Valuation of Life Insurance Liabilities - Chapter 4 - VALUATION OF INTEREST SENSITIVE LIFE PRODUCTS

overview

policies develop CSV based on retrospective accum of (flex) prems less mort and expense charges at a declared or indexed rate
this makes them not compatible w/ trad valn procedures

Flexible Premium UL

premiums less expense charges credited to fund
int credits credited to fund
mort and expense charges deducted from fund
CSV = fund value - SC
Minimum Reserves
- 1983 - NAIC rules - to make UL work w/ trad valn formulas
  - GMP - guaranteed maturity premium - level gross premium that provides for an endowment at the latest possible maturity date
    - calculated at issue using policy guarantees for expesne and mortality charges adn int credits
  - GMF - guaranteed maturity fund - calced as of issued date assuming GMPs are paid
  - r = min(actual fund value / GMF, 1)
  - policy fund projected forward using max(GMF, Actual Fund Value) assuming GMPs paid
    - this produces guaranteed DBs and Guar Maturity benefit for valn purposes
    - PV of these benefits calced on the valn basis
  - NL reserve = r*(PV projected DB - PV projected GMPs) (assuming GMPs paid from issue (not valn))
  - CRVM reserve = NL Reserve - r*unamort CRVM allowance for plan of ins generated at issue on guar basis assuming GMPs paid
- Simplified: Model Reg assumes all UL plans are permanent plans @ issue
- "r" factor to measure if policy is "on track" as permanent plan
- if CV > Vx, excess held elsewhere on statement (was 8G)
Alternative Minimum Reserves (AMR)
- may be req'd if GMP < valn net premiums
- if req'd - max(a,b)
  - a - reserve calculated using reserve method, mort basis and valn i actually used for policy
  - b - reserve calced usnig reserve method actually used, but using min stds of mort and i allowable for V_def(x) & replacing valn net prem w/ GMP
- valn net prem (VNP) not explicity defined in model reg
- most cos interpret VNP = P_NL + EA/adue
- Features that lead to AMR
  - no load products if guar COI and i similar to valn basis
  - Guar COIs < valn mort (esp if i_guar = i_valn adn low/no fe loads)
  - i_guar > i_valn
  - any product features that lower GMPs
Examples
- [t]V_NL = r*(PVFB(t) - P_NL*adue(x+t)
  - PVFB(t) - PV based on project of policy funds using policy guarantees where initial value is max(actual fund, GMF)
- for CRVM - [t]V_NL reduced by r*EA_CRVM*adue(x+t)/adue(x)
- for monthly pay policies, DB incr monthly, for PV, use avg annual DB and continuous commutatoin functions

Fixed Prem UL

key difference for fixed vs flexible premium
- GMP = gross prem
- EA adn rate of amort determined by plan of ins guaranteeed at issue
- r = 1
to calc CRVM
- project future benefits on guar basis - take secondary guar into acct
- value benefits using valn mort and int
- subtract PV cuture CRVM net prems for plan of ins guar at issue

Secondary Guarantees

provides teh PO a guar set of CVs, DB and/or mat benefits regardless of fund performance
1995 valn model reg - if secondary guarantee keeps policy in force 5+ years, reserves = form implied by secondary guar

Off Anniversary Reserves

UL Model Reg defined terminal , but not off-anniv
issues
- r - should it be as of valn date, prior or next anniv
- how to calc GMF on valn date if r is calced on valn date
- use first priciples or mean/mid-terminal/interpolated reserve
generally considered appropriate to calc r as of valn date
use annual GMPs or GMPs consistent w/ planned prem mode? - be consistent w/ reserve method used
advantage if using first principles - avoid net def and unearned prems

Possible Changes and California UL Regulation

some resistance to change since UL tax reserves defined in terms of existnig UL Model Reg (UL-CRVM)
- if change, might need to calc using 2 different methods into the future
Guaranteed Maturity Premium Method (GMP Method)
- Calc GMP, GMF, r
- [t]V_GMP = r*[t]V_CRVM where [t]V_CRVM is reserve for traditional CRVM based product (perm ins w/ mat date = latest possible date under UL plan)
- if Fund(t) <= GMF(t) then (above)
- else [t]V_GMP = [t]V_CRVM + Fund(t) - GMF(t) (if Fund(t) > GMF(t))
- if r < 1, this generates save value as model reg
- if r > 1, felt this is a reasonable approx for most products
California Method (1991 for 1992+ issues)
- simmilar to UL model reg exept valn i <= credited rate guar in contract or alt reserve = mean(CV,fund value)
NY147 (1994) - allows CA method as elective alt basis for UL reserves
SVL - reserves >= min aggregate amt req'd by state statement if filed, therefore if filing in CA, need to test for this
- even if use CA reserve, need model reg calc for tax reserves

Minimum vs Adequate Reserves

using CV as reserve for flex prem UL can effectively defer losses to later years
CV can become > CRVM reserves once SC wear off
renewal losses can occurr when CV increases not supportable by the gross prem
this would fall under unusal CSV provision of Model Reg of Trad, but UL is specifically exempt

Copyright © 2004 Steve Welander.
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