tim rozar fsa, maaa, cera derek kueker fsa lapse and mortality of post-level period term plans...
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Tim Rozar FSA, MAAA, CERA
Derek Kueker FSA
Lapse and Mortality of Post-Level Period Term Plans
International Actuarial Association
Background
2
-
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Level Period Post-Level Period
Annu
al P
rem
ium
Duration
10-Year Term - Sample Premium StructureMale Age 45, $500,000 Death Benefit
Super-Preferred Non-Smoker
Introduction to Post-Level Term
10-Year Term: Premium Structure with Jump to ART
$7,395 Duration 11
Premium
20 times Premium Jump
$375 Level Premium
3
The Sick…
Who Pays the $7,395 Rather Than Dropping Coverage or Getting a New Policy?
4
The Lazy…
The Unaware……And ALL 3 have extra mortality risk!
0%
50%
100%
150%
200%
250%
300%
6 7 8 9 10 11 12 13+
Level Period Tail Period
0%
10%
20%
30%
40%
50%
60%
70%
6 7 8 9 10 11 12 13+
Level Period Tail Period
Lapse Rate
2008 VBT Mortality Ratio
• Sharp increase in premium after level period leads to large anti-selective shock lapse.
• Mortality on persisting policyholders is substantially worse in the post-level period.
5
SOA/RGA Post-Level Term StudyLapse Study Experience Results
6
Shock Lapse Experience Results Overview
2000-2012 Policy-Year Study
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
2014 Study 2010 Study Change
Number of Companies w/ Post Level Experience 36 25 144%Post-Level Lapses with Premiums 436,307 87,544 498%
Post-Level Lapses without Premiums 258,030 170,171 152%
Number of Companies w/ Post Level Experience 15 7 214%Post-Level Lapses with Premiums 37,673 12,191 309%
Post-Level Lapses without Premiums 1,364 1,359 100%
10-Year Term
15-Year Term
7
Shock Lapse Experience (Jump to ART)
T10 By Duration
8
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
1
10
100
1,000
10,000
100,000
1,000,000
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
6 7 8 9 10 11 12 13 14 15 16+
Level Period Post-Level Period
Nu
mb
er o
f L
ap
ses
La
pse
Rat
e
Lapse Rate Median Lapse Rate Number of Lapses (right axis)
Shock Lapse Experience
T15 By Duration
9
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
1
10
100
1,000
10,000
100,000
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
11 12 13 14 15 16 17 18 19+
Level Period Post-Level Period
Nu
mb
er
of
La
ps
es
La
ps
e R
ate
Lapse Rate Median Lapse Rate Number of Lapses (right axis)
Shock Lapse Experience (Jump to ART)
T10 By Premium Jump Ratio
10
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
1
10
100
1,000
10,000
100,000
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Nu
mb
er o
f L
apse
s
Lap
se R
ate
Duration 11/10 Premium Jump RatioDuration 10 Lapse Rate Count Duration 10 Lapses
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Duration 11/10 Premium Jump RatioDuration 10 Lapse Rate Duration 11 Lapse Rate Duration 12 Lapse Rate
Shock Lapse Experience (Jump to ART)
T10 By Duration & Premium Jump
11
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Shock Lapse Experience (Jump to ART)
T10 By Duration & Premium Jump
Duration 11/10 Premium Jump
Ratio Band
Dur 11 / Dur 10
Dur 12 / Dur 11
1.01x - 2x 79.5% 59.5%2.01x - 3x 77.0% 46.7%3.01x - 4x 73.2% 44.9%4.01x - 5x 73.1% 42.7%5.01x - 6x 70.5% 45.4%6.01x - 7x 73.5% 45.1%7.01x - 8x 73.2% 46.3%8.01x - 9x 74.5% 45.9%
9.01x - 10x 78.7% 54.7%10.01x-12x 79.1% 49.7%12.01x-14x 79.7% 49.4%14.01x-16x 82.9% 56.8%
16.01x + 86.0% 59.8%Subtotal Prem Data Available 59.4% 42.9%
No Prem Data Available 55.0% 43.1%Grand Total 57.4% 42.9%
12
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Duration 11/10 Premium Jump RatioDuration 10 Lapse Rate Duration 11 Lapse Rate Duration 12 Lapse Rate
Dur 11 / Dur 10 Dur 12 / Dur 11
Shock Lapse Experience
T10 By Duration and Issue Age
13
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0-19 20-29 30-39 40-49 50-59 60-69 70+
Issue Age
Duration 6-9 Duration 10 Duration 11 Duration 12+
Shock Lapse Experience (Jump to ART)
T10 By Premium Jump and Issue age – duration 10
14
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
1
10
100
1,000
10,000
100,000
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
<40 40-49 50-59 60+ <40 40-49 50-59 60+ <40 40-49 50-59 60+ <40 40-49 50-59 60+ <40 40-49 50-59 60+
1.01x - 3x 3.01x - 5x 5.01x - 7x 7.01x - 9x 9.01x +
Nu
mb
er o
f L
ap
se
s
Lap
se R
ate
Duration 10 Lapse Rate Duration 10 Lapses
Shock Lapse Experience
T10 By Duration & Face Amount Band
15
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
< $50,000 $50,000 -$99,999
$100,000 -$249,999
$250,000 -$999,999
$1,000,000 -$4,999,999
$5,000,000 +
Face Amount
Duration 6-9 Duration 10 Duration 11 Duration 12+
Shock Lapse Experience (Jump to ART)
T10 By Premium Jump and Face Amount Band – duration 10
16
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
1
10
100
1,000
10,000
100,000
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
<100k 100k-249k
250k-999k
1M+ <100k 100k-249k
250k-999k
1M+ <100k 100k-249k
250k-999k
1M+ <100k 100k-249k
250k-999k
1M+ <100k 100k-249k
250k-999k
1M+
1.01x - 3x 3.01x - 5x 5.01x - 7x 7.01x - 9x 9.01x +
Nu
mb
er
of
La
ps
es
La
ps
e R
ate
Duration 10 Lapse Rate Duration 10 Lapses
Shock Lapse Experience
T10 By Duration & Gender
17
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Male Female
Gender
Duration 6-9 Duration 10 Duration 11 Duration 12+
Shock Lapse Experience
T10 By Duration & Risk Class
18
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Super-Preferred Preferred Non-Preferred Undiff Preferred Non-Preferred Undiff
Non-Smoker Smoker Unk/Agg
Risk Class
Duration 6-9 Duration 10 Duration 11 Duration 12+
Shock Lapse Experience
T10 By Duration & Premium Payment Mode
19
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Annual Semi-Annual Quarterly Monthly
Premium Payment Mode
Duration 6-9 Duration 10 Duration 11 Duration 12+
SOA/RGA Post-Level Term StudyMortality Study Experience Results
20
Mortality Experience Overview
2000-2012 Calendar Year Study
2014 Study 2010 Study Change
Number of Companies w/ Post Level Experience 36 24 150%Post-Level Claims with Premiums 2,651 382 694%
Post-Level Claims without Premiums 729 381 191%
Number of Companies w/ Post Level Experience 6 5 120%Post-Level Claims with Premiums 432 145 298%
Post-Level Claims without Premiums 12 13 92%
10-Year Term
15-Year Term
21
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
Mortality Experience (Jump to ART)
T10 By Duration
22
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
1
10
100
1,000
10,000
0%
50%
100%
150%
200%
250%
300%
350%
400%
450%
6 7 8 9 10 11 12 13 14 15 16+
Level Period Post-Level Period
Nu
mb
er
of
De
ath
s
Mo
rta
lity
Re
lati
ve t
oD
ura
tio
ns
6-1
0
A/E Mortality Median A/E Mortality Number of Deaths (right axis)
Mortality Experience
T15 By Duration
23
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
1
10
100
1,000
10,000
0%
50%
100%
150%
200%
250%
300%
350%
400%
450%
11 12 13 14 15 16 17 18 19+
Level Period Post-Level Period
Nu
mb
er
of
De
ath
s
Mo
rta
lity
Re
lati
ve t
o
Du
rati
on
s 1
1-1
5
A/E Mortality Median AE Rate Number of Deaths (right axis)
Mortality Experience (Jump to ART)
T10 Duration 11 Mortality by Premium Jump
24
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
1
10
100
1,000
10,000
0%
200%
400%
600%
800%
1000%
1200%
1400%
1600%
1800%
2000%
1.01x -2x
2.01x -3x
3.01x -4x
4.01x -5x
5.01x -6x
6.01x -7x
7.01x -8x
8.01x -9x
9.01x -12x
12.01x-15x
15.01x-18x
18.01x +
Nu
mb
er
of
De
ath
s
Mo
rta
lity
Re
lati
ve t
oD
ura
tio
ns
6-1
0
Duration 11/10 Premium Jump Ratio
Relative Mortality Ratio Number of Deaths (right axis)
Mortality Experience (Jump to ART)
T10 Duration 11+ Mortality by Issue Age
25
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
0%
50%
100%
150%
200%
250%
300%
350%
400%
0-29 30-39 40-49 50-59 60+Issue Age
Duration 6-10 Duration 11+ Post-Level Relative to Dur 6-10
Mortality Experience (Jump to ART)
T10 Duration 11+ Mortality by Face Amount Band
26
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
0%
50%
100%
150%
200%
250%
300%
350%
400%
450%
500%
< $50,000 $50,000 -$99,999
$100,000 -$249,999
$250,000 -$999,999
$1,000,000 +
Face Amount Band
Duration 6-10 Duration 11+ Post-Level Relative to Dur 6-10
Mortality Study Experience Results – Jump to ART
T10 Duration 11+ Mortality by Gender
27
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
0%
50%
100%
150%
200%
250%
300%
350%
Male FemaleGender
Duration 6-10 Duration 11+ Post-Level Relative to Dur 6-10
Mortality Study Experience Results – Jump to ART
T10 Duration 11+ Mortality by Risk Class
28
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
0%
50%
100%
150%
200%
250%
300%
350%
400%
450%
500%
550%
Super-Preferred
Preferred Non-Preferred Undiff Preferred Non-Preferred Undiff
Non-Smoker Smoker Unk/Agg
Risk ClassDuration 6-10 Duration 11+ Post-Level Relative to Dur 6-10
Mortality Experience (Jump to ART)
T10 Duration 11 Mortality by Duration 10 Shock Lapse
by Company
29
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
0%
150%
300%
450%
600%
750%
900%
1050%
1200%
1350%
1500%
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Du
rati
on
11
Mo
rtal
ity
Rel
ativ
e to
Du
rait
on
s 6
-10
Duration 10 Shock Lapse
>=35 claims
<35 claims
Expon. ()
Practical Applications
30
Shock Lapse Experience
Skewness of Lapses
31
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
6-9 10 11 12+
Pro
po
rtio
n o
f L
ap
se
s
Duration
12
11
10
9
8
7
6
5
4
3
2
1
• Grace period creates mismatch between exposure basis for claims and premiums
• No duration 11 premium received, but effective duration 10 exposure extends into grace period.
• Premium-paying persisters must subsidize “free insurance” during the grace period for policyholders who intended to lapse on their anniversary.
• Much bigger impact with shock lapse
• Small number of premium-payers…lots of lapsers
• Magnitude increases for higher lapse rates or longer grace periods
Grace Period Subsidy
32
• Assumptions:
• Cohort mortality = 0.1 / 1000 monthly in durations 10 & 11
• Lapse on anniversary at end of duration 10
• All lapsers will passively lapse and enter the grace period
• 2-month grace period
Grace Period Subsidy - Example
33
Grace Period Subsidy – Example5% Lapse Rate; No Anti-Selection
34
BOM Monthly Lapses BOM Monthly Lapses BOM Monthly LapsesYear Month Lives Mort Rate (Anniv) Lives Mort Rate (Anniv) Lives Mort Rate (Anniv)
10 1 100,000 0.10 10.0 100,000 0.10 10.0 100,000 0.10 10.0
10 2 99,990 0.10 10.0 99,990 0.10 10.0 99,990 0.10 10.0 10 3 99,980 0.10 10.0 99,980 0.10 10.0 99,980 0.10 10.0 10 4 99,970 0.10 10.0 99,970 0.10 10.0 99,970 0.10 10.0 10 5 99,960 0.10 10.0 99,960 0.10 10.0 99,960 0.10 10.0 10 6 99,950 0.10 10.0 99,950 0.10 10.0 99,950 0.10 10.0 10 7 99,940 0.10 10.0 99,940 0.10 10.0 99,940 0.10 10.0 10 8 99,930 0.10 10.0 99,930 0.10 10.0 99,930 0.10 10.0 10 9 99,920 0.10 10.0 99,920 0.10 10.0 99,920 0.10 10.0 10 10 99,910 0.10 10.0 99,910 0.10 10.0 99,910 0.10 10.0 10 11 99,900 0.10 10.0 99,900 0.10 10.0 99,900 0.10 10.0 10 12 99,890 0.10 10.0 4,994 99,890 0.10 10.0 99,890 0.10 10.0 4,993 11 1 94,886 0.10 9.5 99,880 0.10 10.0 94,887 0.10 10.0 11 2 94,877 0.10 9.5 99,870 0.10 10.0 4,993 94,877 0.10 10.0 11 3 94,867 0.10 9.5 94,867 0.10 9.5 94,867 0.10 9.5 11 4 94,858 0.10 9.5 94,858 0.10 9.5 94,858 0.10 9.5 11 5 94,848 0.10 9.5 94,848 0.10 9.5 94,848 0.10 9.5 11 6 94,839 0.10 9.5 94,839 0.10 9.5 94,839 0.10 9.5 11 7 94,829 0.10 9.5 94,829 0.10 9.5 94,829 0.10 9.5 11 8 94,820 0.10 9.5 94,820 0.10 9.5 94,820 0.10 9.5 11 9 94,810 0.10 9.5 94,810 0.10 9.5 94,810 0.10 9.5 11 10 94,801 0.10 9.5 94,801 0.10 9.5 94,801 0.10 9.5 11 11 94,791 0.10 9.5 94,791 0.10 9.5 94,791 0.10 9.5 11 12 94,782 0.10 9.5 94,782 0.10 9.5 94,782 0.10 9.5
Exposure Mort Rate Deaths Lapses Exposure Mort Rate Deaths Lapses10 100,000 1.20 119.9 4,994 100,000 1.20 119.93 4,993 11 94,886 1.20 113.8 - 94,887 1.21 114.80 -
Total 194,886 1.20 233.7 4,994 194,887 1.20 234.73 4,993
Duration 11/10: 100% Duration 11/10: 101%
w/ Grace PeriodExperience Study Basis
DeathsDuration
Deaths Deaths
No Grace Period w/ Grace Period
Grace Period Subsidy – Example60% Lapse Rate; No Anti-Selection
35
BOM Monthly Lapses BOM Monthly Lapses BOM Monthly LapsesYear Month Lives Mort Rate (Anniv) Lives Mort Rate (Anniv) Lives Mort Rate (Anniv)
10 1 100,000 0.10 10.0 100,000 0.10 10.0 100,000 0.10 10.0
10 2 99,990 0.10 10.0 99,990 0.10 10.0 99,990 0.10 10.0 10 3 99,980 0.10 10.0 99,980 0.10 10.0 99,980 0.10 10.0 10 4 99,970 0.10 10.0 99,970 0.10 10.0 99,970 0.10 10.0 10 5 99,960 0.10 10.0 99,960 0.10 10.0 99,960 0.10 10.0 10 6 99,950 0.10 10.0 99,950 0.10 10.0 99,950 0.10 10.0 10 7 99,940 0.10 10.0 99,940 0.10 10.0 99,940 0.10 10.0 10 8 99,930 0.10 10.0 99,930 0.10 10.0 99,930 0.10 10.0 10 9 99,920 0.10 10.0 99,920 0.10 10.0 99,920 0.10 10.0 10 10 99,910 0.10 10.0 99,910 0.10 10.0 99,910 0.10 10.0 10 11 99,900 0.10 10.0 99,900 0.10 10.0 99,900 0.10 10.0 10 12 99,890 0.10 10.0 59,928 99,890 0.10 10.0 99,890 0.10 10.0 59,916 11 1 39,952 0.10 4.0 99,880 0.10 10.0 39,964 0.10 10.0 11 2 39,948 0.10 4.0 99,870 0.10 10.0 59,916 39,954 0.10 10.0 11 3 39,944 0.10 4.0 39,944 0.10 4.0 39,944 0.10 4.0 11 4 39,940 0.10 4.0 39,940 0.10 4.0 39,940 0.10 4.0 11 5 39,936 0.10 4.0 39,936 0.10 4.0 39,936 0.10 4.0 11 6 39,932 0.10 4.0 39,932 0.10 4.0 39,932 0.10 4.0 11 7 39,928 0.10 4.0 39,928 0.10 4.0 39,928 0.10 4.0 11 8 39,924 0.10 4.0 39,924 0.10 4.0 39,924 0.10 4.0 11 9 39,920 0.10 4.0 39,920 0.10 4.0 39,920 0.10 4.0 11 10 39,916 0.10 4.0 39,916 0.10 4.0 39,916 0.10 4.0 11 11 39,912 0.10 4.0 39,912 0.10 4.0 39,912 0.10 4.0 11 12 39,908 0.10 4.0 39,908 0.10 4.0 39,908 0.10 4.0
Exposure Mort Rate Deaths Lapses Exposure Mort Rate Deaths Lapses10 100,000 1.20 119.9 59,928 100,000 1.20 119.93 59,916 11 39,952 1.20 47.9 - 39,964 1.50 59.90 -
Total 139,952 1.20 167.9 59,928 139,964 1.28 179.84 59,916
Duration 11/10: 100% Duration 11/10: 125%
w/ Grace PeriodExperience Study Basis
DeathsDuration
Deaths Deaths
No Grace Period w/ Grace Period
Grace Period Subsidy – Example90% Lapse Rate; No Anti-Selection
36
BOM Monthly Lapses BOM Monthly Lapses BOM Monthly LapsesYear Month Lives Mort Rate (Anniv) Lives Mort Rate (Anniv) Lives Mort Rate (Anniv)
10 1 100,000 0.10 10.0 100,000 0.10 10.0 100,000 0.10 10.0
10 2 99,990 0.10 10.0 99,990 0.10 10.0 99,990 0.10 10.0 10 3 99,980 0.10 10.0 99,980 0.10 10.0 99,980 0.10 10.0 10 4 99,970 0.10 10.0 99,970 0.10 10.0 99,970 0.10 10.0 10 5 99,960 0.10 10.0 99,960 0.10 10.0 99,960 0.10 10.0 10 6 99,950 0.10 10.0 99,950 0.10 10.0 99,950 0.10 10.0 10 7 99,940 0.10 10.0 99,940 0.10 10.0 99,940 0.10 10.0 10 8 99,930 0.10 10.0 99,930 0.10 10.0 99,930 0.10 10.0 10 9 99,920 0.10 10.0 99,920 0.10 10.0 99,920 0.10 10.0 10 10 99,910 0.10 10.0 99,910 0.10 10.0 99,910 0.10 10.0 10 11 99,900 0.10 10.0 99,900 0.10 10.0 99,900 0.10 10.0 10 12 99,890 0.10 10.0 89,892 99,890 0.10 10.0 99,890 0.10 10.0 89,874 11 1 9,988 0.10 1.0 99,880 0.10 10.0 10,006 0.10 10.0 11 2 9,987 0.10 1.0 99,870 0.10 10.0 89,874 9,996 0.10 10.0 11 3 9,986 0.10 1.0 9,986 0.10 1.0 9,986 0.10 1.0 11 4 9,985 0.10 1.0 9,985 0.10 1.0 9,985 0.10 1.0 11 5 9,984 0.10 1.0 9,984 0.10 1.0 9,984 0.10 1.0 11 6 9,983 0.10 1.0 9,983 0.10 1.0 9,983 0.10 1.0 11 7 9,982 0.10 1.0 9,982 0.10 1.0 9,982 0.10 1.0 11 8 9,981 0.10 1.0 9,981 0.10 1.0 9,981 0.10 1.0 11 9 9,980 0.10 1.0 9,980 0.10 1.0 9,980 0.10 1.0 11 10 9,979 0.10 1.0 9,979 0.10 1.0 9,979 0.10 1.0 11 11 9,978 0.10 1.0 9,978 0.10 1.0 9,978 0.10 1.0 11 12 9,977 0.10 1.0 9,977 0.10 1.0 9,977 0.10 1.0
Exposure Mort Rate Deaths Lapses Exposure Mort Rate Deaths Lapses10 100,000 1.20 119.9 89,892 100,000 1.20 119.93 89,874 11 9,988 1.20 12.0 - 10,006 2.99 29.96 -
Total 109,988 1.20 131.9 89,892 110,006 1.36 149.89 89,874
Duration 11/10: 100% Duration 11/10: 250%
w/ Grace PeriodExperience Study Basis
DeathsDuration
Deaths Deaths
No Grace Period w/ Grace Period
Grace Period Subsidy – Example90% Lapse Rate; 200% Anti-Selection
37
BOM Monthly Lapses BOM Monthly Lapses BOM Monthly LapsesYear Month Lives Mort Rate (Anniv) Lives Mort Rate (Anniv) Lives Mort Rate (Anniv)
10 1 100,000 0.10 10.0 100,000 0.10 10.0 100,000 0.10 10.0
10 2 99,990 0.10 10.0 99,990 0.10 10.0 99,990 0.10 10.0 10 3 99,980 0.10 10.0 99,980 0.10 10.0 99,980 0.10 10.0 10 4 99,970 0.10 10.0 99,970 0.10 10.0 99,970 0.10 10.0 10 5 99,960 0.10 10.0 99,960 0.10 10.0 99,960 0.10 10.0 10 6 99,950 0.10 10.0 99,950 0.10 10.0 99,950 0.10 10.0 10 7 99,940 0.10 10.0 99,940 0.10 10.0 99,940 0.10 10.0 10 8 99,930 0.10 10.0 99,930 0.10 10.0 99,930 0.10 10.0 10 9 99,920 0.10 10.0 99,920 0.10 10.0 99,920 0.10 10.0 10 10 99,910 0.10 10.0 99,910 0.10 10.0 99,910 0.10 10.0 10 11 99,900 0.10 10.0 99,900 0.10 10.0 99,900 0.10 10.0 10 12 99,890 0.10 10.0 89,892 99,890 0.10 10.0 99,890 0.10 10.0 89,874 11 1 9,988 0.20 2.0 99,880 0.10 10.0 10,006 0.10 10.0 11 2 9,986 0.20 2.0 99,870 0.10 10.0 89,874 9,996 0.10 10.0 11 3 9,984 0.20 2.0 9,986 0.20 2.0 9,986 0.20 2.0 11 4 9,982 0.20 2.0 9,984 0.20 2.0 9,984 0.20 2.0 11 5 9,980 0.20 2.0 9,982 0.20 2.0 9,982 0.20 2.0 11 6 9,978 0.20 2.0 9,980 0.20 2.0 9,980 0.20 2.0 11 7 9,976 0.20 2.0 9,978 0.20 2.0 9,978 0.20 2.0 11 8 9,974 0.20 2.0 9,976 0.20 2.0 9,976 0.20 2.0 11 9 9,972 0.20 2.0 9,974 0.20 2.0 9,974 0.20 2.0 11 10 9,970 0.20 2.0 9,972 0.20 2.0 9,972 0.20 2.0 11 11 9,968 0.20 2.0 9,970 0.20 2.0 9,970 0.20 2.0 11 12 9,966 0.20 2.0 9,968 0.20 2.0 9,968 0.20 2.0
Exposure Mort Rate Deaths Lapses Exposure Mort Rate Deaths Lapses10 100,000 1.20 119.9 89,892 100,000 1.20 119.93 89,874 11 9,988 2.40 23.9 - 10,006 3.99 39.93 -
Total 109,988 1.31 143.9 89,892 110,006 1.45 159.86 89,874
Duration 11/10: 200% Duration 11/10: 333%
w/ Grace PeriodExperience Study Basis
DeathsDuration
Deaths Deaths
No Grace Period w/ Grace Period
0
25
50
75
100
125
150
175
0%
50%
100%
150%
200%
250%
300%
350%
1 2 3 4 5 6 7 8 9 10 11 12
Nu
mb
er
of
De
ath
s
200
8 V
BT
Mo
rta
lity
Ra
tio
s
Months since start of Duration 11
2008 VBT Mortality Ratios Number of Deaths (right axis)
Mortality Experience
Duration 11 Mortality by Month
38
Source: http://www.soa.org/Research/Experience-Study/Ind-Life/Persistency/research-2014-post-level-shock.aspx
SOA/RGA Post-Level Term StudyAssumption Survey Results
39
Sent to top 100 term providers based on 2012 term insurance sales Responses from 41 companies Responses represented 62% of 2012 term sales
Assumption Survey Results
Overview
40
x=5% x=15% x=30%
5 Year Term 1.20% 3 1 0
10 Year Term 22.70% 42 36 8
15 Year Term 8.60% 32 6 1
20 Year Term 52.00% 44 44 42
25-30 Year Term 15.10% 33 23 9
Other 0.40% 5 2 1
Level Premium Term Product Mix by Level Period
Product Level PeriodAggregate Distribution
for Respondents
Number of companies where product represents at least x% of individual
company's term sales
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Assumption Survey Results
Post-Level Premium Structure
Dominant Structure is Jump to an ART Scale
Product Structure Responses
Premium jump to ART 40Premium grade to ART 4
Jump to new level period 3Face amount decrease 1
Product terminates 2Flexible Premiums (Term UL) 1
Post-Level Product Design
41Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Assumption Survey Results
Expected Changes to Post-Level Premium Structure
No change expected for most term new business Minimal changes reported to inforce term business
No change 23Grade premiums into an ART scale over 'x' years 3Other 3
Changes to Post-Level Premium Structure for Term New Business
DescriptionImplemented in
last 5 yearsConsidering
Lower post-level premiums 1 5Grade into an ART scale 3 3
Other 0 2
Changes to Post-Level Premium Structure for Term In Force
42Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Lapse Assumptions
Post-Level Lapse Rate Structure
Most companies assume only one shock lapse, generally grading down thereafter
10-Year Term 20-Year TermDuration L Shock, then level 8 7Duration L Shock, then grade down 12 102 Shocks, Duration L>=L+1 6 52 Shocks, Duration L+1>L 3 2
Responses
Lapse Rate Trend By Duration
Description
43Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Used a common pricing cell for consistent comparisons in upcoming charts
Lapse Assumptions
Factors impacting shock lapse assumptions
44
Additional Variations
Vary by These ParametersNo Other Variance
Premium Mode
Premium Jump Ratio
Risk Class & Premium
Jump RatioNo Variance 9
Issue Age & Level Period 5 1 1 1Level Period 5 1
Issue Age & Risk Class 2 1Risk Class 1
Premium Jump Ratio 1 1
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Lapse Assumptions
Annual and cumulative lapse assumptions by duration, 10-year term
45Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 11 12 13 14 15
Lap
se R
ate
Duration
80thpercentileMedian
20thpercentile
0%
10%
20%
30%
40%
50%
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90%
100%
10 11 12 13 14 15
Cu
mu
lati
ve
Lap
se R
ate
Duration
80thpercentileMedian
20thpercentile
Lapse Assumptions
Duration 10 lapse assumptions by issue age, 10-year term
46Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
25 35 45 55 65
Lap
se R
ate
Issue Age
80th percentile
Median
20th percentile
2009 Median
Lapse Assumptions
Post-Level Lapse Rate Assumption by Premium Jump, 10-year term
Broad range of assumptions by premium jump
Trend is somewhat inconsistent with experience
47Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0.0 5.0 10.0 15.0 20.0 25.0 30.0
Sh
ock
Lap
se
Premium Jump
Mortality Deterioration Assumptions
Post-Level Mortality Deterioration Structure
Assumptions vary broadly by structure of mortality deterioration
10-Year Term 20-Year TermLevel all durations 7 6Decreasing or grade to ultimate level 13 11Increasing then decreasing 6 1Generally increasing 1 3
Description
Mortality Deterioration Assumption Trend By DurationResponses
48Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
The same pricing cell that was used in the Lapse Assumptions charts is used in this section
Mortality Deterioration Assumptions
Factors impacting mortality deterioration assumptions
49Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Additional Variations
Vary by These ParametersNo other Variation
Risk Class and Gender Gender
Size of Shock Lapse
Duration, Level Period and Issue Age 6 4 1Policy Duration 5
Constant 4Duration and Level Period 3 1
Level Period 2Issue Age 1
Mortality Deterioration Assumptions
Post-Level Mortality Methodology
Dukes-MacDonald (or derivatives) and Flat Multiple are the primary assumptions used in developing mortality after the shock lapse
50Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
Method of Developing Mortality AssumptionMethod Responses
N/A - 100% shock lapse 9Dukes-MacDonald or derivatives of Dukes-MacDonald 14Canadian Institute of Actuaries Valuation Technique Paper #2 4Flat Multiple 13Other: Set by reinsurer/external consultant 3Other: Internally developed method 3
Mortality Deterioration Assumptions
Annual mortality deterioration multiple, 10 year term
51Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
0%
50%
100%
150%
200%
250%
300%
350%
400%
450%
500%
11 12 13 14 15 20
Mo
rtal
ity
Det
erio
rati
on
Mu
ltip
le
Duration
80th percentile
Median
20th percentile
2009 Median
Mortality Deterioration Assumptions
Post-Level Mortality Assumptions vs. Premium Jump
Mortality deterioration assumptions do not differ dramatically by premium jump, inconsistent with experience
52Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
0%
100%
200%
300%
400%
500%
600%
700%
800%
900%
1000%
0.0 5.0 10.0 15.0 20.0 25.0 30.0
Mo
rtal
ity
Det
erio
rati
on
Du
rati
on
11
Premium Jump
Mortality Deterioration Assumptions
Post-Level Mortality Assumptions vs. Premium Jump and Lapse Rate
When split by lapse rate, it does not appear assumptions vary dramatically by premium jump
53Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
0%
100%
200%
300%
400%
500%
600%
0% 20% 40% 60% 80% 100%
Mo
rtal
ity
Det
erio
rati
on
Du
rati
on
12
Cumulative Lapse Rate Duration 10 through 11
1-10X Jump
11-20X Jump
20X Jump or Greater
Lapse Assumptions
Skewness assumptions from the level period through the post-level period Today’s skewness assumptions do not always follow past experience
54
Monthly Lapse Skewness During Level Premium PeriodResponse Respondents
Lapses are uniformly distributed 18Lapses occur on premium payment modes 10
Lapses occur at the end of the year 7
Other 4
Monthly Lapse Skewness During Year of Shock LapseLapses are uniformly distributed 5
Lapses occur on premium payment modes 3Lapses occur at the end of the year 17
Lapses graded toward end of the year with shock in month 12 12
Monthly Lapse Skewness During Post-Level PeriodLapses are uniformly distributed 6
Lapses occur on premium payment modes 7Lapses occur at the end of the year 9
Lapses skewed to the beginning of L+1, Uniform thereafter 8
Source: http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf
SOA/RGA Post-Level Term StudyAssumptions vs. Experience
55
Survey Responses vs. Experience Study
56
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Ass
um
ptio
nS
urv
ey
(Ph
ase
1)
Exp
eri
ence
Re
sults
(P
has
e 2
)
Ass
um
ptio
nS
urv
ey
(Ph
ase
1)
Exp
eri
ence
Re
sults
(P
has
e 2
)
Ass
um
ptio
nS
urv
ey
(Ph
ase
1)
Exp
eri
ence
Re
sults
(P
has
e 2
)
Ass
um
ptio
nS
urv
ey
(Ph
ase
1)
Exp
eri
ence
Re
sults
(P
has
e 2
)
Ass
um
ptio
nS
urv
ey
(Ph
ase
1)
Exp
eri
ence
Re
sults
(P
has
e 2
)
Ass
um
ptio
nS
urv
ey
(Ph
ase
1)
Exp
eri
ence
Re
sults
(P
has
e 2
)
10 11 12 13 14 15
La
ps
e R
ate
Duration
T10 Jump to ARTLapse Rates by Duration
Phase 1 vs. Phase 2
80th percentile
Median
Aggregate
20th percentile
Survey Responses vs. Experience Study
57
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Ass
um
ptio
nS
urv
ey
(Ph
ase
1)
Exp
eri
ence
Re
sults
(P
has
e 2
)
Ass
um
ptio
nS
urv
ey
(Ph
ase
1)
Exp
eri
ence
Re
sults
(P
has
e 2
)
15 16
La
ps
e R
ate
Duration
T15 Lapse Rates by DurationPhase 1 vs. Phase 2
80th percentile
Median
Aggregate
20th percentile
Survey Responses vs. Experience Study
58
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Ass
um
ptio
nS
urv
ey
(Ph
ase
1)
Exp
eri
ence
Re
sults
(P
has
e 2
)
Ass
um
ptio
nS
urv
ey
(Ph
ase
1)
Exp
eri
ence
Re
sults
(P
has
e 2
)
Ass
um
ptio
nS
urv
ey
(Ph
ase
1)
Exp
eri
ence
Re
sults
(P
has
e 2
)
Ass
um
ptio
nS
urv
ey
(Ph
ase
1)
Exp
eri
ence
Re
sults
(P
has
e 2
)
Ass
um
ptio
nS
urv
ey
(Ph
ase
1)
Exp
eri
ence
Re
sults
(P
has
e 2
)
25 35 45 55 65
La
ps
e R
ate
Issue Age
T10 Jump to ARTDuration 10 Lapse Rates by Issue Age
Phase 1 vs. Phase 2
80th percentile
Median
Aggregate
20th percentile
Survey Responses vs. Experience Study
59
0%
100%
200%
300%
400%
500%
600%
700%
800%
900%
Ass
um
ptio
nS
urv
ey
(Pha
se 1
)
Exp
erie
nce
Res
ults
(P
hase
2)
Ass
um
ptio
nS
urv
ey
(Pha
se 1
)
Exp
erie
nce
Res
ults
(P
hase
2)
Ass
um
ptio
nS
urv
ey
(Pha
se 1
)
Exp
erie
nce
Res
ults
(P
hase
2)
Ass
um
ptio
nS
urv
ey
(Pha
se 1
)
Exp
erie
nce
Res
ults
(P
hase
2)
Ass
um
ptio
nS
urv
ey
(Pha
se 1
)
Exp
erie
nce
Res
ults
(P
hase
2)
11 12 13 14 15
Mo
rta
lity
De
teri
ora
tio
n(R
ela
tive
to
Du
rati
on
6-1
0)
Duration
T10 Jump to ARTMortality Deterioration by Duration
Phase 1 vs. Phase 2
80th percentile
Median
Aggregate
20th percentile
Survey Responses vs. Experience Study
60
0%
200%
400%
600%
800%
1000%
1200%
1400%
1600%
1800%A
ssum
ptio
nS
urve
y (P
hase
1)
Exp
erie
nce
Re
sults
(P
hase
2)
Ass
umpt
ion
Sur
vey
(Pha
se 1
)
Exp
erie
nce
Re
sults
(P
hase
2)
Ass
umpt
ion
Sur
vey
(Pha
se 1
)
Exp
erie
nce
Re
sults
(P
hase
2)
45 55 65
Mo
rta
lity
Det
erio
rati
on
(Re
lati
ve t
o D
ura
tio
n 6
-10)
Issue Age
T10 Duration 11Mortality Deterioration by Issue Age
Phase 1 vs. Phase 2
80th percentile
Median
Aggregate
20th percentile
SOA/RGA Post-Level Term StudyPredictive Model
61
Multivariate Lapse Rate Model – T10 Duration 10 Shock Lapse Model:
Generalized Linear Model (GLM) Target variable follows distribution in the exponential family Response variable = observed lapse count
Follows a Poisson distribution Benefits:
Elimination of possible bias from a uni-variate approach Systematic way of controlling lapse assumption complexity Transparent insight into true drivers of lapse rates Distribution of target variables
Predictive Model
62
Predictive Model – Model 1
Model Parameter
Intercept - -2.676 <2.0E-16
Issue Age Numerical 0.0552 <2.0E-16
(Issue Age)^2 Numerical -0.000316 <2.0E-16
Risk Class Categorical
Super-Pref NS 0 1.00 0 11.3% 82.6% 82.6% 100.1%
NS -0.06736 0.93 <2e-16 76.9% 69.1% 68.8% 100.4%
SM -0.01296 0.99 0.0339 11.8% 63.5% 63.5% 100.0%
Face Amount Categorical
<50K 0 1.00 0 1.2% 14.9% 17.9% 83.2%
50-100K 0.600 1.82 <2.0E-16 3.9% 61.8% 62.7% 98.5%
100K-250K 1.262 3.53 <2.0E-16 51.9% 67.5% 67.4% 100.1%
250K-1M 1.559 4.75 <2.0E-16 36.9% 74.4% 73.8% 100.8%
>1M 1.585 4.88 <2.0E-16 6.1% 80.7% 80.4% 100.4%
Premium Mode Categorical
Annual 0 1.00 0 22.9% 85.8% 85.3% 100.5%
Semi/Quarter -0.1365 0.87 <2.0E-16 24.5% 74.9% 75.1% 99.7%
Monthly/BiWeekly -0.3506 0.70 <2.0E-16 45.4% 56.9% 56.6% 100.5%
Other/Unknown -0.08481 0.92 <2.0E-16 7.2% 85.3% 84.8% 100.7%
Cross Term Mixed
Issue Age:Face Amt <50 0 0
Issue Age:Face Amt 50-100K -0.001288 0.3162
Issue Age:Face Amt 100-250K -0.01074 <2e-16
Issue Age:Face Amt 250K-1M -0.01653 <2e-16
Issue Age:Face Amt >1M -0.0172 <2e-16
Validation of ResultsData
Proportion
Actual Lapse Rate
Predicted Lapse Rate
Variable Type P-ValueCoefficientActual /
PredictedFactor
63
Predictive Model – Model 2
64
Model Parameter Premium Jump Categorical
Premium Jump 1.01-2x 0 1.00 -
Premium Jump 2.01-3x 1.135 3.11 <2.00E-16
Premium Jump 3.01-4x 1.492 4.45 <2.00E-16
Intercept - 3.246 2.03E-14 Premium Jump 4.01-5x 1.826 6.21 <2.00E-16
Issue Age Numerical 0.1621 <2.00E-16 Premium Jump 5.01-6x 2.082 8.02 <2.00E-16
(Issue Age)^2 Numerical -0.0006419 <2.00E-16 Premium Jump 6.01-7x 2.118 8.31 <2.00E-16
log(Issue Age) Numerical -2.7250000 <2.00E-16 Premium Jump 7.01-8x 2.176 8.81 <2.00E-16
Risk Class Categorical Premium Jump 8.01-10x 2.246 9.45 <2.00E-16
Super-Pref NS 0 1.00 - Premium Jump 10.01-12x 2.304 10.01 <2.00E-16
NS 0.03427 1.03 0.00 Premium Jump 12.01-16x 2.342 10.40 <2.00E-16
SM 0.1205 1.13 <2.00E-16 Premium Jump 16.01-20x 2.385 10.86 <2.00E-16
Face Amount Categorical Premium Jump 20.01x+ 2.356 10.55 <2.00E-16
<50K 0 1.00 - Cross Term Mixed
50-100K 0.3153 1.37 0.00 Issue Age:Premium Jump 1.01-2x 0 0
100K-250K 0.3437 1.41 <2.00E-16 Issue Age:Premium Jump 2.01-3x -0.02241 <2.00E-16
250K-1M 0.3652 1.44 <2.00E-16 Issue Age:Premium Jump 3.01-4x -0.02589 <2.00E-16
>1M 0.3645 1.44 <2.00E-16 Issue Age:Premium Jump 4.01-5x -0.03042 <2.00E-16
Premium Mode Categorical Issue Age:Premium Jump 5.01-6x -0.03383 <2.00E-16
Annual 0 1.00 - Issue Age:Premium Jump 6.01-7x -0.03381 <2.00E-16
Semi/Quarter -0.03244 0.97 0.00 Issue Age:Premium Jump 7.01-8x -0.03479 <2.00E-16
Monthly/BiWeekly -0.2755 0.76 <2.00E-16 Issue Age:Premium Jump 8.01-10x -0.03567 <2.00E-16
Other/Unknown 0.02057 1.02 0.06 Issue Age:Premium Jump 10.01-12x -0.03615 <2.00E-16
Issue Age:Premium Jump 12.01-16x -0.03665 <2.00E-16
Issue Age:Premium Jump 16.01-20x -0.03687 <2.00E-16
Issue Age:Premium Jump 20.01x+ -0.03601 <2.00E-16
Variable Type Coefficient Factor P-Value
Predictive Model – Model 1
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0-19 20-29 30-39 40-49 50-59 60-69 70+
Expo
sure
Laps
e Ra
te
Issue Age
Model Predicted vs. Actual Lapse Rate
Exposure
Predicted
Actual
65
Predictive Model – Model 2
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
0%
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20%
30%
40%
50%
60%
70%
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100%
Expo
sure
Laps
e Ra
te
Premium Jump
Model Predicted vs. Actual Lapse Rate
Exposure
Predicted
Actual
0
5,000
10,000
15,000
20,000
25,000
30,000
35,000
40,000
0%
10%
20%
30%
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100%
0-19 20-29 30-39 40-49 50-59 60-69 70+
Expo
sure
Laps
e Ra
te
Issue Age
Model Predicted vs. Actual Lapse Rate
Exposure
Predicted
Actual
66
67
Multivariate Lapse Rate Model - With Premium Jump10-Year term Duration 10 Lapse Rate
AssumptionsIssue Age 45Risk Class NSFace Amount 250K-1MPremium Mode AnnualPremium Jump Premium Jump 8.01-10x
Model VariablesBeta Coefficients
(a)Sample Value of xi
(b)
Sample Calculation
(c) = (a) * (b)VariablesIntercept 3.2460468406 1 3.2460
Issue Age 0.1620764522 45 7.2934
(Issue Age)^2 -0.0006419533 2025 (1.3000)
log(issue Age) -2.7246684047 4 (10.3719)
Risk Class
NS 0.0342716521 1 0.0343
Face Amount
250K-1M 0.3651595476 1 0.3652
Premium Mode
Annual 0.0000000000 1 -
Premium Jump
Premium Jump 8.01-10x 2.2456634786 1 2.2457
Cross Term
Issue Age:Premium Jump 8.01-10x -0.0356704787 45 (1.6052)
Results
Linear Predictor = Sum(Beta i * xi) = Sum (c) (0.0924)
Modeled Lapse Rate = eLinear Predictor 91.2%
“Jump to an ART Scale” continues to be the dominant post-level structure, although some are considering changes
Wide range of lapes and mortality assumptions are currently being used in the post-level period
Many companies have not implemented appropriate skewness assumptions for lapses based on past experience
2013 SOA Post-Level Term Survey Report
Key Takeaways
68
Lapse rates beyond the level period are largely driven by the level of the premium compared to the original level premium
Mortality in the post-level period is driven by the size of the shock lapse
Lapses are skewed towards the end of the last duration of the level period and the beginning of the first duration after the level period
Grace period can lead to excess mortality, especially at the higher shock lapse levels
Advanced analytics, such as predictive modeling, can be critical in understanding the correlations of the many drivers of post-level term experience
2014 SOA Post-Level Term Experience Report
Key Takeaways
69
Questions?
70
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