28. Pricing health and care contracts

Question 1

What are the two approaches to pricing IP?

Answer 1

• Multi-state modelling
• Claim inception/disability annuity approach

Question 2

Explain how multi-state modelling could be used to price IP

Hint: states&raquo_space; mu and p&raquo_space; value&raquo_space; variation by prev times ill&raquo_space; duration&raquo_space; many subcohorts&raquo_space; can use combos&raquo_space; value of claims&raquo_space; value of premiums&raquo_space; investment income and expenses&raquo_space; ph expected next month

Answer 2

• Track ph through different states:
  
  • Healthy
  • Sick within deferred period
  • Sick and claiming
  • Dead
  • Lapsed
• Make assumptions about forces of transitions between states and find probability of being in states at future times
• Use probabilities to value benefits and premiums
• Transition probabilities may vary according to # of previous times cohort has been ill
• Transition rates may be function of duration within stage
• May lead to many subcohorts of transition probabilities&raquo_space; spurious accuracy
• Can use appropriate combinations of subcohorts to have fewer and more reliable probabilities

Valuing premiums and benefits:
* Value of claims depends on # of lives in benefit receiving state
* Value of premiums depends on # of lives in premium receiving state
* Must allow for investment income and expenses
* Transition intensities applied to each state to find # of of ph expected in next month

Question 3

Explain how the claim-inceotion/disability approach can be used to price IP

Hint: functions; expected cost of claims producing mid-year values; disability annuity; claim inception rate; allowance

Answer 3

Makes use of two functions:
* claim inception rate and disabled life annuity

• Expected cost of claims incepted in each future year can be found from:
  survival probability X claim inception rate X disability annuity
  …producing mid-year values

Disability annuity:
* PV at claim date of expected claim payments to ph disabled after deferred period until policy expiry
* Only for current claims ending on death, recovery or policy expiry.
* Based on double ddcrement table for sick lives: death and recovery
* Annuity value varies by the deferred period

Claim inception rates:
* Probability claim will be payable for ph in year of age x to x+1
* Broadly = sickness inception rate X probability of sick staying sick through deferred period.
* 3 cariations of inception rates:
- initial claim inception rate
- central claim inception rate (claim inceptions)
- central claim inception rate (sickness inceptions)

Allowance made for:
* Benefit escalation
Prob of death and recovery between end of deferred period *and maturity

Question 4

Describe the 3 variations of claim inception rates under inception/annuity approach

Answer 4

Initial claim inception rate i(x,d):
* Prob of claim inceptions following deferred period during year of age [x,x+1]…
* Arising from sickness inceptions at [x-d,x-d+1]
* Survival prob is prob of being healthy at exact age x-d

Central claim inception rate ia(x,d):
* Expected number of claim inceptions over year of age [x,x+1] …
* Relative to ave number of lives alive during year of age
* Survival prob is prob of being alive at average age x+1/2

Central claim inception rate ib(x,d):
* Expected number of sickness inceptions over year of age [x,x+1] which become inceptions d years later…
* Relative to ave number of lives alive during year of age
* Survival prob is prob of being alive at average age x+1/2

Question 5

Explain how you would price CI

Answer 5

Claim incidence rate = i(x) X probability of surviving survival period

Claim incidence rate is of form:
i(x) = i(x){Heart disease}+ i(x){Stroke} + i(x){Cancer} + i(x){Other}

Accelarated CI incidence:
i(x) + (1-k(x))q(x) where k(x) is prop of deaths over [x,x+1] due to CI

Question 6

How us LTCI priced?

Answer 6

Use multi-state model or inception/annuity methods

Question 7

Factors to consider when evaluating appropriateness of muti-state modelling

Answer 7

• Amount of data
• Does data have granularity required for the approach?
• Appropriateness of data given changes in economic conditions, benefit definitions, target markets etc
• Time and resources
• Consulting external sources and costs thereof
• Expert judgement where there isn’t credible data
• Spurious accurace
• Accuracy vs risk of having time and data required