Chapter 18: Modelling

Question 1

What is a model?

Answer 1

A model can be defined as a ‘cut-down, simplified version of reality that captures the essential features of the problem and aids understanding and in producing potential solutions to the problem

It is important to be able to communicate the results effectively

Question 2

Modelling requires a balance to be struck between which two things?

Answer 2

1. Reality, and hence complexity
2. Simplicity, for easy of use, verification and interpretation of results

Question 3

What is the advantage of an actuarial model over a formula?

Answer 3

A model is better able to reflect uncertain future events by giving an indication of the effects of varying the assumptions.

This is important so that the client understands the uncertainty involved in the underlying assumptions

Question 4

Where might a model come from and what factors affect the decision about where to get it

Answer 4

Internal
- New model developed from scratch
- Modify an existing model

External
- Commercially available models

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The decision depends on:

• Availability of a model
• Do you have in-house expertise
• Do you have time
• How often you are going to use the model
• Costs
• Level of flexibility required
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Question 5

Outline the operational issues that need to be considered when designing and constructing a model

Answer 5

SCARCER DVR’S

Simple, but retains key features
Clear results (Output reasonable)
Adequately documented
Range of implementation methods (to facilitate testing and parameterisation, and based on the focus of the results)
Communicable workings and output
Easy to understand
Refineable and developable over time

Dynamic: Assumptions used to model assets and liabilities must be consistent
Valid for purpose
Rigorous
Sensible joint behavior of variables (eg higher expense inflation means higher claims inflation, etc).

Question 6

Define what is meant by ‘dynamism’ of a model

Answer 6

If a model is dynamic, then the assumptions used to model assets and liabilities are consistent with each other and are programmed to interact under different scenarios as they do in reality.

For example:

• Inflation rates and investment returns
• Bonus rates and investment returns
• Withdrawal rates and economic conditions

Question 7

Developing a deterministic/stochastic model

Answer 7

Specify the problem

• Pricing vs Reserving
• Are we interested in snapshot reserves or cashflows over time
• Internal or external use

Collect and modify data where necessary

Choose:

• Model (whether to use a stochastic or deterministic model or a hybrid, and which one of the available models)
• Variables (claims, expenses and premiums)
• Parameters (economic, demographic, …)
• Stochastic: prob density function and correlation matrix)

Construct the model and check for errors

Check “goodness of fit”

• Output reasonable
• Can you replicate last year’s results
• Scenario/sensitivity tests
• Spot checks

If okay, calculate and interpret the results

Question 8

Outline the two factors to consider in choosing the time period (or frequency) for the projection of the cashflows in a model

Answer 8

1. The more frequently the cashflows are calculated the more reliable the output from the model, although there is a danger of spurious accuracy (false accuracy)
2. The less frequently the cashflows are calculated the faster the model can be run, and results obtained

Question 9

What are the RELATIVE merits of deterministic vs stochastic models?

Answer 9

Deterministic:

• Quicker, cheaper and easier to design, build and run
• Clearer what scenarios have been tested
• Results are easier to explain to a non-technical audience

Stochastic:

• Allows naturally for the uncertainty of outcomes
• Enable better modelling of the correlations between variables
• Test a wider range of scenarios
• Good at identifying extreme outcomes, which may not have been thought of under a deterministic scenario
• Important in assessing the impact of financial guarantees

Question 10

Outline how a deterministic model could be used to determine a set of new premium rates for a term assurance contract

Answer 10

1. An objective would be set based on profit criterion and an appropriate time horizon
2. Data relating to the existing profile of customers would be collected and model points created. It would be modified for any perceived future differences in the profile of customers
3. Parameter values for key assumptions such as mortality, expenses, lapses and investment returns would be set based on past experience
4. For each model point, the model would be run, projecting future cashflows and discounting the net profits at the risk discount rate (RDR). The premium would be varied until the required profit criterion is met.

Question 11

List four methods of assessing statistical risk

Answer 11

1. In some situations, analytically – by considering the variances of the individual parameter values used
2. By using sensitivity analysis, with deterministically assessing variations in parameter values
3. By using stochastic models for some, or all, if the parameter values and simulation
4. By comparison with any available market data

Question 12

What should the rate used to discount the net cashflows in model reflect

Answer 12

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

NOTE: In theory a different discount rate should be used for each cashflow (as the risk is different); In practice a single rate is often used based on the average risk of the product

Question 13

What are model points? Why are they used? How may they be chosen?

Answer 13

A model point is a representative single policy

The business being modelled may comprise a very large number of different policies and it may be too time consuming to run all of these through a model.

So, policies are classified into relatively homogeneous groups.

A model point for each group is chosen that is representative of the whole group.

The model point is run through the model and the output is then scaled up by the number of policies in the group to give the results of the whole group.

For pricing purposes, model points are chosen to reflect the expected profile of future business to be sold. This could be based on the existing profile, or that of a similar product.

Question 14

When are model points not used?

Answer 14

Model points are not generally used when VALUING LIABILITIES for calculating reserves.

The normal procedure for determining the value of life assurance or pension scheme liabilities is to value the benefits for each actual policy or scheme member individually.

In many territories this may be a regulatory requirement

However, model points may be required in order to answer various ‘what if’ questions

Question 15

How can models be used in risk management?

Answer 15

Models can be used to determine:
- The extent of a risk event that will occur with a given probability

• The amount of capital that is needed to support such an event

Question 16

Explain briefly how a model could be used to assess the capital requirements and the return on capital when writing a new contract.

Answer 16

Take the cashflows from the pricing model and scale/gross up for the expected volumes of new business

The capital requirement will be equal to the new business strain plus any one-off development costs, to the extent that they are not amortized and already included in the cashflows used.

The expected return on capital can be calculated by equating the capital requirement with the NPV of the profit stream that is expected to emerge.

Question 17

Other than profitability and marketability, what is another big consideration in determining a suitable set of premium rates?

Answer 17

1. The capital requirement of the contract
2. The return on capital

Question 18

Outline five factors that might be reconsidered, if the premium rates are not thought to be marketable/competitive

Answer 18

1. The design of the contract, to remove feature that increase the riskiness of the net cashflows or to add differentiating features
2. The distribution channels
3. The profit criterion (company’s profit requirement)
4. The size of the market
5. The decision to market the contract in the first place

Question 19

Explain why a life insurance company may decide that the profit criterion does not need to be met for all model points

Answer 19

If all model points were profitable in their own right, this may result in a set of premium rates that is:
- Not smooth between different types of policyholder

• Not competitive

It is more usual to try to ensure that the profit criterion is met in aggregate

Question 20

What are the different ways of allowing for risk in a model?

Answer 20

1. It can be allowed for through the risk element of the risk discount rate
2. Alternatively, use a pre-determined discount rate but incorporate margins in the individual parameter values, e.g. mortality rates, expenses.
3. If a probability distribution can be assigned to a parameter, it may be possible to derive analytically the variance of the profit or capital requirement.
4. A stochastic model or sensitivity testing could be used to show the variation in results. (Risk could be allowed for by taking a more prudent confidence level result)

Question 21

Define model error and state how it can be assessed

Answer 21

Model error – the risk that the model is inappropriate for the contracts being modeled
- It can be assessed using goodness of fit tests

Question 22

Define parameter error and state how it can be assessed

Answer 22

Parameter error – The risk of mis-estimation of parameter values
- It can be assessed using a sensitivity analysis. The results of the analysis can help in assessing the margins to be incorporated into the parameter values or to quantify the effect of departures from the chosen parameter values

Question 23

Explain why even a stochastic model does not illustrate the complete variability of results

Answer 23

The results of a stochastic model are dependent on the probability distributions chosen for the stochastically modelled assumptions, the parameter values of this distribution and the correlation of the assumptions

Not all assumptions are modelled stochastically in a stochastic model. Some of the deterministic parameter values may be uncertain

The stochastic model could be re-run using:

• Different probability distributions
• Different parameters for the distributions
• Different correlation coefficients
• Different values of the deterministically modelled assumptions

Question 24

Two model validation tools

Answer 24

1. Sensitivity Analysis - vary individual assumptions and inputs to assess the impact on the results.
2. Scenario Testing - changing assumptions in combination to represent an economic scenario such as a recession.