159
|
4.237
|
Relativity for Age groups
AGE GROUPS
|
CLAIMS
|
POPULATION
|
FREQUENCY
|
RELATIVITY
|
GROUP 1
|
80
|
1800
|
0.044
|
1.0
|
GROUP 2
|
188
|
1200
|
0.157
|
3.525
|
The final overall
rating factor is the product of the individual location relativity against the individual age group relativity. The below result
shows a different value ( Age group 2 owning Small cars should be charged a
premium 14 times of age group 1 owning large cars.
AGE GROUPS
|
LOCATION
|
|||
NORTH
|
EAST
|
WEST
|
||
No.
|
Relativity
|
1.000
|
1.725
|
4.237
|
1
|
1
|
1.0
|
1.7
|
4.2
|
2
|
3.525
|
3.5
|
6.1
|
14.9
|
this method still
fails to make the relativities as steep as necessary to reflect multiple combined risk from many variables due to various assumptions being used.
VIEWS
To
accurately reflect the relative risk characteristics of the pool of underlying
policyholders,
one solution is to use some form of multiple regression approach which removes any distortions caused by different mixes of business.
one solution is to use some form of multiple regression approach which removes any distortions caused by different mixes of business.
A flexible approach is a regression method
known as generalized linear models (GLMs). Many different types of models which
suit insurance data fall under this framework. The additional benefit of using
GLMs over one-way tables is that the models are formulated within a statistical
framework allowing standard statistical tests (such as Z tests and F tests)
to be used for comparing models, as well as providing residual plots for the
purpose of model diagnostic checking.
