Chapter 18 - Modelling

Question 1

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

Answer 1

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

Question 2

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

Answer 2

1. A new model might be developed in-house
2. An existing model might me modified
3. A commercial model might be purchased externally
4. The factors that need to be considered are:
   CAN IF

• COST and timeline of each option
• ACCURACY level required
• Expected NUMBER of times the model is to be used
• IN-HOUSE Expertise available
• Desired FLEXIBILITY of model

Question 3

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

Answer 3

SCARCER FILES

Simple, but retains key features
Clear results
Adequately documented
Range of implementation methods should be available to facilitate testing
Communicable workings and output
Easy to understand
Refineable and developable

Frequency of cashflows (balance accuracy vs practicality)
Independent verification of outputs
Length of run not too long
Expense not too high
Sensible joint behavior of variables

Question 4

Set out the steps involved in developing and running a deterministic model

Answer 4

1. Specify the purpose of the investigation
2. Collect, group and modify data
3. Choose the form of the model and its parameters / variables
4. Ascribe values to those parameters using past experience / estimations
5. Construct a model based on expected cashflows
6. Test the model and correct if necessary
7. Check goodness of fit using past data, modify if poor
8. Run using estimates of future values of variables
9. Run the model several times to assess the sensitivity of the results to different parameter values

Question 5

Additional / Alternative steps in a stochastic model

Answer 5

1. Specify the purpose of the investigation
2. Collect, group and modify data
3. Choose a density function for each of the variables to be modelled stochastically
4. Specify correlations between the variables
5. Ascribe values to those variables that are not being modelled stochastically
6. Construct a model based on expected cashflows
7. Test the model and correct if necessary
8. Check goodness of fit using past data
9. attempt to fit a different model if the first model does not fit well
10. Run model many times using a random sample from the chosen density function
11. Produce a summary of results that shows the distribution of the modelled results after many simulations have been run
12. Choose a density function for each of the stochastic variables
13. Specify correlations between the variables
14. Run model many times using a random sample from the chosen density function
15. Produce a summary of results – a distribution (e.g. summarized at various confidence levels)

Question 6

What are the relative merits of deterministic vs stochastic models?

Answer 6

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:
GATE I

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

Question 7

List four methods of assessing statistical risk

Answer 7

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 8

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

Answer 8

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 9

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

Answer 9

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 10

When are model point not used?

Answer 10

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 11

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

Answer 11

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

Question 12

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

Answer 12

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
4. The size of the market
5. The decision to market the contract in the first place

Question 13

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

Answer 13

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 14

Define model error and state how it can be assessed

Answer 14

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

Question 15

Define parameter error and state how it can be assessed

Answer 15

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 16

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

Answer 16

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 17

What is a deterministic model

Answer 17

It is where the parameter values are fixed at the outset of running the model and the result of running the model is a single outcome.

Question 18

What is a stochastic model?

Answer 18

It estimates at least one of the parameters by assigning it a probability distribution. The model is run a large number if times, with the values of stochastic parameters being selected from their distributions on each run