CH17 - Modelling

Question 1

Finding a model (3) + (5)

Answer 1

1. A commercially produced product could be purchased
2. An existing model could be reused, possible after modification
3. A new model could be developed

The merits of each of these approaches will depend on the following:

1. the level of accuracy required
2. the ‘in-house’ expertise available
3. the number of times the model is to be used
4. the desired flexibility
5. the cost of each option

Question 2

Operational issues to consider for a model (8)

Answer 2

The model should:

1. be well documented
2. be easily communicable, with clearly displayed results
3. have sensible joint behaviour of variables (this means that the model needs to make an allowance for variables that are linked to each other)
4. be capable of independent verification (the outputs from the model should be capable of independent verification for reasonableness and should be communicable to those to whom advice will be given)
5. not be overly complex and time-consuming to run
6. be capable of development and refinement
7. be capable of being implemented in a range of ways (a range of methods of implementation should be available to facilitate testing, parameterisation and focus on results)
8. have an appropriate time period between projected cashflows, balancing the reliability of the output with the speed of running a model. (the more frequently the cashflows are calculated the more reliable the output from the model, although there is a danger of spurious accuracy. the less frequently the cashflows are calculated the faster the model can be run and results obtained)

Question 3

Key steps in developing and running a model (7)

Answer 3

1. Specify the purpose and key features of the model
2. Obtain and adjust the data
3. Set the parameters / assumptions, including any dynamic links
4. Construct the model cashflows
5. Check the accuracy and fit of the model, and amend if necessary
6. Run the model as many times as required
7. Output and summarise the results

Question 4

The premiums / charges resulting from the model need to be considered relative to the market. This may require reconsideration of (5)

Answer 4

1. The product design
2. The distribution channel (s)
3. The profit requirement
4. The size of the market
5. Whether to go ahead with the product

Question 5

List ten areas of a life insurance company’s activities that involve taking a view on uncertain future events, and hence might require an actuarial model.

Answer 5

1. Calculating provisions
2. Setting premium rates
3. Assessing reinsurance requirements
4. Estimating future investment returns
5. Estimating future mortality improvements
6. Estimating future discontinuance rates
7. Estimating future expense levels
8. Determining future capital requirements
9. Estimating future new business levels
10. Valuing guarantees and/or options

Question 6

What is a model?

Answer 6

A model can be defined as ‘a cut-down, simplified version of reality that captures the essential features of a problem and aids understanding’.
The final phrase in this definition recognises the importance of being able to communicate the results effectively.
Modelling requires a balance to be struck between realism (and hence complexity) and simplicity (for ease for application, verification and interpretation of results).

Question 7

Deterministic model

Answer 7

A deterministic model is one where the parameter values are fixed at the outset of running the model and the result of running the model is a single outcome. Sensitivity analysis and scenario testing can then be carried out to assess the potential variability of the results.

Question 8

Stochastic model

Answer 8

A stochastic model estimates at least one of the parameters by assigning it a probability distribution. The model is run a large number of times, with the values of stochastic parameters being selected from their distributions of each run. The outcome is a range of values, giving an understanding of the likely distribution of outcomes.

Question 9

Advantages of a deterministic model (3)

Answer 9

1. A deterministic model is more readily explicable to a non-technical audience, since the concept of variables as probability distributions is not easy to understand.
2. It is clearer what economic scenarios have been tested.
3. The model is usually cheaper and easier to design, and quicker to run.

Question 10

Disadvantages of a deterministic model (2)

Answer 10

1. It requires thought as to the range of economic scenarios that should be tested.
2. Users can get ‘blinded by science’ by complex models, assuming they must be working correctly, but without verifying or testing this.

Question 11

Advantages of a stochastic model

Answer 11

A stochastic model tests a wider range of economic scenarios. It does depend on the parameters that are used in any standard investment model.

The actuary needs to decide whether the increased amount of information that a stochastic valuation will provide justifies the significant additional computations needed.

Question 12

Disadvantages of a stochastic model (5)

Answer 12

1. Programming is more complex
2. Run time is longer
3. A degree of spurious accuracy may be introduced
4. Increased difficulty in interpreting and communicating the results
5. Accuracy of the distribution functions that are replacing the deterministic values

Question 13

Steps for developing a deterministic model (9)

Answer 13

Deterministic modelling could involve the following steps:

1. specify the purpose of the investigation
2. collect, group and modify data
3. choose the form of the model, identifying its parameters or variables
4. ascribe values to the parameters using past experience and appropriate estimation techniques
5. construct a model based on the expected cashflows
6. test the model in order to identify any build errors, and correct if necessary
7. check that the goodness of fit is acceptable (and attempt to fit a different model if the first choice does not fit well)
8. run the model using estimates of the values of variables in the future
9. run the model several times to assess the sensitivity of the results to different parameter values

The model might also be run under different scenarios to test the robustness of the results to many parameters changing at the same time.

Question 14

Steps for developing a stochastic model (9) + (4)

Answer 14

Deterministic modelling could involve the following steps:

1. specify the purpose of the investigation
2. collect, group and modify data
3. choose the form of the model, identifying its parameters or variables
4. ascribe values to the parameters using past experience and appropriate estimation techniques
5. construct a model based on the expected cashflows
6. test the model in order to identify any build errors, and correct if necessary
7. check that the goodness of fit is acceptable (and attempt to fit a different model if the first choice does not fit well)
8. run the model using estimates of the values of variables in the future
9. run the model several times to assess the sensitivity of the results to different parameter values

Stochastic modelling would involve the same process as above, with the following additional or alternative steps:

1. choose a suitable density function for each of the variables to be modelled stochastically
2. specify correlation between variables
3. run the model many times, each time using a random sample from the chosen density function(s)
4. produce a summary of the results that shows the distribution of the modelled results after many simulations have been run, e.g. at various confidence levels.

Question 15

The use of model points

Answer 15

The underlying business being modelled will typically comprise a very wide range of different policies, and these will need to be brought together into a manageable number of relatively homogeneous groups. The groupings need to be made in a way that each policy in a group is expected to produce similar results when the model is run. It is then sufficient for a representative single policy in each group to be run through the model, the result to be found, and for this result to be scaled up to give the result of the total set of policies in the group.
The representative single policy in a group is termed a ‘model point’ and a set of such model points can then be used to represent the whole of the underlying business.

Question 16

Characteristics that should be captured by the model points that would be used when modelling a without-profit term assurance product in order to set premiums (7)

Answer 16

1. term of the policy
2. sum assured payable on death
3. claim basis of policy (single life, joint life, last survivor)
4. age of life / lives covered
5. gender of life / lives covered
6. smoker status of life / lives covered
7. health status of life / lives covered

Question 17

Number of model points depend on (5)

Answer 17

1. the computing power available
2. time constraints
3. the heterogeneity of the class
4. the sensitivity of the results to different choices of model points
5. the purpose of the exercise

Question 18

Risk discount rate allows for (2)

Answer 18

1. the return required by the company
2. the level of statistical risk attaching to the cashflows under the particular contract, i.e. their variation about the mean as presented by the cashflows themselves

Question 19

Ways the level of statistical risk could be assessed (4)

Answer 19

1. in some situations, analytically - by considering the variances of the individual parameter values used
2. by using sensitivity analysis, as described below, with deterministically assessed variations in the parameter values
3. by using stochastic models for some, or all, of the parameter values and simulation
4. by comparison with any available market data

Question 20

The premiums, or charges, produced need to be considered for marketability. This might lead to a reconsideration of (5)

Answer 20

1. the design of the product, so as either to remove features that increase the risks within the net cashflows, or to include features that will differentiate the product from those of competing companies
2. the distribution channel to be used, if that would permit either a revision of the assumptions to be used in the model, or a higher premium or charges to be used without loss of marketability
3. the company’s profit requirement
4. the size of the market
5. whether to proceed with marketing the product