Discount Unwind -- Concept behind it and catering for mid quarter discount rates

Having a hard time trying to figure out the Premium Liabilities change of basis table currently updating for valn report...

Courtesy of BobA...

Xuan

how does discount unwinding work

4:11 PM    BobA

if theres a claim in 5 years time worth $100 undiscounted, then at 4% pa then itll b worth say $80 discounted (roughly)

at t = 0

then

at t = 1 (ie. this time next year)

itll b worth $100 undiscounted at 4% pa = $84

coz its only 4 years away now

so the 4% increase over the year due to shorter timeframe is the discount unwind

at t = 2 itll b $88, etc.

so it constantly unwinds until payment date at t = 5

and by then all the discounting has unwound, so $100 = undiscounted = discounted

4:14 PM   Xuan

mm....

so...

i have this set of discount rates

4:14 PM   BobA

yep

what timeframe r u unwinding it over?

4:15 PM   Xuan

gimme a sec, lemme find it

\SUNRollforward1109_bal.xlsx, inputs tab, I03

so what i dont understand is that MC/TL seem to use one quarter more than they need to

and take the average of two,

so to calculate the discount unwind

between 1109 and now

they dont use time 0 and time 1's discount rate

they use time 1 and time 2

and then average time 1 and time 2 discount rate

and use that rate to unwind the PL discounting

4:22 PM   Xuan

hmmm

i think i get it now

it's just to cater for this dodgy thing how they have all the discount rates as mid quarter

4:24 PM   BobA

i think we do something similar

doz the rates r in the middle of the period.. so the avg of the next 2 periods (t = 1 & t = 2) is actually (0.5 + 1.5) / 2

4:26 PM  Xuan

which is one year since prev valn...

For mid quarter discount rates adopted, here’s how it works:

Say now is 1112, and prev valn is 1109.

Using 1109 discount rates adopted, Since time 0 (t0) stands for 0.125 since 1109 and time 1 (t1) = 0.375 since 1109 then average of that is:

(0.125+0.375)/2 = 0.25, which gives us one full quarter since 1109 --> i.e. brings us to end of quarter 1112.

So for two quarters since prev valn, say now is 1203, prev valn is 1109, we want:

use 1109 discount rates adopted,

t1 = 0.375yrs since 1109

t2 = 0.625yrs since 1109,

avg is (0.375 + 0.625)/2 = 0.5, which brings us one full half year since 1109 to end-of-quarter 1203 present value.

So we can then use a table of discount rates such as below, and take {[1/(avg of t1 & t2 rate) +1 ]^0.5 -1} multiplied by the PL from last time (1109, at 1109$) to see the impact of the discount unwinding.

Discount rates: most recent forward and neutral

(inputs tab, I03)

	Pay qtr	0	1	2	3	4	5	6	7	8	9	10	11
Time or Term		0.125	0.375	0.625	0.875	1.125	1.375	1.625	1.875	2.125	2.375	2.625	2.875
1112 Actual
	Yield	4.71%	4.72%	4.74%	4.77%	4.80%	4.83%	4.84%	4.84%	4.85%	4.85%	4.86%	4.87%
	Factor	0.994257587	0.982858475	0.97147187	0.9600265	0.94861291	0.93723311	0.926057977	0.915142276	0.904334485	0.893633824	0.8829526	0.872272563
1112 neutral from 1106
	Yield	4.71%	4.72%	4.74%	4.77%	4.80%	4.83%	4.84%	4.84%	4.85%	4.85%	4.86%	4.87%
	Factor	0.994257587	0.982858475	0.97147187	0.9600265	0.94861291	0.93723311	0.926057977	0.915142276	0.904334485	0.893633824	0.8829526	0.872272563
1112 neutral from 1012
	Yield	5.24%	5.32%	5.40%	5.48%	5.51%	5.51%		5.53%	5.54%	5.55%	5.56%	5.58%
	Factor	0.993637918	0.980743966	0.96766241	0.9544057	0.94143812	0.92890983	#VALUE!	0.903969773	0.891671187	0.879547438	0.867499952	0.855530143