Age Last vs Age Nearest

[mdr237]

I have some questions regarding the application of Age Nearest tables, and I was hoping to get some opinions on a simple example I put together for a Single Life Immediate Annuity. The actuarial system we are using seems to be doing an Age Last methodology, even if the baseline table was meant to be Age Nearest.

The spreadsheet should be pretty easy to follow. You can PM me if you want a walk through. Is my understanding of Age Nearest Birthday correct (method 2 in workbook)?

Follow up: Method 3-6 are ways to approximate the age nearest calculation in a system using Age Last methodology. If anyone else has a clever way to approximate ANB using an ALB system, please let me know.

Note: In order to reduce file size, I had to paste values for all formulas beyond row 30. You can fill down row 29 if you want to see it with all the formulas live.

[mdr237]

I have seen a lot of people viewed the post, but no responses. I guess it was a lot to ask people to look at a spreadsheet. My question boils down to the following:

If the Age Nearest table has a qx at 60 of .53%, is that .53% the probability of dying between age 59.5 and 60.5 or age 60 and 61?

[GargoyleWaiting]

I have seen a lot of people viewed the post, but no responses. I guess it was a lot to ask people to look at a spreadsheet. My question boils down to the following:

If the Age Nearest table has a qx at 60 of .53%, is that .53% the probability of dying between age 59.5 and 60.5 or age 60 and 61?

It should be the first one, as the person will be in the "age 60 nearest" bucket when they are between 59.5 and 60.5.

[JMO]

I have seen a lot of people viewed the post, but no responses.
If you still don't have the answer you need, try moving the thread to Life instead of General Actuarial. Go to the first post and click on "thread tools."

[Steve Grondin]

It should be the first one, as the person will be in the "age 60 nearest" bucket when they are between 59.5 and 60.5.
Well, in one sense it is between ages 59.5 and 61.5. Because most studies are based on policy years. ANear 60 means the person is 60 on an age near basis at the beginning of the policy year. So it could cover a person whose age is 59.5 at the beginning of the policy year to 60.5 at the end. On the other extreme it can also cover a person 60.5 at the beginning and 61.5 at the end.

There is a common ANB to ALB conversion formula that escapes me right now. I'm sure I've even posted it here before. It might be easier to search for the introduction of the 1980 CSO table in SOA Transactions (IIRC it was in 1981). It is in plenty of other places as well.

[Double High C]

I agree with Charles Grodin.

[OldGuy]

The answer is "yes". Since the mortality tables you are using have been smoothed and modified from the observed data, the inherent error between using one or the other age definition is probably less than the observed difference between the table mortality and the actual mortality.

Just be consistent.

[mdr237]

Thanks for the responses. A few follow up questions about how this is applied in practice.

1) When you calculate ages for valuation, does your system use exact ages (60 yrs and 2 months) or rounded ages (60 yrs even) at valuation date.

2) Assuming rounded ages for number 1, would your system apply the age 60 qx for 6 months of the projection or for 12 months? If you use exact ages, do you apply the age 60 qx for 4 months or 10 months?

3) I have seen the SOA guidance for the Age Nearest to Age Last mortality table conversion (link below for anyone interested). If you don't change the qx for a full year until the age 61 anniversary (what I consider to be age last methodology), do you convert the SOA tables from Age Nearest to Age Last?

4) If you do a conversion in number 3, do you do anything for Mortality Improvement factors and Select / Ultimate rates?

Thanks.

http://www.google.com/url?sa=t&rct=j&q=1980%20cso%20and%201980%20cet%20mortality%20tabl es%20on%20an%20age%20last%20birthday%20basis&source=web&cd=1&ved=0CFkQFjAA&url=http%3A%2F%2Fwww.soa.org%2Flibrary%2Fresearch% 2Ftransactions-of-society-of-actuaries%2F1981%2Fjanuary%2Ftsa81v3324.aspx&ei=ivnZT9GoFYqi8gSo0onsBQ&usg=AFQjCNErJex8S7oRnrc_XPOC1wyKDXtmZQ

[JMO]

Thanks for the responses. A few follow up questions about how this is applied in practice.

1) When you calculate ages for valuation, does your system use exact ages (60 yrs and 2 months) or rounded ages (60 yrs even) at valuation date.
At a former employer, the annuities in payout status were calculated using exact ages. For everything else, age was issue age (ANB or ALB as applicable) plus policy duration expressed as an integer ("rounded" if that is the term down). This sort of rounded approach is almost universal - the exact age calculation seems to be the exception.

2) Assuming rounded ages for number 1, would your system apply the age 60 qx for 6 months of the projection or for 12 months? If you use exact ages, do you apply the age 60 qx for 4 months or 10 months?
Throughout the policy year, the age remains unchanged. It goes up 1 whole year on the anniversary.

3) I have seen the SOA guidance for the Age Nearest to Age Last mortality table conversion (link below for anyone interested). If you don't change the qx for a full year until the age 61 anniversary (what I consider to be age last methodology), do you convert the SOA tables from Age Nearest to Age Last?
Use of ANB or ALB is based on which calculation was used for the issue age. Once a policy is issued, you don't switch back and forth.
At one time, all companies used ANB. Then, some began switching over to ALB. You just need to know which one is in use, and follow it throughout the calculation.

4) If you do a conversion in number 3, do you do anything for Mortality Improvement factors and Select / Ultimate rates?
n/a

Thanks.
np