PAD_Task Force PAI_Jogja
STANDARD METHOD
PROVISION OF ADVERSE DEVIATION
PAD Task Force Team
CONTENTS
1
Scope
2
Calculation Methods of PAD
3
Simulation
4
Summary
Scope
Products
Variables
Special Cases
Traditional
Mortality
Single Premium
Unit Link
Morbidity
Annuity
Credit Life
Lapse
Term ROP
Expense
Calculation Methods of PAD
Data: > 5 years
One-tailed t-distribution
25% PAD 6
+
75% PAD 5
PAD method
Data: 3 - 5 years
Bootstrap one-tailed normal
standard
25% PAD 3
+
75% PAD 2
Data: < 3 years
Benchmark standard of PAD
value or value from other
countries
One-Tailed t-Distribution
Method 1
One Tailed t-Distribution
Assume that A/E have t-distribution
Set the confidence interval to 75% and 95%
t5
0,95
A/E table of mortality, morbidity, lapse, or expense
0,05
0
Calculate sample mean and its standard error
Critical Value of -distribution for � = 25% and � = 5%
with df = � - 1
Calculate PAD value
Calculating PAD Value
PAD =
�,�−
ҧ
− ҧ
=
ҧ+
�,�−
ҧ
∙
�
Implementation : BE × (1+PAD)
PAD =
�,�−
− ҧ= ҧ+
�,�−
Implementation : BE + PAD
∙
�
− ҧ
=
− ҧ=
ҧ+
�,�−
�,�−
ҧ
∙
�
∙
�
−
=
�,�−
ҧ
∙
�
One-Tailed Standard Normal
with Bootstrapping Data
Method 2
Bootstrap Method
Construct the empirical
distribution of A/E from �
ordered experience data
Use inverse transformation
method, draw � pseudosample � ∗
Step 3
Calculate the standard
error of statistic � within this
formula:
Repeat step 2 - 4 �-times
(number of simulation) so
then we get � ∗ , � ∗ , … , ��∗
ෞ�� =
Step 5
Step 1
BOOTSTRAP
METHOD
�−
Step 4
Step 2
Generate � random number
from uniform (0,1)
distribution
Calculate statistic � from
pseudo-sample � ∗
called � ∗
: ҧ
�*
Step 6
Calculate the estimation of
statistic � within this
formula:
� ∗ =
�
�
��∗
�=
�
��∗ − � ∗
�=
Step 7
Reference Data - PAD Value
from Other Countries
Method 3
Reference Data
If the experience data owned by the insurance company are not sufficient, we
strongly propose to either use standard PAD value from the data of insurance
market experience (represented by 10 life insurance companies) or use
benchmark PAD value from other countries
Assumption
Thailand
Malaysia
Australia
Mortality
17%
10% - 25%
10% - 40%
Morbidity
17%
10% - 25%
10% - 40%
Expense
5%
5%
2.5% - 20%
Lapse
12%
25%
25% - 100%
Simulation
Simulation
Year
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
A/E
97%
79%
92%
88%
87%
88%
87%
89%
83%
85%
Count (�)
Mean
Standard Deviation
= 10
= 87%
= 5%
Student-t Distribution
Confidence Interval 75%
Degree of Freedom
t-Value
ҧ + �,�− ∙ / �
PAD = 2%
=9
= 1.23
= 89%
Confidence Interval 95%
Degree of Freedom
t-Value
ҧ + �,�− ∙ / �
PAD = 4%
=9
= 2.26
= 91%
Simulation
Student-t Distribution
Year
2011
2012
2013
2014
2015
Confidence Interval 75%
Confidence Interval 95%
A/E
89%
70%
72%
94%
88%
Degree of Freedom = 4
t-Value
= 1.34
= 89%
ҧ + �,�− ∙ / �
Degree of Freedom = 4
t-Value
= 2.78
= 96%
ҧ + �,�− ∙ / �
Count (�)
Mean
Standard Deviation
=5
= 83%
= 11%
PAD = 8%
PAD = 16%
Simulation
Bootstrap
Year
2011
89%
A/E
2012
70%
2013
72%
2014
94%
2015
88%
Data
70%
72%
88%
89%
94%
n
1
1
1
1
1
CDF
0.2
0.4
0.6
0.8
1
Cumulative Distribution Function
F(x)
1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0,0
x=F-1(x)
70%
72%
88% 89%
94%
Simulation
Simulation I
Uniform (0,1) y=F(x)
0.64
0.52
0.58
0.91
0.69
Sample F-1(x)
89%
88%
88%
94%
89%
ҧ�
�
90%
3%
Repeated by � =
times
Cumulative Distribution Function
F(x)
1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0,0
x=F-1(x)
70%
72%
88% 89%
94%
Simulation
Simulation I
Simulation II
Simulation III
Simulation IV
Simulation V
Simulation VI
Simulation VII
Simulation VIII
Simulation IX
Simulation X
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
0.64
89%
0.67
89%
0.86
94%
0.25
72%
0.79
89%
0.57
88%
0.28
72%
0.91
94%
0.38
72%
0.97
94%
0.52
88%
0.25
72%
0.68
89%
0.64
89%
0.06
70%
0.71
89%
0.25
72%
0.14
70%
0.45
88%
0.71
89%
0.58
88%
0.80
89%
0.10
70%
0.46
88%
0.92
94%
0.34
72%
0.80
89%
0.25
72%
0.80
89%
0.87
94%
0.91
94%
0.50
88%
0.41
88%
0.25
72%
0.80
89%
0.90
94%
0.80
89%
0.08
70%
0.51
88%
0.60
88%
0.69
89%
0.94
94%
0.71
89%
0.47
88%
0.56
88%
0.51
88%
0.43
88%
0.97
94%
0.73
89%
0.96
94%
ҧ�
90%
86%
86%
82%
86%
86%
82%
80%
85%
92%
Mean
Standard Error (ෞ�)
= 86%
= 4%
Normal Distribution
Confidence Interval 75%
z-Value
ҧ+ � ∙ �
= 0.67
= 88%
PAD = 3%
Confidence Interval 95%
z-Value
ҧ+ �∙ �
= 1.64
= 91%
PAD = 7%
Comparison
One-tailed t-distribution Method
Bootstrap one-tailed normal standard
Confidence Interval 75%
Confidence Interval 75%
PAD = 8%
PAD = 3%
Confidence Interval 95%
Confidence Interval 95%
PAD = 16%
PAD = 7%
Summary
1
3
2
4
Reference
1.Kellison, S.G., and London, R, L. 2011. Risk Models and Their
Estimation. ACTEX Publications.
2.Hogg, R.V., McKean, J.W., and Craig, A.T. 2005. Introduction
to Mathematical Statistics. Pearson Prentice Hall.
3.Teugels, J.L., and Sundt, B. 2004. Encyclopedia of Actuarial
Science. Wiley.
4.Broverman, S.A. 2013. ACTEX C/4 Study Manual. ACTEX
Publications.
THANK YOU!
Any Questions?
PAD Task Force Team
Nico Demus, FSAI
Citra Kirana, FSAI
Budi Ramdani, FSAI
Nurdin Kosasih, FSAI
Alwin Kurniawan, FSAI
Doni Friyadi, FSAI
Trishadi Rusli, FSAI
Benny Hadiwibowo, FSAI
Ponno Jonathan, FSAI
Agus Sugiharto, FSAI
PROVISION OF ADVERSE DEVIATION
PAD Task Force Team
CONTENTS
1
Scope
2
Calculation Methods of PAD
3
Simulation
4
Summary
Scope
Products
Variables
Special Cases
Traditional
Mortality
Single Premium
Unit Link
Morbidity
Annuity
Credit Life
Lapse
Term ROP
Expense
Calculation Methods of PAD
Data: > 5 years
One-tailed t-distribution
25% PAD 6
+
75% PAD 5
PAD method
Data: 3 - 5 years
Bootstrap one-tailed normal
standard
25% PAD 3
+
75% PAD 2
Data: < 3 years
Benchmark standard of PAD
value or value from other
countries
One-Tailed t-Distribution
Method 1
One Tailed t-Distribution
Assume that A/E have t-distribution
Set the confidence interval to 75% and 95%
t5
0,95
A/E table of mortality, morbidity, lapse, or expense
0,05
0
Calculate sample mean and its standard error
Critical Value of -distribution for � = 25% and � = 5%
with df = � - 1
Calculate PAD value
Calculating PAD Value
PAD =
�,�−
ҧ
− ҧ
=
ҧ+
�,�−
ҧ
∙
�
Implementation : BE × (1+PAD)
PAD =
�,�−
− ҧ= ҧ+
�,�−
Implementation : BE + PAD
∙
�
− ҧ
=
− ҧ=
ҧ+
�,�−
�,�−
ҧ
∙
�
∙
�
−
=
�,�−
ҧ
∙
�
One-Tailed Standard Normal
with Bootstrapping Data
Method 2
Bootstrap Method
Construct the empirical
distribution of A/E from �
ordered experience data
Use inverse transformation
method, draw � pseudosample � ∗
Step 3
Calculate the standard
error of statistic � within this
formula:
Repeat step 2 - 4 �-times
(number of simulation) so
then we get � ∗ , � ∗ , … , ��∗
ෞ�� =
Step 5
Step 1
BOOTSTRAP
METHOD
�−
Step 4
Step 2
Generate � random number
from uniform (0,1)
distribution
Calculate statistic � from
pseudo-sample � ∗
called � ∗
: ҧ
�*
Step 6
Calculate the estimation of
statistic � within this
formula:
� ∗ =
�
�
��∗
�=
�
��∗ − � ∗
�=
Step 7
Reference Data - PAD Value
from Other Countries
Method 3
Reference Data
If the experience data owned by the insurance company are not sufficient, we
strongly propose to either use standard PAD value from the data of insurance
market experience (represented by 10 life insurance companies) or use
benchmark PAD value from other countries
Assumption
Thailand
Malaysia
Australia
Mortality
17%
10% - 25%
10% - 40%
Morbidity
17%
10% - 25%
10% - 40%
Expense
5%
5%
2.5% - 20%
Lapse
12%
25%
25% - 100%
Simulation
Simulation
Year
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
A/E
97%
79%
92%
88%
87%
88%
87%
89%
83%
85%
Count (�)
Mean
Standard Deviation
= 10
= 87%
= 5%
Student-t Distribution
Confidence Interval 75%
Degree of Freedom
t-Value
ҧ + �,�− ∙ / �
PAD = 2%
=9
= 1.23
= 89%
Confidence Interval 95%
Degree of Freedom
t-Value
ҧ + �,�− ∙ / �
PAD = 4%
=9
= 2.26
= 91%
Simulation
Student-t Distribution
Year
2011
2012
2013
2014
2015
Confidence Interval 75%
Confidence Interval 95%
A/E
89%
70%
72%
94%
88%
Degree of Freedom = 4
t-Value
= 1.34
= 89%
ҧ + �,�− ∙ / �
Degree of Freedom = 4
t-Value
= 2.78
= 96%
ҧ + �,�− ∙ / �
Count (�)
Mean
Standard Deviation
=5
= 83%
= 11%
PAD = 8%
PAD = 16%
Simulation
Bootstrap
Year
2011
89%
A/E
2012
70%
2013
72%
2014
94%
2015
88%
Data
70%
72%
88%
89%
94%
n
1
1
1
1
1
CDF
0.2
0.4
0.6
0.8
1
Cumulative Distribution Function
F(x)
1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0,0
x=F-1(x)
70%
72%
88% 89%
94%
Simulation
Simulation I
Uniform (0,1) y=F(x)
0.64
0.52
0.58
0.91
0.69
Sample F-1(x)
89%
88%
88%
94%
89%
ҧ�
�
90%
3%
Repeated by � =
times
Cumulative Distribution Function
F(x)
1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0,0
x=F-1(x)
70%
72%
88% 89%
94%
Simulation
Simulation I
Simulation II
Simulation III
Simulation IV
Simulation V
Simulation VI
Simulation VII
Simulation VIII
Simulation IX
Simulation X
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
Uniform (0,1)
Sample
0.64
89%
0.67
89%
0.86
94%
0.25
72%
0.79
89%
0.57
88%
0.28
72%
0.91
94%
0.38
72%
0.97
94%
0.52
88%
0.25
72%
0.68
89%
0.64
89%
0.06
70%
0.71
89%
0.25
72%
0.14
70%
0.45
88%
0.71
89%
0.58
88%
0.80
89%
0.10
70%
0.46
88%
0.92
94%
0.34
72%
0.80
89%
0.25
72%
0.80
89%
0.87
94%
0.91
94%
0.50
88%
0.41
88%
0.25
72%
0.80
89%
0.90
94%
0.80
89%
0.08
70%
0.51
88%
0.60
88%
0.69
89%
0.94
94%
0.71
89%
0.47
88%
0.56
88%
0.51
88%
0.43
88%
0.97
94%
0.73
89%
0.96
94%
ҧ�
90%
86%
86%
82%
86%
86%
82%
80%
85%
92%
Mean
Standard Error (ෞ�)
= 86%
= 4%
Normal Distribution
Confidence Interval 75%
z-Value
ҧ+ � ∙ �
= 0.67
= 88%
PAD = 3%
Confidence Interval 95%
z-Value
ҧ+ �∙ �
= 1.64
= 91%
PAD = 7%
Comparison
One-tailed t-distribution Method
Bootstrap one-tailed normal standard
Confidence Interval 75%
Confidence Interval 75%
PAD = 8%
PAD = 3%
Confidence Interval 95%
Confidence Interval 95%
PAD = 16%
PAD = 7%
Summary
1
3
2
4
Reference
1.Kellison, S.G., and London, R, L. 2011. Risk Models and Their
Estimation. ACTEX Publications.
2.Hogg, R.V., McKean, J.W., and Craig, A.T. 2005. Introduction
to Mathematical Statistics. Pearson Prentice Hall.
3.Teugels, J.L., and Sundt, B. 2004. Encyclopedia of Actuarial
Science. Wiley.
4.Broverman, S.A. 2013. ACTEX C/4 Study Manual. ACTEX
Publications.
THANK YOU!
Any Questions?
PAD Task Force Team
Nico Demus, FSAI
Citra Kirana, FSAI
Budi Ramdani, FSAI
Nurdin Kosasih, FSAI
Alwin Kurniawan, FSAI
Doni Friyadi, FSAI
Trishadi Rusli, FSAI
Benny Hadiwibowo, FSAI
Ponno Jonathan, FSAI
Agus Sugiharto, FSAI