2015.Fall Q12 Old Version

This is the premium liability duration calculation from the 2016 version of the premium liability paper. Back to CIA.PrLiabs.

• The is the PVfctr calculation for the pre-2016 version of the premium liability reading. It's included for completeness, but you don't really need to know how to do it.
• OBSERVE:
  • The final answer is the sum of col (6): PVfctr(@3%) = 0.9533
  • Columns (1) & (3) are always the same
    • The derivation of APD (Avg Payment Date) in col (1) is explained well in Appendix E, Sheet 4, footnotes (10) & (11) of the old version of the premium liabilities paper.
    • Note that you may not need to know to derive column (1)
      • It should be enough to remember that it starts with 0.2929 and increases by 1 for each row.
    • The first row of col (3) equals 1.0 - (1) and increases by 1 for each row.
  • Calculation of Interp CumPd, column (4) and Incr Pd, col(5) are explained below the table.

APD	@3% PVfctr	Age @yr-end	Interp CumPd	IncrPd	time 0 PVfctr
(1)	(2)=1/1.03^(1)	(3)	(4)	(5)	(6)=(2)x(5)
0.2929	0.9914	0.7071	30.2%	30.2%	0.2992
1.2929	0.9625	1.7071	55.2%	25.0%	0.2406
2.2929	0.9345	2.7071	80.2%	25.0%	0.2336
3.2929	0.9073	3.7071	100.0%	19.8%	0.1798
					0.9533

• IncrPd is just the difference between successive rows of col (4) (IncrPd = Incremental Paid Loss)
• Interp CumPd is calculated by interpolation based on the accident year payment pattern (Interp CumPd = Interpolated Cumulative Paid Loss)
  • It's helpful to rewrite the accident year payment pattern table using age(yr) @ yr-end instead of months:

age(yrs) @ yr-end	CumPd
0.5	25%
1.5	50%
2.5	75%
3.5	100%

• Then the first row of col (4) is interpolated in the usual way:
  • 30.2% = (0.7071 - 0.5) / (1.5 - 0.5) * (50% - 25%) + 25%
• Similarly for the second and subsequent rows of col (4):
  • 55.2% = (1.7071 - 1.5) / (2.5 - 1.5) * (75% - 50%) + 50%

• Unfortunately you now have to do this all over again for the other discount rate of 2.5%.   :-(
• THE END. FINALLY!

Back to CIA.PrLiabs.