Chapter 18 - Models (1)

Question 1

A multinational life insurance company is planning to launch a product in Country A to cover the funeral costs of children. Country A has many regions with high child mortality rates. The insurance company will be the only company that will provide this type of insurance in Country A. The company currently sells this product in Country X, where there is relatively low child mortality.

The products features include:
* The policies will provide cover for all children of the policyholder, and the premium will be the same irrespective of the number of children covered.
* The policy will continue until the policyholder reaches age 65 or the youngest child reaches age 18, whichever occurs later.
* Underwriting will be limited to a few questions, including policyholder’s age and address as well as the age and sex of their child/children.
* The policy will automatically include all future new-born children.

i. Explain why the company would use a cashflow rather than formula approach to price this product

Answer 1

The cashflow approach will allow for the complexity of the product, e.g.:
* multiple lives insured;
* multiple projected decrements (death and withdrawal)

In particular it will also allow the company to investigate the senstivity to profit due to:
* mortality variance;
* variations in average number of children insured; and
* children’s ages

A cashflow approach allows the measurement of the expected return that the
providers of capital will receive.

A cashflow approach will allow for the projection of both statutory reserves and capital requirements.

A cashflow approach will allow flexibility to model country A and X together or
separately.
* The cashflow method may be easier to allow for the different mortality in the two countries
* The cashflow method can allow more easily for different lapse rates in the two countries

The company may wish to allow for stochastic decrements or decrements that may vary over time.

• It is unlikely that stochastic investment returns will be required since this is a protection policy.
• However, mortality could be projected stochastically.
• Similarly for lapses which will impact per policy expenses.

A cashflow method allows the modelling of interdependencies between variables
* and the link between the variables and economic conditions.

A cashflow method will allow the company to model projected birth rates since newborns are automatically insured
* It will also allow this to be varied with factors such as the economy if the company wants to model it.

The risk discount rate can take account of the term structure of interest rates.

Tax and reinsurance will be easier to allow for

Question 2

A multinational life insurance company is planning to launch a product in Country A to cover the funeral costs of children. Country A has many regions with high child mortality rates. The insurance company will be the only company that will provide this type of insurance in Country A. The company currently sells this product in Country X, where there is relatively low child mortality.

The products features include:
* The policies will provide cover for all children of the policyholder, and the premium will be the same irrespective of the number of children covered.
* The policy will continue until the policyholder reaches age 65 or the youngest child reaches age 18, whichever occurs later.
* Underwriting will be limited to a few questions, including policyholder’s age and address as well as the age and sex of their child/children.
* The policy will automatically include all future new-born children.

ii. Discuss how the company could set model points to price this product. [5]

2024_s2

Answer 2

Setting model points:

• The data from Country X may not be useful for the model point data and the company may need to use risk factors to determine model points.
• They may approach the government /reinsurer /census bureau in Country A to determine birthrates and family dynamics to estimate the likely spread of the number of children to be covered
• For the areas which do not have high child mortality in Country A the experience from Country X may be useful to set model points with appropriate adjustments.

For mortality the company could use groupings by:
1. number of children;
2. age of children;
3. sex of children;
4. policyholder’s ages;
5. region

• Allow for likely volumes of sales and expected birth rates

Question 3

State the main requirements that an actuarial model should satisfy [5]

2005_s2 - uk

Answer 3

The requirements depend on the purpose for which model would be used.
* The model should be valid and fit for purpose.
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* it should be rigorous
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* It should be well documented (audit trail)
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* Model points must adequately reflect the distribution of the business being modelled
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* The parameters must allow for the features of the business that could significantly affect the advice being given.
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* The inputs to the parameter values should be appropriate to the business being modelled
* and take into account the special features of the company and the business / economic environment in which it is operating.
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* The outputs should be capable of independet verification for reasonability.
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* The outputs should be capable of being communicated to the recepeints of the advice.
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* The model should not be too complicated so that the results are too difficult to interpret or communicate.
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* The model should not take too long or be too expensive to run.
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* Some level of controls or consistency checking should be built into the model

Question 4

A unit-linked single premium whole life policy allocates 101% of the premium into units. The policy can be surrendered at any time and the policyholder will receive the bid value of units held at that time. However, on the tenth policy anniversary, the policyholder will receive the higher of the bid value of units and the original premium. The only charge under the policy is an annual managemnent charge. A deterministic cashflow model is used to determine an appropriate level for the annual management charge.

i. Explain why this model is unlikely to produce an appropriate charge for the return of premium guarantee at the tenth anniversary. [5]

ii. Explain why a stochastic model would be better than a deterministic model for this purpose [3]

2005_s2 - uk

Answer 4

i.

• For the 10th anniversary guarantee to have a modelled cost there needs to be a cashflow generated from the guarantee biting.
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• This will occur if the model produces a fund value at the 10th anniversary that is lower than the original premium.
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• The deterministic model will project forward the fund position based on an expected level of investment return.
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• With this policy the fund value starts at a level greater than the premium.
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• The fund value then grows at the expected rate that is consistent with the assets backing the unit funds.
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• This is likely to exceed any fund decreases each month as the charge is deducted
• but any commercial charge is likely to be lower than rise in asset values.
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• This means that the fund will rise overall
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• As a result the fund value at the 10th anniversary will be higher than the original premium and so there will be no cashflow generated as a result of the guarantee.
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• The cost of the guarantee as derived by the models will therefore be zero
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• However, in reality there is a risk that investment values will fall over the ten year period and the fund at the 10th anniversary is lower than the gurantee level.
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• In such cases the company would have to pay the shortfall to any policyholder who surrenders.
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• The cost derived by the deterministic model is therefore clearly inappropriate.

ii.

• A stochastic model runs many different investment scenarios, where the future investment returns are governed by a probabiliry distribution function.
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• Some of those investment scenarios will show poor investment performance, where the fund value falls below the original premium level.
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• In these scenarios the cost of the money back guarantee will result in a negative cashflow to the company.
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• The company would run many simulations and the cost of the guarantee determined by the model will be the average shortfall over all simulations.
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• As a result, the company will recognise the need to charge a higher annual management charge for offering the guarantee.
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• The stochastic model is clearly superior in that it can correctly determine the need for such a charge.

Question 5

A small life insurance company writes mainly term assurance contracts targeted at young families. Underwriting is used to assess the terms appropriate for new business.

Past experience has shown that the mortality experience for this product line can be represented as a fixed percentage of standard mortality tables.

i. Describe how the company is currently exposed to model, parameter and random fluctuations risks relating to its mortality assumptions. [7]

2008 - s1 - uk

Answer 5

Model and parameter

• There is a risk that fixed percentages may become out of date and not adequately reflect the mortality of the business written.
• There is a risk that the table may become out of date and unrepresentative of the business that the company writes.
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• There is a risk that the mix of busines changes in future, by:
• sex
• age
• smoker / non smoker
• class of life
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• The fixed percentage will have meant some cross subsidies are likely to have existed in teh past.
• The view of future mortality improvement or deterioration may have changed and hence the level of within the table may not be appropriate,
• or equally may affect different classes of lives in different ways - invalidating the assumption.
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• There may be an anti-selection risk if the market changes and other companies target certain lives (e.g. non smokers, specific classes or age ranges)
• Any changes to the underwriting process will invalidate the assumption.
• There may be potential impact arising from a tranche of selective withdrawals.

Random fluctuations

• The company is small and so is possible that it has a small number of claims in any given year.
• This means that it may be susceptible to random fluctuations.
• Abonormally heavy claim experience may threaten the company’s solvency
• This could happen through particularly large claims or as a result of an unusually high number of claims.
• new diseases or disaster could result in higher claims.

Question 6

A small life insurance company writes mainly term assurance contracts targeted at young families. Underwriting is used to assess the terms appropriate for new business.

Past experience has shown that the mortality experience for this product line can be represented as a fixed percentage of standard mortality tables.

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The company is considering designing a without profits whole life assurance contract targeted at customers aged 50 and over. The company currently has very few customers in this age range. It is common, but not universal, in the marketplace for these contracts to be sold without underwriting. The company has yet to decide whether or not to underwrite this contract.

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ii. Describe the issues the company should consider regarding the mortality risk arising from the proposed product. [10]

2008 - s1 - uk

Answer 6

• The company has little experience in the mortality of the proposed age group
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• Mortality improvements (or deteriorations) over time may be different for different age groups.
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• The fixed percentage approach used for the existing contract may be overly simplistic for this age group
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• It is possible that the customers for the new contract come from a very different socio-economic group to the existing contract type
• The possibility of no underwriting would also make the new population siginificantly different to the existing population.
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• The current model may therefore inappropriate and the current parameters are likely to be inappropriate.
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• By moving into a new market and thereofre, possibly leading to a significant increase in the number of customers, the random fluctuation risk could be reduced.
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  In order to derive a suitable basis for this product the company should:
• consider the information available from published mortality investigations (from actuarial profession or other sources)
• Seek the advice of its reinsurers, as it is very likely that it will reinsure some of the new business
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• The decision whether to underwrite or not is very important
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No underwriting would:
* Possibly more in line with the market for this product
* Be cheaper due to no underwriting costs
* Not increase the number of claims (as whole of life)
* But would accelerate them
* Specifically, there may be some claims close to the point of sale
* The different claim profile is not a problem as long as it is reflected in the pricing basis.
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Having underwriting would:
* mean that your product was cheaper due to select mortality
* But customers may be prepared to pay higher premiums in order to avoid underwriting
* The cost of undewriting may be prohibitive if sum assured is low.
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If not all policyholders are underwritten then the company could be exposed to anti-selection risk
To make the decision would need market research:
* Sales volumes may be higher if there is no underwriting
* A market niche with sufficiently high sums assured could justify underwriting