# 程序代写代做代考 Initial Communication of a Promulgation of Prescribed Mortality Improvement Rates (Subsection 2350) (210064)

Initial Communication of a Promulgation of Prescribed Mortality Improvement Rates (Subsection 2350) (210064)

Memorandum

To: All Fellows, Affiliates, Associates and Correspondents of the Canadian

Institute of Actuaries and Other Interested Parties

From: A. David Pelletier, Chair

Actuarial Standards Board

Date: September 23, 2010

Subject: Initial Communication of a Promulgation of Prescribed Mortality

Improvement Rates Referenced in the Standards of Practice for the

Valuation of Policy Liabilities: Life and Health (Accident and

Sickness) Insurance (Subsection 2350)

Comment deadline: December 1, 2010

Document 210064

INTRODUCTION

Subsection 2350 of the exposure draft released concurrently with this memorandum

(www.actuaries.ca/members/publications/2010/210063e.pdf) provides, with respect to

insurance mortality:

2350.06 If the inclusion of mortality improvement reduces the insurance

contract liabilities, then the resulting reduction would be no greater than

that developed using prescribed mortality improvement rates as

promulgated from time to time by the Actuarial Standards Board. If, at

an appropriate level of aggregation, the inclusion of mortality

improvement increases the insurance contract liabilities, then the

actuary’s assumption would include such improvement. The resulting

increase in insurance contract liabilities would be at least as great as

that developed using prescribed mortality improvement rates as

promulgated from time to time by the Actuarial Standards Board.

With respect to annuity mortality, subsection 2350 provides:

2350.11 The actuary’s assumption would include mortality improvement, the

effect of which is to increase the insurance contract liabilities, such that

the resulting increase would be at least as great as that developed using

prescribed mortality improvement rates as promulgated from time to

time by the Actuarial Standards Board.

The Actuarial Standards Board (ASB) proposes to promulgate the use of the mortality

improvement rates described in the appendix, effective October 15, 2011.

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This promulgation is described in Section D of the ASB’s Policy on Due Process for the

Adoption of Standards of Practice (“Due Process”).

RATIONALE

The proposed Standards of Practice outline a minimum policy liability basis with respect

to the mortality improvement assumption for both insurance and annuity business, and

reference prescribed mortality improvement rates.

The change to the promulgated rates is being proposed for the following reasons:

1. The proposed changes to paragraph 2350.06 of the Standards of Practice include a

new reference to promulgated mortality improvement rates with respect to the

valuation of life insurance business, thus creating the need for a set of

promulgated rates, and

2. The annuity mortality improvement rates are being updated to be consistent with

the new insurance promulgated mortality improvement rates that will be used for

insurance mortality.

A research paper is being concurrently released by the Canadian Institute of Actuaries

(CIA) Committee on Life Insurance Financial Reporting (CLIFR) that provides a

rationale for this proposed promulgation for insurance and annuity mortality secular

trends. The appendix outlines the process for determining the prescribed mortality

improvement rates under various circumstances.

CRITERIA FOR THE ADOPTION OF STANDARDS OF PRACTICE

The proposed mortality improvement rate promulgation meets the criteria set out in

Section B of the ASB’s Policy on Due Process for the Adoption of Standards of Practice.

1. It advances the public interest through the use of a consistent basis for

establishing mortality improvement rates for all business, along with an

appropriate margin for adverse deviations.

2. It provides for the appropriate application of professional judgement within a

reasonable range. The proposed mortality improvement rates are not the only

rates available for use, but rather establish a minimum valuation basis for the

business under consideration.

3. Use of the proposed table is practical for actuaries with relevant training.

4. The specified table is considered to be unambiguous.

PROPOSED EFFECTIVE DATE

It is proposed that the new mortality improvement tables would be used for valuations on

or after October 15, 2011. Early implementation is likely to be permitted, but comments

are welcome on this issue.

FUTURE TIMING

It is hoped that the promulgation of the final mortality improvement rates will occur in

late 2010 or early 2011.

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COMMENTS

Comments on the proposed changes are invited by December 1, 2010. Please send your

comments, preferably in an electronic form, to Chris Fievoli at chris.fievoli@actuaries.ca,

with copies to B. Dale Mathews at dale_mathews@manulife.com and Edward Gibson at

edward.gibson@empire.ca. No other specific forums for submitting comments are

planned.

ADP

mailto:chris.fievoli@actuaries.ca�

mailto:dale_mathews@manulife.com�

mailto:edward.gibson@empire.ca�

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APPENDIX: PRESCRIBED MORTALITY IMPROVEMENT RATES

This appendix describes the proposed prescribed mortality improvement rates, for use in

determining minimum valuation assumptions for future mortality improvement. As a

support to this updated promulgation, the actuary is referred to the research paper on

mortality improvement (www.actuaries.ca/members/publications/2010/210065e.pdf,

published in September 2010).

Prescribed Mortality Improvement Rates

The prescribed rates are developed from a set of base mortality improvement rates and

two mortality improvement scenarios as described below.

Base Mortality Improvement Rates

The base mortality improvement rates should apply for both life insurance and annuities

and should vary by attained age as follows: 2% from age 0 to 40, decreasing linearly

from 2% to 1% from age 40 to 60, 1% from age 60 to 90, and decreasing linearly from

1% to 0% from age 90 to 100 as illustrated in Table 1. The base mortality improvement

rates are the same for both females and males, and for both smokers and non-smokers.

Development of Prescribed Mortality Improvement Rates (Minimum Valuation

Assumption)

In order to determine the minimum valuation assumption the actuary should perform two

valuations using the following mortality improvement scenarios. The first scenario would

be expected to apply in situations where the reflection of mortality improvement

decreases liabilities and the second scenario where the effect is to increase liabilities.

1. Mortality improvement would be projected for 25 years only from the valuation

date using 50% of the base mortality improvement rates as described above. After

25 years no further mortality improvement would be reflected.

2. Mortality improvement would be projected for all future years using 150% of the

base mortality improvement rates as described above for 25 years, and 100% of

the base mortality improvement rates as described above thereafter.

The prescribed mortality improvement rates should be the rates from the mortality

improvement scenario producing the higher liability, determined at an appropriate level

of aggregation. It would be inappropriate to aggregate annuities with life insurance

business.

The actuary would use appropriate judgement in the determination of a best estimate

assumption for future mortality improvement. The provision for adverse deviations for

mortality improvement risk would then be measured as the excess of the reported policy

liability over the policy liability, inclusive of the reflection of the k/ex (insurance) or

percentage of mortality rate (annuities) margin, resulting from the application of the

actuary’s best estimate assumption for mortality improvement.

Calculation Example: Life Insurance, First Mortality Improvement Scenario

The following illustrates the calculation of the total mortality rate, including margins, for

business in which the first mortality improvement scenario produces the higher liability at

an appropriate level of aggregation.

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For life insurance, the margin for adverse deviation for the mortality rate per 1,000 is

k/ex.

The total mortality rates are calculated as follows:

qx(pr) = qx + k/ex

qx+1(pr) = qx+1 * (1-MImpx+1 * 0.5) 1 + k/ex+1

qx+2(pr) = qx+2 * (1-MImpx+2 * 0.5) 2 + k/ex+2

…

qx+25(pr) = qx+25 * (1-MImpx+25 * 0.5) 25 + k/ex+25

…

qx+n(pr) = qx+n * (1-MImpx+n * 0.5)25 + k/ex+n

where:

qx+t(pr) is the mortality rate, which includes prescribed mortality

improvement and margins, at age x+t,

qx+t is the best estimate mortality rate, before mortality improvement, at

age x+t,

ex+t is the curtate expectation of life at age x+t,

MImpx+t is the base mortality improvement rate at age x+t, and

n is greater than 25.

Calculation Example: Life Insurance, Second Mortality Improvement Scenario

The following illustrates the calculation of the total mortality rate, including margins, for

business in which the second mortality improvement scenario produces the higher

liability at an appropriate level of aggregation.

For life insurance, the margin for adverse deviation for the mortality rate per 1,000 is

k/ex.

The total mortality rates are calculated as follows:

qx(pr) = qx – k/ex

qx+1(pr) = qx+1 * (1-MImpx+1 * 1.5) 1 – k/ex+1

qx+2(pr) = qx+2 * (1-MImpx+2 * 1.5) 2 – k/ex+2

…

qx+25(pr) = qx+25 * (1-MImpx+25 * 1.5) 25 – k/ex+25

…

qx+n(pr) = qx+n * (1-MImpx+n * 1.5)25* (1-MImpx+n * 1.0)(n-25) – k/ex+n

where:

qx+t(pr) is the mortality rate, which includes prescribed mortality

improvement and margins, at age x+t,

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qx+t is the best estimate mortality rate, before mortality improvement, at

age x+t,

ex+t is the curtate expectation of life at age x+t,

MImpx+t is the base mortality improvement rate at age x+t, and

n is greater than 25.

Calculation Example: Annuities

The following illustrates the calculation of the total mortality rate, including margins, for

annuity business in which the second mortality improvement scenario produces the

higher liability at an appropriate level of aggregation.

For annuities, the margin for adverse deviation, Mort MFAD, is a percentage of the

mortality rate.

The total mortality rates are calculated as follows:

qx(pr) = qx * (1-Mort MFAD)

qx+1(pr) = qx+1 * (1-Mort MFAD) * (1-MImpx+1 * 1.5) 1

qx+2(pr) = qx+2 * (1-Mort MFAD) * (1-MImpx+2 * 1.5) 2

…

qx+25(pr) = qx+25 * (1-Mort MFAD)*(1-MImpx+25 * 1.5) 25

…

qx+n(pr) = qx+n * (1-Mort MFAD)*(1-MImpx+n * 1.5)25* (1-MImpx+n * 1.0)(n-25)

where:

qx+t(pr) is the mortality rate, which includes prescribed mortality

improvement and margins, at age x+t,

qx+t is the best estimate mortality rate, before mortality improvement, at

age x+t,

MImpx+t is the base mortality improvement rate at age x+t, and

n is greater than 25.

Mortality Improvement Rates for Out-of-Canada Business

For markets other than Canada, the actuary would select appropriate mortality

improvement rates (inclusive of margin) for both life insurance and annuities. These

improvement rates would produce a total liability for each of life insurance and annuities

that is at least as large as what would be produced using the prescribed rates used in

Canada, unless experience indicates otherwise.

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Table 1: Proposed Base Mortality Improvement Rates

(applies to both females and males, and to both smokers and non-smokers)

Attained Base Attained Base Attained Base

Age Rates Age Rates Age Rates

0 to 40 2.00%

41 1.95% 51 1.45% 91 0.90%

42 1.90% 52 1.40% 92 0.80%

43 1.85% 53 1.35% 93 0.70%

44 1.80% 54 1.30% 94 0.60%

45 1.75% 55 1.25% 95 0.50%

46 1.70% 56 1.20% 96 0.40%

47 1.65% 57 1.15% 97 0.30%

48 1.60% 58 1.10% 98 0.20%

49 1.55% 59 1.05% 99 0.10%

50 1.50% 60 to 90 1.00% 100+ 0.00%