28 Pricing health and care contracts Flashcards
Income protection
Methods of pricing
- Multi-state modelling
- simplified inception / disabled life annuity approach
Income protection
Multi-state modelling
Method
Requires determination of the proportion of lives in each status, using relevant duration-based intensities.
policyholders are separately tracked through the various stages:
- healthy premium payers
- lives falling sick within deferred period
- lives becoming claimants following deferred period
- lives recovering, reverting to premium payers
- lives dying
Each subclass will have its own set of transition probabilities
transition intensities = Annual rate at which lives move from one state to another
probabilities may vary according: 1. to the number of previous times that the cohort has been ill. 2. duration within that stage
In addition to the transition probabilities, assumptions regarding the proportion of lives in each state will be required
claims outgo = number of lives within (one of) the benefit-receiving sub-cohorts, in a given month, * relevant average sum insured
Balanced against
the premium coming from those in a premium-paying state,
+ the investment income,
- all relevant expenses and cash outflows in the appropriate month
Transition intensities will be applied to each state to determine the numbers expected in the various states for the following month
Income protection
Multi-state modelling
Limitations
- the available data may not permit this degree of sophistication of the method in practice
- model could be very complex, with hundreds of sub-cohorts open at any time
- lack of detailed statistics to estimate all of the transition intensities
- the avoidance of spurious accuracy
- might lead to: combination of various sub-cohorts and reduction of number of transition intensities required
Income protection
Multi-state modelling
Advantages
- will provide significant insight into the robustness of any rating and reserving structure
- allow sensitivity testing to be performed - very important
- Even without much confidence about any single projected outcome,
- the effect on the outcome of varying the parameter assumptions can be extremely insightful
Income Protection
Inception/disabled life annuity approach
Method
- simplification of the multiple state model approach
- convert our multiple state model into a multiple decrement table format
- Considers two functions: the claim inception rate and disabled life annuity
- Defined claim inception rate
- how to derive the claim inception rate
- defined the disabled life annuity
- allowance for benefit esclation, interest and prob of death and recovery between end of defferred period and policy expiry
- The expected claims outgo is then calculated as the annual benefit amount multiplied by the disabled life annuity multiplied by the claim inception rate
Expected cost of benefits from claim INCEPTING in a particalur year =
Survival probability (probability that the p/h is eligible to claim in the year)
x
the claim inception rate corresponding to the year under consideration
x
value of the annuity then payable for the duration of the claim
x
a discount factor
x
the annual benefit amount
Income Protection
Inception/disabled life annuity approach
Claim inception rate
- Claim inception rates relate to the point in time at which benefit payments commence.
- This corresponds to the end of the deferred period
- Derived from “sickness inception rates”
- probability of sickness inception * the probability of remaining sick throughout the deferred period
Income Protection
Inception/disabled life annuity approach
Disabled life annuity
- the present value at the date of claim inception of expected claim payments to individuals disabled after the deferred period until policy expiry
- Allowance is made for: 1. escalation of the claim amount, 2. interest and the 3. probabilities of death and recovery between the end of the deferred period and expiry date.
Income Protection: Inception/disabled life annuity approach
Valuing disability benefits using rates of claim inception and claim termination
more formalised approach using two double decrement tables
The first double decrement table (healthy)
relates to decrements from the healthy state (falling sick and dying)
This double decrement table is estimated so as to allow for recovery and subsequent sickness.
Inception rate for disability: dependent initial rate of falling sick at age x
The second double decrement table(sick)
relates to policyholders who are receiving disability benefits, and has decrements of recovery from disability and dying
The “survival” (ie neither-recovering-nor-dying) probabilities from this double decrement table are used to determine the present value of a disability annuity
Valuing disability benefits
Intergral formula
the probability that x is alive and well at time t
x
the probability of falling sick in time interval dt
x
the value of the annuity then payable on sickness
x
a discounting factor
Approximate calculation of the integral
Formulae and tables for the examinations
Claim inception rates (a)
based on the results presented in CMIR12
- The claim inception rates are central rates, tabulated by age at claim commencement, x, and prior deferred periods, d, in years
- gives the expected number of claim inceptions occurring over the year of age [x , x+1] following deferred period d), relative to the average number of lives healthy and sick) alive during that year of age
- age at commencement of sickness will be x-d
Critical illness
- accelerated critical illness policy (ie one where the benefit is paid out on the earlier of death or critical illness)
- These formulae are applied to each critical illness definition separately and then combined to provide the overall risk premium for critical illness cover
- expected claim cost is then found by multiplying the claim incidence rate by the critical illness sum assured of the policy.
- Overlaps in incidence of certain critical illnesses may be allowed for explicitly
- Double counting will lead to an overestimate of claim incidence rates, which is a more acceptable (less solvency-threatening) error than understating the rates (for standalone CI)
- Double counting will overstate the proportion of deaths that are also critical illness claims. This would understate the cost of claims and could lead to inadequate premiums or reserves.
