tim rozar fsa, maaa, cera derek kueker fsa lapse and mortality of post-level period term plans...
TRANSCRIPT
![Page 1: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/1.jpg)
Tim Rozar FSA, MAAA, CERA
Derek Kueker FSA
Lapse and Mortality of Post-Level Period Term Plans
International Actuarial Association
![Page 2: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/2.jpg)
Background
2
![Page 3: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/3.jpg)
-
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
![Page 4: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/4.jpg)
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!
![Page 5: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/5.jpg)
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
![Page 6: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/6.jpg)
SOA/RGA Post-Level Term StudyLapse Study Experience Results
6
![Page 7: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/7.jpg)
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
![Page 8: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/8.jpg)
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)
![Page 9: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/9.jpg)
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)
![Page 10: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/10.jpg)
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
![Page 11: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/11.jpg)
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
![Page 12: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/12.jpg)
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
![Page 13: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/13.jpg)
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+
![Page 14: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/14.jpg)
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
![Page 15: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/15.jpg)
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+
![Page 16: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/16.jpg)
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
![Page 17: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/17.jpg)
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+
![Page 18: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/18.jpg)
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+
![Page 19: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/19.jpg)
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+
![Page 20: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/20.jpg)
SOA/RGA Post-Level Term StudyMortality Study Experience Results
20
![Page 21: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/21.jpg)
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
![Page 22: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/22.jpg)
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)
![Page 23: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/23.jpg)
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)
![Page 24: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/24.jpg)
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)
![Page 25: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/25.jpg)
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
![Page 26: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/26.jpg)
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
![Page 27: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/27.jpg)
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
![Page 28: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/28.jpg)
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
![Page 29: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/29.jpg)
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. ()
![Page 30: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/30.jpg)
Practical Applications
30
![Page 31: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/31.jpg)
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
![Page 32: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/32.jpg)
• 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
![Page 33: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/33.jpg)
• 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
![Page 34: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/34.jpg)
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
![Page 35: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/35.jpg)
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
![Page 36: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/36.jpg)
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
![Page 37: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/37.jpg)
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
![Page 38: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/38.jpg)
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
![Page 39: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/39.jpg)
SOA/RGA Post-Level Term StudyAssumption Survey Results
39
![Page 40: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/40.jpg)
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
![Page 41: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/41.jpg)
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
![Page 42: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/42.jpg)
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
![Page 43: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/43.jpg)
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
![Page 44: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/44.jpg)
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
![Page 45: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/45.jpg)
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%
60%
70%
80%
90%
100%
10 11 12 13 14 15
Cu
mu
lati
ve
Lap
se R
ate
Duration
80thpercentileMedian
20thpercentile
![Page 46: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/46.jpg)
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
![Page 47: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/47.jpg)
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
![Page 48: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/48.jpg)
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
![Page 49: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/49.jpg)
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
![Page 50: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/50.jpg)
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
![Page 51: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/51.jpg)
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
![Page 52: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/52.jpg)
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
![Page 53: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/53.jpg)
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
![Page 54: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/54.jpg)
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
![Page 55: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/55.jpg)
SOA/RGA Post-Level Term StudyAssumptions vs. Experience
55
![Page 56: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/56.jpg)
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
![Page 57: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/57.jpg)
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
![Page 58: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/58.jpg)
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
![Page 59: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/59.jpg)
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
![Page 60: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/60.jpg)
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
![Page 61: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/61.jpg)
SOA/RGA Post-Level Term StudyPredictive Model
61
![Page 62: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/62.jpg)
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
![Page 63: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/63.jpg)
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
![Page 64: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/64.jpg)
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
![Page 65: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/65.jpg)
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
![Page 66: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/66.jpg)
Predictive Model – Model 2
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
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%
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
66
![Page 67: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/67.jpg)
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%
![Page 68: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/68.jpg)
“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
![Page 69: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/69.jpg)
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
![Page 70: Tim Rozar FSA, MAAA, CERA Derek Kueker FSA Lapse and Mortality of Post-Level Period Term Plans International Actuarial Association](https://reader030.vdocuments.mx/reader030/viewer/2022032517/56649cc25503460f9498a5d2/html5/thumbnails/70.jpg)
Questions?
70