CLK_F102_Chapter_28

Question 1

Pricing income protection

Multi-state modelling

Answer 1

Modelling whereby the policyholders are tracked separately through the various stages of healthy and claiming as follows:

• healthy premium payers
• lives falling sick within deferred period
• lives becoming claimants following deferred period
• lives recovering, reverting to premium payers
• lives dying etc

Each subclass will have its own transition probabilities: sickness, inception, lapse, mortality, recovery, policy expiry

these transition probabilities may vary according to the number of previous times the cohort has been ill and all transition rates may be a function of the duration within that stage

• In practice pricing using this approach will require assumptions regarding the proportion of lives in each state using relevant duration based intensities
• claim outgo = no of lives within one of the benefit receiving sub-cohorts on a month * average SA
• this will be balanced against premiums (from those in the premium paying state) plus investment income less all relevant expenses and other outgoings in a month
• transition intensities will be applied to each state to determine the numbers expected in the various states for the next month

issues with pricing method

• in theory the model can be very complex with 100s of cohorts open any time eg for H to S sick for one year or sick for over a year, each sick category can be classified by major sickness disability
• although the multi state modelling approach is the more technically accurate approach there is unlikely to be sufficient data available to follow approach and it may lead to spurious accuracy
• due to increased granularity it allows for sensitivity testing which is not as easily achievable using the inception/disabled approach

a more meaning and straightforward approach is one that combines some cohorts and reduces the number of transition intensities required

Question 2

Pricing income protection

Claim inception and disability annuity approach

Answer 2

The inception/disabled annuity approach makes use of two functions, the claim inception rate and the disabled life annuity to value benefits

allowance is made for any escalation of the benefit amount, interest and the probability of death and recovery between the end of the deferred period and the policy expiry

Expected cost of benefit under approach =

• probability that policyholder is eligible to claim in year under consideration
• *claim inception rate

  - probability that claim will become payable to individual in year of age x, x+1
  - individual would have been sick throughout the deferred period d
  - where d = 0, claim inception rate = sickness inception rate 
  - rate = sickness inception rate * probability of remaining sick through d

• *disability annuity

  - PV at date of claim inception of expected claim payments to individuals disabled after the deferred period until policy expiry

• *a discount factor (to discount the annuity value back from the point of claim to policy inception)
• *the annual benefit amount

Question 3

Pricing income protection

Claim inception and disability annuity approach

Answer 3

three variations of the claim inception rates:

An initial claim inception rate ixd

• probability of claim inception (following deferred period d) occurring during the year of age x,x+1
• relevant survival probability is probability of being healthy at exact age x-d

A central claim inception rate iaxd

• expected number of claim inceptions (following deferred period d) occurring during the year of age x,x+1, relative to average number of lives (healthy and sick) alive that year
• relevant survival probability is probability of being alive at average age x+0.5

A central claim inception rate ibxd

• expected number of sickness inceptions occurring during the year of age x,x+1, which ultimately become sickness inceptions d years later, relative to average number of lives (healthy and sick) alive that year
  
  • relevant survival probability is probability of being alive at average age x+0.5

CMIR12 derives inception rates 2 and 3

S(ID) tables include:

used to calculate expected claims cashflows for initially healthy lives aged 3

• inception rates of type 2
• current claim disability annuity values

used to calculate costs of benefits and premiums using a formula approach for policies with expiry age 65

• expected PV of sickness annuities for currently healthy lives

Question 4

Pricing Critical Illness

Answer 4

approach is simpler than IP since benefit is a lump sum and not an income

standalone CI claim incidence

• ix * probability of surviving survival period

accelerated CI claim incidence rate

• ix + (1-kx)qx where kx is the proportion of deaths over x,x+1 that are due to CI

overall CI incident rate would be:

• ix = ixhd + ixs + ixc + ixo
• where hd = heart disease, s = stroke, c = cancer and o = other

expected claim cost = ix * SAci

overlaps in incidence of certain critical illnesses may be allowed for explicitly:

• overlaps arise where more than 1 CI cause underlies the same individual claim but only one is paid under the policy
• overlaps should not be an issue if assumptions for incidence rates have been derived by analysing claim experience data, provided care is taken to attribute each claim to a single cause only
• if population medical records are used to estimate future incidence rates then there is a potential for double counting as medical data can record disease incidence by cause without indicating whether other diseases are present at the same time
  • doubling counting will lead to an overestimation of claim incidence rates which is more acceptable and less solvency threatening than understating the rates.
  • too much overestimation can be a bad thing as it can lead to uncompetitive premiums
  • doubling counting could cause problems for claim accelerated CI contracts. In the formula ix = (1-kx)qx if kx = proportion of deaths cause by CI claims is overstated it would understate the cost of claims abs could lead to inadequate premiums or reserves

Question 5

Pricing LTCI

Answer 5

Approach is similar to IP

Can choose between inception/annuity method or multi state modelling

Question 6

Factors to consider when changing from inception/disabled approach to multi state modelling approach

Answer 6

• data: does insurer have large amounts of data to apply multi state modelling?
• granularity: does insurer have level of granularity in the data required to facilitate multi state modelling?
  • granularity in terms of changes in economic conditions
  • benefit definitions
  • target market
  • claim management processes
• time and resources to build a multi state model from scratch
• cost of using external experts to assist with modelling and data
• availability of expert judgement where there is a lack of credible data in particular sub cohorts
• risk versus benefit of increased accuracy in using a multi state model versus the risk of insufficient data and time and effort required to build a multi state model
• whether is makes sense to reduce the number of sub cohorts in order to avoid spurious accuracy