Study Notes and Published Refences - Note SN 8I-201-00 - GROSS PREMIUMS FOR DISABILITY WAIVER BENEFITS

Introduction

insurers limit coverage at older ages
- dis rates increase dramatically at older ages
- hard to tell between dis and normal ret at older ages
Calc of PV of benefits is a 2-step process
- benefit provided at point of where dis occurs must be calced
  - benefit is a disabled life annuity = PV waived prems using int and rates of termination of dis
- PV @ issue of each benefit is calces using int, active life mort and rates of dis
  - calced at each point dis can occur and summed
calc of actual gross prem can be simplified by loading published valn net prem
- loading determined by fitting adjusted experience prems to valn net prems

Assumptions for Experience Premiums

Prems Waived
- prems used in benefit calc s/b net cost to insurer of prems actually waived
- consider
  - commissions paid on waived prems
  - prem taxes not paid on waived prems
  - if offered, sex-distinct prems s/b used
  - if prems vary by size of policy, either
    - avg size s/b used or
    - sep prems calced for each band
  - YRT - S&U - simplified by calcing single AA table based on ultimates
  - Term Conversions - should use permanent plan's premium in calc
  - if prems vary by s/ns - blended rates or sep prems
Interest
- significant impact b/c long dur benefit
- conservative LT rate s/b used
Expenses
- cost of initial and ongoing claims investigation
- acctg for waived prems
- reserving for coverage
- command prem tax on premium for benefit
- some cos charge share of overhead
Active Life Mortality
- used to determine survivorship for non-disabled lives for
  - PV (@ issue) of benefits
  - annuities used to calc net ann prem
- use same experience assumption used for pricing base coverage
- table of commutation functions D([x]+k) = v^(x+k)*l([x]+k)
Lapse Rates
- conservative to assume no lapses
- use base contract rates if using any
Morbidity
- Rates of Disablement - measure chance of life aged (x) becoming disabled at age (x+k) (and remaining alive and disabled to end of waiting period)
  - probability of disablement - r(x+k)
  - absolute annual rate of disablement - r'(x+k)
- Rates of Termination of Disability
  - needed to calc dis life annuity values
  - measure probability of leaving the group of disabled lives (from recovery or death)
  - highly select by duration since disablement
    - usually monthly for first 2 years
  - very few people beyond retirement age recover from disabled status
  - Termination rates used to construct table for dis lives
  - l_i([x+k]+m/12+s)
    - k+1 - year disablement occurs
    - m - months in waiting period
    - s - duratoin since end of waiting period
  - D_i([x+k]+m/12+s) = v^(x+k+m/12+s)*l_i([x+k]+m/12+s)

Experience Premium Formulas

Assume
- disabilities occur mid policy year
- prem and benefit payments payable continuously throughout policy year
- waiting period is 6 months
B(k+1) - benefit provided if dis occurs in year k+1
P(k) - prem/14m payable during k+1
u = age wvr benefits end
h - prem paying period of base plan
n - cvoerage period for waiver provisoin = min(h,u-x)
h' - prem paying period for waiver provision
B(k+1) = sum(P(k+s+1)*(D_bar_i([x+k+1/2]+1/2+s) / D([x+k+1/2]+1/2))) from s=0 to n-k-2
- if P is level = P*abar_i([x+k+1/2]+1/2:n-k-1|)
if coverage retroactive, B(k+1) increased by half prem payable in k+1 (0.5*P(k))
PVB = B(k+1)*v^(x+k+1)*l([x]+k+1/2*r'(x+k) / D([x])
- = B(k+1)*v^(1/2)*r'(x+k)*D([x]+k+1/2) / D([x])
NWSP = sum(PVB) from k = 0 to n-1 -> net waiver single premium
NAWP = NWSP / active life annuity
- = sum(B(k+1)*v^(1/2)*r'(x+k)*D([x]+k+1/2)) / sum(D_bar([x]+k)) for (numerator) k = 0 to n-1 and (den) k=0 to h'-1
To load for expenses
- E_wp(pi) - exp prem, loaded for expenses
- B'(k+1) - expense loaded benefit if dis in k+1
- c(k) = active life % prem expense in k+1
- e(i) - active life per pol expense in k+1
- c_i(s+1) - dis life % benefit expenses paying in dis year s+1
- e_i(s+1) - dis life per pol expense in s+1
- assuming per pol expenses paid @ BOY and % expenses paid continuously
- B'(k+1) = .5*P(k) + sum{[P(k+s+1)*(1+c_i(s+1)) + e_i(s+1)]*[D_bar_i([x+k+1/2]+1/2+s)/D_bar_i([x+k+1/2])]} for s = 0 to n-k-2
- E_wp(pi) = sum{[e(k)*D([x]+k) + B'(k+1)*v^(1/2)*r'(x+k)*D([x]+k+1/2)]} / sum{(1-c(k))*D_bar([x]+k)} for (num) k=0 to n-1 and (den) k=0 to h'-1

Special Considerations

substandard risks
- waiver usually restricted to least substd risks
- waiver prems usually multiples of std business wvr prems
Payor Benefit
- waives premiums if payor of juvenile policy is death/dis until juv attaines 21/25
- prems depend on age of applicant, plan of ins, age of insured
- gross prems usually published at table of factors
Riders on Insured Spouse or Children
- waives rider prems
- based on base insured, not spouse or children
Non-traditional Products
- indeterminate prem products
  - using guar prems in calc is conservative
    - might be uncompetitive
  - use judgement re: most likely scale of prems to be charged and use in calcs
- UL
  - waiver of coi
  - specified amt - use specified amt in formulas and is aount req'd to keep contract in force if all guarantees realized
    - does not have any relationship to prms actually paid into contract
  - either case, use same formulas, just different P(k) stream

Copyright © 2004 Steve Welander.
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