18 - Modelling

Question 1

Give the different sources of model used to solve a financial or actuarial problem.

Answer 1

1. Commercially produced product
2. Modify and reuse an existing model
3. Developing a new model

Question 2

Define:
1.Sensitivity analysis

2.Scenario testing

Answer 2

1. Sensitivity analysis - varying individual assumptions and assessing the impact on the results
2. Scenario testing – changing many assumptions in combination, for example, to look at the many assumptions that may change if the economy were to move into a recession

Question 3

How do we assess the VARIABILITY of the solution/results to a problem that is solved through modelling?

Answer 3

1. Sensitivity testing

2. Scenario testing

Question 4

Give the two main objectives of modelling that contradict each other.

Answer 4

1. Realism

2. Simplicity - for ease of application, verification and interpretation

Question 5

Give factors that need to be considered in finding the right model (5)

Answer 5

1. The level of accuracy required
2. The ‘in-house’ expertise available - staff with knowledge of specific coding languages
3. The number of times the model is to be used or reused
4. The desired flexibility of the model
5. The cost of each option

Question 6

Give the activities of a life insurance company that could require the use of models.

Answer 6

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

Question 7

What should a chosen set of model points aim to represent?

Answer 7

The expected new business under a new product - similar existing products and market information

Question 8

Give the factors to consider when choosing the number of model points. (5)

Answer 8

1. Available computing power
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 9

What should the discount rate in modelling aim to capture?

Answer 9

1. The return required by the company

2. The level of statistical risk attached to the cashflows under a particular contract.

Question 10

Give the main risks when constructing a model?

Answer 10

1. Model risk
2. Parameter risk
3. Random fluctuation risks
4. Data risk

Question 11

How is the level of statistical risk assessed when constructing a model?

Answer 11

1. Analytically - considering the variances of individual parameters
2. Sensitivity analysis - with deterministically assessed variations in the parameter values
3. Stochastic models - for certain parameters with simulation / Use stochastic RDR
4. Comparison with available market data

Question 12

Between economic and demographic assumptions, which is modelled deterministically and which are modelled stochastically?

Answer 12

Economic - stochastic

Demographic - deterministic

Question 13

Define: Model error

Answer 13

The model is not appropriate for the problem being modelled.

Question 14

How do we check for model error?

Answer 14

Using goodness of fit tests

Question 15

Define: parameter error

Answer 15

The effect of mis-estimation of parameter values

Question 16

How does one check for parameter error?

Answer 16

Sensitivity testing

Question 17

Describe the two courses of action available if there is an unacceptable impact of a specific assumption within a model.

Answer 17

1. Redesign the product - remove features that create the financial impact of a certain parameter
2. Increase the margins for prudence

Question 18

Give the operational issues that need to be considered when constructing a model.

(Requirements of a good model)

Answer 18

MODEL INPUTS

1. Have feasible joint behaviour of variables
2. Parameters allow for significant features

MODEL WORKINGS

3. Be well documented
4. Not be overly complex or time-consuming to run
5. Be capable of development and refinement
6. Be capable of being implemented in a range of ways
7. Balance speed and reliability of results when choosing a time period between cashflows and time horizons
8. Should be dynamic and allow for interactions between parameters
9. Simple but retain key features
10. Reflects risk profile of contracts modelled

MODEL OUTPUT

11. Be easily communicable with clearly displayed results
12. Be capable of independent verification
13. Results displayed clearly

Question 19

Outline the key steps in developing a model.

Answer 19

1. Specify the purpose and key features of the model
2. Obtain and adjust the data
3. Set the parameters, their correlations, assumptions and dynamic links - past data and estimation
4. Construct the model cashflows
5. Check the accuracy of the fit of the model - to address model errors
6. Run the model as many times as required - to check parameter errors through scenario and sensitivity testing.
7. Output and summarise the results

Question 20

Give the advantages of adapting an existing model to a new problem.

Answer 20

1. A company might already be selling similar products
2. Adapting an existing model may be cheaper than purchasing a new one or developing a new one
3. Current staff will have an understanding of the limitations and working of existing models.
4. Can ensure consistency with existing models
5. Current staff will develop skills in modelling, which could reduce the requirement on commercial models in the future.

Question 21

Give the advantages of purchasing a commercial model.

Answer 21

1. The model should be well designed and validated

2. The model may be more flexible than existing models and may be more useful for future other purposes.

Question 22

Give the advantages of deterministic models.

Answer 22

1. Simple
2. Relatively cheap
3. Clarity as to which economic scenarios have been tested
4. Speed of design
5. Speed of running
6. Ease of communication

Question 23

Give the advantages of stochastic models

Answer 23

1. Tests a wide range of economic scenarios
2. Including scenarios that may not have been thought of in a deterministic model
3. Allows better for the random nature of variables
4. Allows better for the correlations between variables
5. Is more useful for assessing the impact of financial guarantees
6. Is more useful for allowing for mismatching

Question 24

Define: model point

Answer 24

A representative single policy or group of policies capturing the most important characteristics of the policies it represents

Question 25

Give the general characteristics of an insurance policy that a model point should aim to capture. (9)

Answer 25

1. Duration in force
2. Claim amount
3. Sum assured
4. Claim basis - single/joint/last survivor
5. Age
6. Gender
7. Smoker status
8. Health status
9. Term of the policy

Question 26

Give the factors of a pricing model and product design that influence the competitiveness of a product.

Answer 26

1. The product design
2. The distribution channels
3. The profit requirement
4. The size of the market
5. Whether the product is viable at all

Question 27

Give two non-product design factors that should be considered when doing a product design model.

Answer 27

1. Business strategy

2. Capital requirements

Question 28

List the decrements to take into account when modelling financing strategies for benefit schemes.

Answer 28

1. Death before retirement
2. Death after retirement
3. Withdrawal from active service
4. Transfer out
5. Ill-health retirement
6. Normal / early / late retirement
7. Options on benefits

Question 29

Give the limitations of models

Answer 29

1. Results are only as good as the underlying model - model error
2. Results depend on the quality of the data used - data error
3. The results depend on the suitability of assumptions used - parameter error
4. The level and timing of cashflows is uncertain so the actual experience will differ from the model result - random fluctuation error