Chapter 29: Modelling

Question 1

What is a model?

Answer 1

A cut-down, simplified version of reality that captures the essential features of a problem and aids understanding.

A model is a small representation of the real thing, designed to show all the important features of the real thing - consistent with the model’s scale and use.

Question 2

Where might the model come from and what factors might affect the decision?

Answer 2

It may be

• a new model, developed in house
• a modification of an existing model
• or a commercial product purchased externally.

The decision will depend on 
● the level of accuracy required
● the “in-house” expertise available
● the number of times the model is to be used
● the desired flexibility of the model
● the cost of each option.
- expertise,
- the usage of the model,
- whether the model is fit for purpose.

Question 3

9 Requirements of a good model

Answer 3

A good model will

• be valid, rigorous and well documented
• reflect the risk profile of the business being modelled
• allow for all the significant features of the business being models
• be easy to appreciate and communicate
• have appropriate input parameters and parameter values
• have output that can be verified independently
• not be overly complex or time-consuming to run
• be capable of development and refinement
• be capable of being implemented in a range of ways

Question 4

What is a dynamic model?

Answer 4

By dynamic we mean that the asset and liability parts are programmed to INTERACT AS THEY DO IN REALITY and the assumptions affecting assets and liabilities, for example inflation and interest rates, are consistent.

Question 5

Which cash-flows should a model allow for?

Answer 5

All cashflows that may arise.
In particular:
- cashflows relating to both guaranteed and discretionary benefits
- cashflows arising from the requirement to calculate provisions
- cashflows relating to options

Question 6

Advantages of deterministic models

Answer 6

• quicker to design, build and run
• clearer what scenarios have been tested
  ● more readily explicable to a non-technical audience, since the concept of variables as probability distributions is not easy to understand.

Question 7

10 Steps involved in using a deterministic model

Answer 7

• Specify the purpose
• Collect, group and modify the date
• Choose the form of the model
• Identify the parameters and variables
• Ascribe the parameter values
• Construct a model based on expected cashflows
• Check if the goodness of fit is acceptable
• Fit a new model if the first choice does not fit well
• Run the model using estimates of the values of the variables, in the future
• Sensitivity test the parameters

Question 8

9 Steps involved in using a stochastic model

Answer 8

• Specify the purpose
• Collect, group and modify the data
• Choose a suitable density function for each stochastic variable
• Specify the correlations between the variables
• Construct a model based on expected cashflows
• Check that the goodness of fit is acceptable
• Fit a new model if the first choice does not fit well
• Run the model many times using randomly generated values of the stochastic variables
• Produce a summary of the results

Question 9

Specifying the purpose of a model, involves setting an overall time horizon and a time period for the output of cashflows.
How should the time period be chosen?

Answer 9

The time period should be frequent enough that the output is reliable that there is spurious accuracy or that the model takes too long to run.

Question 10

What is a model point and why are they used?

Answer 10

A model point is a representative single policy.

It may be too time consuming to run every actual policy through a model, so policies are classified into relatively homogeneous groups.
A model point for each group is chosen. The output is then scaled up to give the results for the whole group.

Question 11

How are model points chosen?

Answer 11

Model points are chosen to reflect the expected profile of future business.
This could be based on the existing profile or that of a similar product.

Question 12

What should the discount rate used in a model reflect?

Answer 12

The return required by the company.
The level of statistical risk attaching to the cashflows.

In theory, a different discount rate should be used for each cashflows. In practice, a single rate is often used.

Question 13

4 Ways in which the level of statistical risk attaching to the cashflows is ascertained.

Answer 13

• analytically, by considering the variances of the individual parameters used
• by using sensitivity analysis
• by using a stochastic model
• by comparison with any available market data.

Question 14

When using a model to set premiums, what questions should be asked about the resultant premiums?

Answer 14

• Are the premiums marketable?
• Is the contract profitable on aggregate, when scaled up for expected new business volumes and built into a model of the whole company?
• What are the capital requirements of the contract?

Question 15

If the contract is not marketable, what might need revising?

Answer 15

The design of the contract to remove risky features or to add differentiating features.

Alternatively, reconsider the sales channel, the profit criterion, or the decision to market the contract in the first place.

Question 16

How would you assess the capital requirements of a contract using a model?

Answer 16

Scale up the capital requirements for individual model points by the expected new business volumes.
Add in the one-off contract development expenses.

Question 17

Why are model points not generally used for calculating provisions?

Answer 17

Regulations often require that provisions be calculated separately for each individual contract, which means that model points can not be used.

Question 18

For a benefit scheme, modelling can be used to set the future financing strategy.
What might be true of the relation between the asset and liabilities for a pension fund that would not be true for an insurer?

Answer 18

The benefit scheme can show a deficit at a point in time, as long as the scheme sponsor will be able to make up that shortfall over an appropriate time period.

Question 19

What type of model should be used for valuing options and guarantees?

Answer 19

A stochastic model

Question 20

What errors are involved in running models?

Answer 20

• Model error

- Parameter error

Question 21

What are the different ways of allowing for risk margins and assumptions?

Answer 21

• Through the risk element of the risk discount rate.
• Alternatively, use a predetermined discount rate but incorporate margins in the individual experience assumptions,
• Or use a stochastic model.

Question 22

2 Disadvantages of a deterministic model

Answer 22

It REQUIRES THOUGHT as to the range of economic scenarios that should be tested.

Since only a limited number of economic scenarios will be tested, there is a danger that certain scenarios, which could be particularly detrimental to the company, are not identified.