Projection of RP2000 Mortality

[Rolf Trautmann]

We are attempting to duplicate the 2007 Mortality tables, which were published in the "Updated Mortality Tables for Determining Current Liability" regulations around 2/2/2007. We are matching qx values for most ages but are slightly off for ages between 41 and 49 and between 71 and 79, which is where the Non-annuitant and Annuitant tables are smoothed. Has anyone been able to match these factors?

An example may help:

Male age 76

qx from published table =.034523

qx per our calculation below =.034489

Non-annuitant qx (using smoothed transition since no actual non-annuitant qx at age 76)

.030710 = .009922 + (.064368 - .009922) x 21/55 (smooth transition discussed in proposed regs on Mortality Tables dated 5/29/2007)

(.064368 is age 80 annuitant qx and .009922 is age 70 non-annuitant qx from published table)

Annuitant qx

.042169 from published table

Non-annuitant qx (projected to 2007)

.022520 = .030710 x (1-.014)^22 (.014 is from projection Scale AA for 76 year old male, 22 years from 2000 to 2007 plus 15)

Annuitant qx (projected to 2007)

.034615 = .042169 x (1-.014)^14 (.014 is from projection Scale AA for 76 year old male, 14 years from 2000 to 2007 plus 7)

Calculated qx formula

.034489 = .022520 x (1-.9896) + .034615 x .9896

(98.96% of those age 76 are annuitants using weighting factors from "Updated Mortality Tables for Determining Current Liability" proposed regulations on 12/2/2005)

Any help would be greatly appreciated.

[Guest Doug Goelz]

We are attempting to duplicate the 2007 Mortality tables, which were published in the "Updated Mortality Tables for Determining Current Liability" regulations around 2/2/2007. We are matching qx values for most ages but are slightly off for ages between 41 and 49 and between 71 and 79, which is where the Non-annuitant and Annuitant tables are smoothed. Has anyone been able to match these factors?

An example may help:

Male age 76

qx from published table =.034523

qx per our calculation below =.034489

Non-annuitant qx (using smoothed transition since no actual non-annuitant qx at age 76)

.030710 = .009922 + (.064368 - .009922) x 21/55 (smooth transition discussed in proposed regs on Mortality Tables dated 5/29/2007)

(.064368 is age 80 annuitant qx and .009922 is age 70 non-annuitant qx from published table)

Annuitant qx

.042169 from published table

Non-annuitant qx (projected to 2007)

.022520 = .030710 x (1-.014)^22 (.014 is from projection Scale AA for 76 year old male, 22 years from 2000 to 2007 plus 15)

Annuitant qx (projected to 2007)

.034615 = .042169 x (1-.014)^14 (.014 is from projection Scale AA for 76 year old male, 14 years from 2000 to 2007 plus 7)

Calculated qx formula

.034489 = .022520 x (1-.9896) + .034615 x .9896

(98.96% of those age 76 are annuitants using weighting factors from "Updated Mortality Tables for Determining Current Liability" proposed regulations on 12/2/2005)

Any help would be greatly appreciated.

RP2000_Table_Notes___2007.xls

[Guest Doug Goelz]

Sorry, I also meant to upload this file as well.

Smoothing_Note_on_CL_Mortality.doc

[Rolf Trautmann]

Doug,

Thanks for the information. We realized that we were smoothing the 2000 rates instead of the projection year rates. With that change we match the published values.

Thanks,

Rolf