Lapse and Mortality of Post-Level Period Term Plans

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

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12,000

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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%

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6 7 8 9 10 11 12 13+

Level Period Tail Period

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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

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

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Lapse Rate Median Lapse Rate Number of Lapses (right axis)


Shock Lapse Experience

T15 By Duration

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Lapse Rate Median Lapse Rate Number of Lapses (right axis)



T10 By Premium Jump Ratio

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Duration 11/10 Premium Jump RatioDuration 10 Lapse Rate Duration 11 Lapse Rate Duration 12 Lapse Rate


T10 By Duration & Premium Jump

11




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


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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



T10 By Duration and Issue Age

13


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Issue Age

Duration 6-9 Duration 10 Duration 11 Duration 12+



T10 By Premium Jump and Issue age – duration 10

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T10 By Duration & Face Amount Band

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< $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




T10 By Premium Jump and Face Amount Band – duration 10

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T10 By Duration & Gender

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Male Female

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T10 By Duration & Risk Class

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Super-Preferred Preferred Non-Preferred Undiff Preferred Non-Preferred Undiff

Non-Smoker Smoker Unk/Agg

Risk Class




T10 By Duration & Premium Payment Mode

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Annual Semi-Annual Quarterly Monthly

Premium Payment Mode



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



Mortality Experience (Jump to ART)

T10 By Duration

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A/E Mortality Median A/E Mortality Number of Deaths (right axis)


Mortality Experience

T15 By Duration

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A/E Mortality Median AE Rate Number of Deaths (right axis)



T10 Duration 11 Mortality by Premium Jump

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Duration 11/10 Premium Jump Ratio

Relative Mortality Ratio Number of Deaths (right axis)



T10 Duration 11+ Mortality by Issue Age

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Duration 6-10 Duration 11+ Post-Level Relative to Dur 6-10



T10 Duration 11+ Mortality by Face Amount Band

26


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< $50,000 $50,000 -$99,999

$100,000 -$249,999

$250,000 -$999,999

$1,000,000 +

Face Amount Band



Mortality Study Experience Results – Jump to ART

T10 Duration 11+ Mortality by Gender

27


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Male FemaleGender



Mortality Study Experience Results – Jump to ART

T10 Duration 11+ Mortality by Risk Class

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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



T10 Duration 11 Mortality by Duration 10 Shock Lapse

by Company

29


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Duration 10 Shock Lapse

>=35 claims

<35 claims

Expon. ()


Practical Applications

30


Skewness of Lapses

31


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• 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


35


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


Total 139,952 1.20 167.9 59,928 139,964 1.28 179.84 59,916



DeathsDuration

Deaths Deaths



36


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


Total 109,988 1.20 131.9 89,892 110,006 1.36 149.89 89,874



DeathsDuration

Deaths Deaths


Grace Period Subsidy – Example90% Lapse Rate; 200% Anti-Selection

37


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


Total 109,988 1.31 143.9 89,892 110,006 1.45 159.86 89,874



DeathsDuration

Deaths Deaths


0

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Months since start of Duration 11

2008 VBT Mortality Ratios Number of Deaths (right axis)

Mortality Experience

Duration 11 Mortality by Month

38



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

http://www.soa.org/Files/Research/Projects/research-shock-lapse-survey-report.pdf


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



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



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



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



Lapse Assumptions

Annual and cumulative lapse assumptions by duration, 10-year term


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Lapse Assumptions

Duration 10 lapse assumptions by issue age, 10-year term


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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


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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



The same pricing cell that was used in the Lapse Assumptions charts is used in this section


Factors impacting mortality deterioration assumptions


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



Post-Level Mortality Methodology

Dukes-MacDonald (or derivatives) and Flat Multiple are the primary assumptions used in developing mortality after the shock lapse


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



Annual mortality deterioration multiple, 10 year term


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2009 Median



Post-Level Mortality Assumptions vs. Premium Jump

Mortality deterioration assumptions do not differ dramatically by premium jump, inconsistent with experience


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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


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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



SOA/RGA Post-Level Term StudyAssumptions vs. Experience

55

Survey Responses vs. Experience Study

56

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T10 Jump to ARTLapse Rates by Duration

Phase 1 vs. Phase 2

80th percentile

Median

Aggregate

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57

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T15 Lapse Rates by DurationPhase 1 vs. Phase 2

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25 35 45 55 65

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T10 Jump to ARTDuration 10 Lapse Rates by Issue Age

Phase 1 vs. Phase 2

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Median

Aggregate

20th percentile


59

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T10 Jump to ARTMortality Deterioration by Duration

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T10 Duration 11Mortality Deterioration by Issue Age

Phase 1 vs. Phase 2

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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


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


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Model Predicted vs. Actual Lapse Rate

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65


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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

Documents

Lapse and Mortality of Post-Level Period Term Plans