Valuation of Life Insurance Liabilities - Chapter 2 - RESERVE METHODOLOGIES AND BASES
Valuation Standards in the US
- determined as of policy issue date by state valn laws then in effect
- most state laws based on SVL
- min Vx defined in terms of net prem valn
- defines minimum standards of mortality and interest
- 1980 amendments - dynamic valn int rate - allows automatic adjustments to int rate changes
Valuation Bases in the US
- Valn Mortality
- Pre-80 SVL Amendments
- AA mortality tables w/ setbacks for females
- 80 SVL Amendments
- adopted 80 CSO table
- had to choose from
- 80 CSO M/F
- smoker/ns versions of both 80 CSO M/F
- Unisex 80CSO
- Unisex S/NS 80 CSO
- ANB/ALB
- 10/15 year select factors
- all states allow unisex for nonf
- some states require M/F for valn
- Int Rates
- 1947-1974 most states used 3.5% for all classes
- max was a problem as investment rates increased
- rates were increased
- 80 amendments - changed to dynamic max valn rate - linked to Moody's Corp
- resulted in rates that ary by duration of contract guarantees
Reserve Methods in teh US
- NLP Reserve Method
- designed to cover benefits only
- no explicit recognition of any expenses is made
- for a plan/issue age, net prem = constant % of gross prem
- sum(k*GP(t)v^(t-1)*l(x+t-1)/l(x)) = sum(DB(t)v^t*d(x+t-)/l(x))
- NP(t) = k*GP(t)
- if WL then NP = P(x) = A(x)/adue(x)
- typically produces highest Vx
- typically requires significant V(1) therefore avoided by surplus conscious cos
- Expense Allowances
- used to reflect large first year expenses intended to be recovered from future margins
- Modified Reserves - basically NL reserves less an unamortized expense allowance
- note:DAC is essentially an expense allowance
- EA = beta_mod(x) - alpha_mod(x)
- beta_mod(x) = renewal net premium for modified Vx method
- alpha_mod(x) - 1st year net premium
- V_mod = V_nl - EA*adue(x+t)/adue(x)
- FPT Reserves - 1st year net prem = 1 year term net prem & renewal net prem = NLP for remaining coverage @ IA + 1
- for WL, EA = A(x+1)/adue(x+1) - c(x) (c(x) = A'(x:1|) results is V(1) = 0
- for stat valuations, expense allowance is limited to a max
- expense allowance is formula based and not limited by actual first year expenses incurred
- CRVM
- FPT reserves if FPT adj NP < 20 pay life adj FPT prems
- if DB non-level, then DB = AvgDB(2-10) per AG17
- valn NP for years 2+ are constant % (k) of gross prems
- sum(k*GP(t)v^(t-1)l(x+t-1)/l(x)) = sum[t=1](DB(t)v^td(x+t-1)/l(x)) + 19P(x+1) - DB(1)c(x) (P_FPT > 19P(x+1))
- sum(k*GP(t)v^(t-1)l(x+t-1)/l(x)) = sum[t=2](DB(t)v^td(x+t-1)/l(x)) (P_FPT <= 19P(x+1))
- AG21 - if beta - alpha < 0, excess to be taken as 0
- AG25 - COLA policies to be reserved w/ increases = i_valn - contanst based on type of guarantee
- CRMV produces 0 V(1) from most policies which helps surplus strain on NB
- Other Methods
- Grade from CRVM to NL after x years (typically 20 years)
- reason: to offer products w/ higher (than min) 20yr CV by < Vx
- (P_G - P_NL)*adue(x+1:19|) = EA_CRVM*adue(x+1)/adue(x)
- in general, NL reserve method defined by magnitude of EA and period over which it is amortized
- Other Alternatives
- Arguments for a change to SVL
- based on artificial, predetermined i, fixed for life of contract
- embedded conservatism deliberately adds a solvency margin ~ volume business transacted
- this is in addition to RBC
- several insolvencies illustrate weaknesses in current system
Valuatino Standards in Canada (mostly skipping b/c Canada)
- < 1978 - similar to US
- 1978-1991 - Valn Actuary - modified NP
- PPM - expenses treated explicitly therefore gross prem valn
Copyright © 2004 Steve Welander.
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