Chapter 18 Pricing (2) Individual business

Question 1

Products considered (individual, not group)

For which individual healthcare insurance contracts do we consider pricing in terms of the risk premium calculation required? (6)

Answer 1

We consider methods to value the benefits payable under the major Health and Care insurance products:

• PMI and related products,
  
  • PMI
  • Cash plans
  • Personal Accident Cover
• Critical Illness Cover
• LTCI

Question 2

Risk premium: definition, office premium

What do we mean by ‘risk premium’? (2)

What do we mean by ‘office premium’ (1)

Answer 2

Risk premium

• The risk premium (for a short-term insurance policy) is the element of the premium required to cover only the expected claim amount
• It includes no allowance for expenses, profit, etc

Office premium

• Necessary loadings are added onto the risk premium in order to give the office premium

Question 3

PMI: risk premium, stages

What are the stages involved in the process of calculating the risk premium for PMI contracts? (7)

Answer 3

• choose a base period over which to collect claims and exposure data
• collect data, checking for accuracy and appropriateness of data
• split data into homogenous groups (risk cells)
• calculate historical burning cost premium (BCP) for each group
• analyse data (BCPs) eg to identify trends
  
  • analyse freq and severity separately
• adjust base (BCP) values and project forward to obtain future risk premiums.

Question 4

PMI: risk premium, choosing base period

What is the first step in calculating the risk premium for PMI contracts?

What factors must be considered when performing the above-mentioned first step?

Answer 4

First step

• choosing base period over which to collect claims/exposure data

Allow for

• Sufficient volume (so as to draw reasonable conclusions)
• Period should be long enough for trends in claim frequency/amounts to emerge
• Detail should be sufficient if high variability in claims is prevalent
• Unknowns: most recent data will be most relevant, but this may be most uncertain due to estimates of outstanding claims needed

Question 5

PMI: risk premium, collect data

Once a suitable base period has been selected over which to collect claims/exposure data, allowing for the various necessary factors, what is the next step in the calculation of the PMI risk premium? (1)

What checks are performed when carrying out thiis next step? (2)

For the above step, either internal or external information may be sourced/used; if external, what factors should also be considered? (5)

Answer 5

Nex step

• collect data, checking for accuracy and appropriateness

If external data is used, consider following factors which may cause distortion in the data

• policy acceptance/basis on which policies are accepted, underwriting methods, and waiting periods
• policy coverage - risks covered under contracts in question relative to period ahead
• marketing and distribution
• claim payment/settlement delays

Question 6

PMI: risk premium, homogenous groups

Once we have collected sufficient adequate data, we split the data into homogenous groups; what is an alternative name for these ‘grouping’ (1) and why is splitting the data into risk cells useful? (3)

What important factors may influence the grouping done? (3)

Into what groups may claims be divided for PMI policies? (12+4)

Answer 6

Groups may also be known as ‘risk cells’ and it is important because

• allows for greater understanding of risks being priced, and
• reduces dangerous impact of cross-subsidy

Very important

• need to maintain credible volume of data in each risk cell
• regulations/market expectations may limit factors according to which risk cells can be grouped

Claims may be divided into

• age, gender, smoker status, occupation, family size, ethnicity, disease profile, benefit category, by level of underwriting, geographical area, past medical history, family medical history, etc
• May further subdivide by
  
  • in-patient, out-patient,
  • chronic, day-to-day groups

Question 7

PMI: risk premium, burning cost premium (BCP)

What do we mean by the burning cost premium (BCP) (3)

Give formulae for the BCP (2)

Answer 7

BCP meaning

• a common starting point in calc of risk premium is burning cost
• BCP is calculated per risk cell according to which data was split
• BCP is the true past risk premium of an actual portfolio of data ie actual cost of claims incurred per policy or per unit of exposure

Formula for BCP

• BCP = Total claims / total exposed to risk, or
• BCP = Avg claim amt * Claim incidence rate

Question 8

PMI: risk premium, analyse BCPs

Once we’ve calculated BCPs per risk group, what is the next step? (3)

Why do we do this? (1)

What factors should be considered when performing the above step? (3)

Answer 8

Once we’ve calculated BCPs, we then analyse data/BCP results

• either per policy within given risk cells, or
• per risk cell

We do this to identify potential trends in the data

When analysing data, we can consider

• claim frequency
• claim severity
• exposure per policy

Question 9

PMI: risk premium, adjusting base values

For what various factors may base data/BCP values need to be adjusted once the BCPs have been calculated and analysed per risk cell? (20)

Answer 9

unusually heavy/light experience in base period

• either aggregate more years to make experience more typical.

large or exceptional claims

• decide whether such claims are truncated or left in the data
• depends on likelihood of recurrence

trends/seasonality within claims experience/base period

• more weight should be given to most recent period if trends are identified.
• investigate if trends are likely to continue

changes in risk

• these may appear as trends and can be dealt with as trends
• or insurer should seperate the risk elements and project separately

changes in cover

• if cover changes these should be allowed for in projections
• will involve treatment, limits, and co-payments

incomplete claims

• dalay in most recent data, or late reported claims
• will have to make provision

seasonal variation in claims

changes in reinsurance (cost, or other)

change in agreements with suppliers

• eg lower tariffs in new period ahead

Question 10

PMI: risk premium, project base values forward

After adjusting the BCPs (an historical figure), what is the next step? (1)

What should we consider when perofrming the above step? (5)

What periods/frame of time should be considered? (3)

Answer 10

We need to project past claims costs into the future allowing for:

• changes in policyholders profile/business mix
  
  • eg by benefit options
  • need to allow for selective effect
• claims inflation/expected inflation
  
  • between - the mean payment date of claims in base period - and the mean payment date of claim arising during the exposure period of new rating series.
• trends
• other changes in cover

Time frame to consider

• period of exposure containing the base experience
• period during which policies will be written under new premium rates
• full period of exposure covering all the claims that can arise from the policies written under the new rates.

Question 11

PMI : risk premium, risk class of policyholders

In what way do we need to take the risk class of policyholders in account? (5)

Answer 11

We take account of the risk class of policyholders by producing rates as a function of factors such as age and gender (where allowed by regulation)

Risk premium _(age,gender) =

• SUM [ i_(k) * AC_k ]
• where i_(k) is incidence rate for benefit _k
• AC_k is the average claim cost for benefit/procedure _k
• ….summed over all classes _k

Question 12

PMI: risk premium, loadings + other considerations

For PMI which other loadings should the risk premium be adjusted for? (4)

What other considerations should be factored in at this phase (ie after the risk premiums have been calculated, and projected forward)? (3)

Answer 12

Loadings

• investment income
  
  • either explicity or implicitly, depending on assets classes
• contingency loadings

Other considerations:

• risk premium may be adjusted for excesses
• the presence of a no claims discount
• competition

Question 13

Cash plans: risk premium, intro

What approach can be taken to price/calculate the risk premium for health insurance cash plans? (5)

What steps would be involved in the process? (3)

Answer 13

Similar principle taken compared to PMI

Differs in that the cost of claim of some benefit classes is defined with a

• fixed amount per treatment, or
• fixed amount per day of care.
  
  • will need to estimate expected number of days of treatment in order to calculate AC_k (average claim cost for benefit/procedure _k)

Steps involved

• Calculating expected claims for each benefit
• Establishing suitable age ranges for flat rates
• Allowing for the impact of inertia

Question 14

Cash plans: risk premium, process overview

Briefly describe some important points involved in calculating risk premiums for health cash plans; consider

Calculating expected claims for each benefit (4)

Establishing suitable age ranges for flat rates (2)

Impact of inertia (4)

Answer 14

Calculate expected claims for each benefit

• [Expected Claims] = [Average Claim] x [Claims Incidence Rate]
• should account for excesses & co-payments
• some claims will be “limited indemnity benefits”, some “lump sum fixed amounts”
• for many benefits, approximations based on company’s past experience can be used

Establish suitable age ranges for flat rates, applicable across

• Difficulties can arise in establishing age estimate on which to determine a flat rate.
• This is because rate of premiums are flat over broad age ranges but incidence rates may vary significantly by age

Total calculated needs to be adjusted to take account of intertia ie the propensity not to claim even when claim is valid. This arises because:

• people take cover thinking of one benefit, not others covered by same policy
• benefit might be so small policyholders do not claim. or forget to
• no need to adjust for this if the base data already allows for it

Question 15

Accidental death and TPD: risk premium

Give an overview of how the risk premiums are determined for policies which provide cover in the event of accidental death or TPD (total permanenet disability) (5)

Answer 15

• Similar to PMI and cash plan, may have some experience rating.
• Rating method based on calculating expected claims for accidental death/disability benefits.
• Risk premium ie expected claim or average claim cost
  
  • [Claims Incidence Rate] * [Sum insured]
• Often, an average rate is agreed for each group

Question 16

CI: risk premium, intro

What is the general approach taken to pricing/calculating the risk premium for CI contracts? (3)

Give a general formula for the incidence rates which may be calculated when pricing CI contracts (6)

Answer 16

Pricing for CI contracts

• easier to price than PMI, as benefit is a known lump sum
• most important aspect of pricing is calculating the incidence rates
• we calculate different incidence rates for different critical illnesses
• this process/approach works for single-state or multi-state modelling ie modelling the incidence rates, and multipliying by lump sum

Assuming i_(x,d) this is the incidence rate at age x cause by illness d.

• d may include:
  
  • hd - heart disease
  • s - stroke
  • c-cancers
  • o - other causes
• i_(x) = i_(x,hd) + i_(x,s) + i_(x,c) + i_(x,o)
• overlaps may arise when more than one allwable CI cause underlies same individual claim, and allowed for explicitly

Question 17

CI: risk premium, stand-alone CI

Give an overview of the risk premium calculation for CI contracts which are ‘stand-alone’ /provide stand-alone benefits (5)

Answer 17

Overview

• such contracts pay a lump sum on diagnosis with a critical illness, but, crucially, often have a ‘survivorship’ requirement…ie, because they do not pay a death benefit, the insured must not die from the CI before the benefit is paid (usually over a certain survival period)
• given the lump sum is known, the incidence rate is the key thing to be modelled when calculating the risk premium/pricing

Calculation: risk premium incidence rate

• i_(x)*( probability of surviving the survival period)
• these formula are applied to each CI definition separately and then combined to provide overall risk premium for CI cover.

Question 18

CI: risk premium, accelerated CI

Give an overview of the risk premium calculation for CI contracts which are ‘accelerators’ /provide accelerator benefits (5)

Answer 18

Overview

• such contracts essentially pay a lump sum on earlier of death or diagnosis with a critical illness
• given the lump sum is known, the incidence rate is the key thing to be modelled when calculating the risk premium/pricing

Calculation

• a relative approximation for incidence rate used in the risk premium rates for an acceleralted CI policy is derived below:
  
  • ai_x = i_x + [1-k_(x)]*q_(x), where
    
    • i_x is the CI incidence rate
    • k_(x) is the proportion of deaths due to CI
    • q_(x) mortality rate
  • basically, we add the CI incidence rate to the mortality rate, given that the accelerator benefit will be paid on either 2 events occuring…
  • …however, the deaht benefit will only be paid if the insured survives diagnosis from a particular CI in question, denoted by the factor of [1-k_(x)]
  • essentially, we are reducing the critical illness rate by k_x q_x, the deaths caused by critical illness already included in mortality rate

Question 19

LTCI: risk premium, intro

Give an overview for how pricing is often/usually done for LTCI contracts (2)

Answer 19

• Multiple-state or inception/annuity methods can be/are often used to value the benefits.
• Within this pricing method, policyholders are essentially ‘tracked’ through arious stages/states that they may be in during their policy lifetime.

Question 20

LTCI: risk premium, multi-state modelling, intro

What do we mean by multi-state modelling? (1)

What states may included in multiple state modelling? (6)

What are these various states used for? (2)

What is one of the biggest issues in setting up a multi-state model to price LTCI contracts? (1)

Answer 20

With multi-state modelling, olicyholders are essentially ‘tracked’ through various stages/states that they may be in during their policy lifetime.

We may find the following states:

• Capable & premium paying
• Lives incapacitated within deferred period
• Lives claiming after deferred
• Lives moving to futher stages of incapacity (state for each level)
• Lives dying
• Lives receiving benefits recovering (if applicable)

The states are used to calculate transition intensities/rates:

• u^ij_x = force of transition at age x from state i to state j; i ≠ j
• these may be a function of duration in a particular state

Biggest problem with multi-state models for LTCI contracts is

• data may not be available for the level of sophistication required

Question 21

LTCI: risk premium, multi-state modelling, in practice

What steps are usually followed in practice for pricing of LTCI contracts if a multi-state model is used? (6)

Answer 21

Multi-state modelling in practice

• pricing using multi-state model needs determining the proportion of lives in each status, using relevant duration-based intensities;
• claims outgo: value will depend on
  
  • number of lives within (one/each of)the benefit-receiving cohorts, in a given month, multiplied by…
  • …relevant average sum insured
• other cashflows: consider premium being received in premium state, investment income, all relevant expenses and other outgo
• transition intensities will be applied to each status to determine numbers appropriate to various cells for each/next month

Question 22

LTCI: risk premium, multi-state modelling, issues/benefits

What major issues arise within this modelling process? (4)

In spite of the issues identified above, what benefits may arise from multi-state modelling used to value LTCI contracts in practice? (3)

Answer 22

Issues arising in practice

• model could be very complex, with hundreds of sub cohorts
• lack of detailed statistics to estimate intensities and avoidance of spurious accuracy
  
  • => simpler approach might be better by combining cohorts and transition intensities

Benefits of multi-state modelling for LTCI contracts?

• even with approximations
  
  • provides insight into rating and reserving structure
  • allows sensitivity testing