A.1 Valuation Methodologies

Question 1

Reserve Methodologies:

• Net Level Premium
• Modified Reserve Method
• Full Preliminary Term Method
• CRVM

Answer 1

Net Level Premium
- reserves net premium = % of GPs
- no explicit recognition of expenses or lapses
- largest of the methods
V = PVFB - PVNP
PVFB = A (x+t)
PVNP = PVFB / a(x)
GP ratio = GP(t) / GP(0)

Modified reserve method

• NLP that also includes an EA to lower the reserves
• EA = a formula that reflects acquisition costs from year 1
• EA is amortized over the premium paying period
• mod reserves = NLP reserve - Unamortized EA
• the amortized expenses get added to the premiums
• higher premium = lower reserves than NLP
• the actual EA used depends on the method: CRVM vs FPT

Full Preliminary Term FPT
EA = PVFB / a(x+1) - c(x)
= NP(1) - c(x)
c(x) = v * q(x) * DB = year 1 COI
- for t = 0; NP = c(x)
- for t >= 1; NP = PVFB(1) / a(x+1) * GPratio
-at the end of yr 1, the FPT reserve = 0 because NP(1) = NP(0)
- the first year NP is exactly enough to pay the mortality cost for the first year, so reserves are completely exhausted at EOY 1

CRVM method:
- similar to FPT but limits the EA that can be used
- CRVM EA is lesser of:
a. EA under the FPT
b. EA under FPT assuming a 20 pay WL contract
- when the 20 pay EA limitation applies; CRVM reserves will be >0 at EOY 1
- smallest reserve allowed by SVL
- usually same as FPT unless contract can be paid more quickly than 20 years
- if premium pay period < 20 years, CRVM reserves will be higher than FPT
…additional rules for (b - 20 pay):
1. if non-level DBs, calculate the 20 pay EA using level DBs = average of years 2-10
2. if EA is negative, floor at 0

Question 2

Continuous reserves

semi, full, and discounted

Answer 2

pg 37

Question 3

Immediate payment of claims reserves IPCR

Answer 3

• DBs are paid at time of death rather than at the EOY
• if payments are made without interest:
  IPCR = i / 3 * PVFB
• if IR is paid
  IPCR = i / 2 * PVFB