Chapter 23: Capital Modelling - practical considerations

Question 1

How might a capital model be used to inform management decision making in:
reinsurance

Answer 1

optimising the purchase of reinsurance - this may involve deciding on the retention level that optimises the savings in reinsurance premiums and the capital required.

Question 2

How might a capital model be used to inform management decision making in:
investment

Answer 2

assessing the impact of a change in the investment mix on the capital required and expected return.

Question 3

How might a capital model be used to inform management decision making in:
pricing

Answer 3

assessing return on capital for pricing and performance measurement

Question 4

How might a capital model be used to inform management decision making in:
reserving

Answer 4

quantifying the uncertainty in claims reserves - the capital model may be used to give a range of outcomes around a deterministic best estimate.

Question 5

How might a capital model be used to inform management decision making in:
strategy

Answer 5

this could include assessing the capital implications of a proposed acquisition to determine whether the capital diversification benefits from some risks will outweigh the impact of increased aggregations in other risk areas

assessing the risks and diversification benefit of new strategies, eg assessing the capital implications of a proposed new class by analysing the diversification benefits and comparing this to the expected return on the class.

Question 6

How might a capital model be used to inform management decision making in:
risk management

Answer 6

identifying key risks based on the model output and assessing the impact of mitigation.

Question 7

Claims characteristics

Answer 7

Refer to the ways and speeds with which claims

• originate
• are notified
• are settled and paid
• and reopened.

Claim frequency and amount, as well as potential accumulations are relevant.

Question 8

How are attritional claims modelled?

Answer 8

AGGREGATE DISTRIBUTION using a Lognormal/similar.

• Due to the high number of losses classified as attritional, the stability of the distribution means that the aggregate distribution is appropriate.
• The loss distribution can also be linked to premium income.

Question 9

How are large losses modelled?

Answer 9

FREQUENCY-SEVERITY
allows more details of the available information to be used, expecially important where there is scarce data.

FREQUENCY ~ Poisson/Negative Binomial

SEVERITY ~ Pareto/LogNormal or other heavy-tailed distribution.

• The additional detail is worth the effort due to the larger values and will enable reinsurance limits to be tested more adequately.
• Need to decide on a threshold per class of business above which large losses will be modelled.

Question 10

How will catastrophe losses be modelled?

Answer 10

• Catastrophe losses will be modelled using different approaches depending on the peril. Generally, historic data is not sufficient to model such perils. Proprietary CAT models are widely used by insurers.

Earthquake and natural cat events: may use proprietary catastrophe model which applies losses to the exposure base.
Factors which will affect the size of the loss include event magnitude and location.

Other perils such as hail/flood etc. may be modelled using a frequency-severity approach.

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Question 11

Reasons why capital allocation is desirable:
Performance measurement

Answer 11

Capital has a cost. Therefore to accurately assess the performance of a particular class we need to calculate the profit/return as a percentage of the capital required to write that class, i.e. return on equity. 
This requires knowing the capital cost for each class.

Question 12

Reasons why capital allocation is desirable:
Business planning and strategy setting

Answer 12

If the insurer can allocate capital to different areas of the business (and hence understand risk adjusted performance) then it can make decisions about which areas of the business to develop based on return and capital.

Question 13

Reasons why capital allocation is desirable:
Pricing

Answer 13

Premiums charged should have a capital/profit loading to reflect the cost of capital held to write the business. Any pricing exercise should allow for diversification benefits between policies, which results in the total capital requirement being lower. This allows the insurer to charge more competitive premiums. The insurer will thus want to allocate capital to products or even policies so that premium rates can accurately take account of the risk of the product/policy.

Question 14

Describe the process the company may follow in modelling earthquake risk

Answer 14

• The company will likely need to purchase model output from a company that is an expert in modelling earthquakes as this is different to the core business of employees of the insurer.
• The model output will include something along the lines of potential earthquake events with their associated locations, severities and frequencies.
• A simulation model would then be able to simulate whether each of the events happens or not in a particular year.
• The key modelling function is to then determine the cost to the insurer if each earthquake were to occur.
• This will be a function of the amount of exposure the insurer has (measured in terms of EML) at or within a near range of the location of the simulated earthquakes.
• For large buildings, the insurer may wish to model damage separately.
• The reinsurance model should be able to calculate recoveries on treaties.
• Key parameters should be sensitivity tested to understand model sensitivity to each factor and decide which factors are worth putting more time into estimating accurately, including more research.

Question 15

How might the calculation of economic capital differ from the calculation of regulatory capital?

Answer 15

Economic capital is typically calculated using an insurer’s own internal model, whilst regulatory capital would usually be calculated using a prescribed model or formula.

Economic capital would use a DETAILED BREAKDOWN of assets and risk exposures, using an insurer’s own risk profile, whereas regulatory capital would use data which are summariesd to a degree, and applying market risk profiles/characteristics.

The economic capital requirement may be on a more REALISTIC BASIS, without any prudence which may exist on a regulatory basis. Even a regulatory basis which is on a best estimate basis may include a risk margin which represents an adjustment for uncertainty.

Economic capital may use a HIGHER LEVEL OF CONFIDENCE than the regulatory figure, especially if this is a published risk disclosure.

Risks and events may be correlated in a very complex manner in an economic setting, whilst this is normally more simply applied in a regulatory setting.

Question 16

3 Main categories of ways in which reinsurance can improve an insurer’s solvency position.

Answer 16

An insurer’s solvency position is improved if its solvency margin increases relative to its solvency requirement.

Reinsurance can assist by:

• Increasing the value of the assets
• Decreasing the value of the liabilities
• Decreasing the regulatory minimum solvency requirement

Question 17

How could reinsurance help to increase the value of the assets? (4)

Answer 17

• Financing can be obtained through the reinsurance commission associated with proportional reinsurance.
• Financial reinsurance can be sought:
• – such arrangements can effectively be loans repaid from the future profits of the underlying business.
• – As the “repayments” of the “loan” are contingent on profits, they do not appear as a liability on the balance sheet, which would have been the case with a bank loan.

Question 18

How could reinsurance help in decreasing the value of the liabilities

Answer 18

• By reinsuring, the insurer is reducing the value of its liabilities as some are ceded to the reinsurer.
• Reinsurance allows the insurer to get a better spread of risks which may result in more certainty in aggregate results and therefore less need for margins in reserves.
• reciprocal arrangements can also assist with this.
• Non-proportional cover can assist in dealing with:
• – large claims
• – accumulations of risk

Question 19

How does reinsurance help to decrease the regulatory minimum solvency requirement?

Answer 19

• The required solvency level is often calculated with reference to the proportion of business reinsured, i.e., more reinsurance means a lower solvency requirement and therefore a stronger solvency position.
• However, this reduction may be subject to a limit, since there is a legal requirement for an insurance company’s free reserves to exceed a Required Minimum Margin.

Question 20

State a good starting point for deciding on the level of detail to use in a capital model.

Answer 20

The size of reserves for a particular portfolio would usually be a good starting point for deciding upon the level of detail for modelling the relevant capital requirements. Other factors to consider, if applicable:   large volumes of catastrophe business riskier investment portfolios  complexity of reinsurance covers  classes of business with losses linked to economic cycles  credit or surety business, etc. _

Question 21

Give examples of colleagues we should consult with, in order to improve our understanding of the products being modelled.

Answer 21

We should work with underwriters, claims managers and marketing executives to understand the cover provided by the policies in the portfolio being modelled. We should also consider information regarding current and future claims and hence reserve uncertainty; that is, we should consult the claims department regarding likely future court precedents, possible legislative changes (such as changing Ogden rates) and economic and social factors that may affect attitudes to claiming and the size of claims

Question 22

List ways in which a capital model may be used in other areas of the business.

USE TEST?

Answer 22

1. reinsurance: optimising the purchase of reinsurance
2. investment: assessing the impact of a change in the investment mix
3. pricing: assessing return on capital for pricing and performance measurement
4. reserving: quantifying the uncertainty in claims reserves
5. planning: comparing different plans in terms of their risks, not just expected profits
6. strategy: assessing the risks and diversification benefit of new strategies
7. risk management: identifying key risks and assessing the impact of mitigation.

Question 23

Lack of data for capital modelling - how to deal with it?

Answer 23

Use benchmark data, but it may not reflect the insurer’s risk profile discuss with how pricing and reserving actuaries are dealing with it and take a consistent approach. qualitative views of other SMEs

Question 24

5 Types of correlation to allow for in our models

Answer 24

Correlation between the following categories:

• Underwriting classes of business (e.g. motor and household)
• Risk Types (e.g. underwriting risk and reserving risk)
• Successive years (one year correlated with the previous)
• Legal entities within a group