CH 18: Modelling

Question 1

What is a model?

3

Answer 1

• A model can be defined as a ‘cut-down, simplified version of reality that captures the essence of the problem and aids understanding
• It is important to be able to communicate the results effectively
• Can be purchased,reused,developed depending on costs,expertise and level of accuracy available

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:
   - Fit for purpose
   - Expertise available in-house
   - Need for flexibility
   - Cost of each option
   - Expected number of times the model is to be used
   - Desired level of accuracy

Question 3

Developing a model

3

Answer 3

• Actuarial problems require assumptions about uncertain future events.
• Varibility of answers are important as assumptions vary.
• Assess variability using:
  Sensitivity analysis: vary individual assumptions and assess impact
  Scenaro testing: Combination of assumption changes and assess impact

Question 4

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

2

Answer 4

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 5

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

Answer 5

Simple, but retains key features, approx instead of model
Clear results
Adequately documented: Key assumptions, approx
Range of implementation methods
Communicable workings and output
Easy to understand
Refineable and developable

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

SCARCER FILES

Question 6

What are model points? Why are they used? How are they used?

4

Answer 6

• A model point is a representative single policy from a large homogeneous group that captures most important characteristics of the group
• 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.
• 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 7

When are model points not used?

3

Answer 7

• 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 8

Risk discount rate and model points

2

Answer 8

• For each MP CF’s will be projected, allowing for reserving and solvency margins on base parameter values.
• Projected CF’s are then discounted@ discount rate

Question 9

What factors make up the risk discount rate?

2,4

Answer 9

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

Assess Statistical risk:
* Analytically: variance of parameter values
* Sens analysis: assess variation or parameters
* Stoch models: simulate dbn of parameter values
* Compare: to Market data

Question 10

Determinstic Models

1,3,3

Answer 10

• Model where parameter values are fixed and a single outcome is provided. Sens/Scen tests to check variability

Advantages:
- Cheaper, faster and easier to design, build and run
- Clearer what scenarios have been tested
- Results are easier to explain to a non-technical audience

Disadvantages:
* Results are highly dependant on assumptions
* Can lead to inaccurate results
* Test small range of scenarios

Question 11

Stochastic Models

1,5,3

Answer 11

• Atleast 1 parameter is assigned a distribution. Model is run on multiple simulations and parameter values vary. Outcomes are a distribution.

Advantages:
- Allows naturally for the uncertainty of outcomes
- Enable better modelling of the correlations between variables more accurate results
- 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

Disadvantages:
* Large amt of info required
* Slower and more expensive to develop and run
* More difficult to explain

Combined model: High risk variable are stoch while others deterministic
eg Stoch for econ assumptions and det for demographic assumptions

Question 12

Define what is meant by ‘dynamism’ of a model

1,1

Answer 12

• If a model is dynamic, then the asset and liability parts of the model and all the assumptions are consistent with each other and are programmed to interact under different scenarios as they do in reality.
• Interactions need to be determined using actuarial judgement. more NB than type of model.

For example:
- Inflation rates and investment returns
- Bonus rates and investment returns
- Withdrawal rates and economic conditions

Question 13

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

Answer 13

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. Sensitivity tests (and maybe scenario test) using different parameter values

Question 14

Additional / Alternative steps in a stochastic model

Answer 14

1. Choose a density function for each of the stochastic variables
2. Specify correlations between the variables
3. Run model many times using a random sample from the chosen density function
4. Produce a summary of results – a distribution (e.g. summarized at various confidence levels)

Question 15

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

Answer 15

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 16

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

2

Answer 16

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

Question 17

Explain the reliability of results and Variability of experience factors of sensitivity testing

1,2

Answer 17

Reliability of results:
* Depend on the paramter values correctness

Variability of experience:
* Stoch model can show range of variability but results depend on correctness of parameters(assumptions)
* Det model uncertainty is greater as fewer scenarios tested

Question 18

Explain parameter error

2

Answer 18

Parameter error:
* The risk of mis-estimation of parameter values
* Assessed using a sens 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 19

Define model error and state how it can be assessed

2

Answer 19

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

Question 20

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

4

Answer 20

1. Statistical risk allowed for through the risk element of the risk discount rate. Rf rate req by shareholders + risk margin
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

Explain the factors used to determine Pricing models

3

Answer 21

• Models used to determine premiums that meet companys profit criterion
• MP used to represent profile of NUB and existing business

i.Profit criterion
ii.Competitive premiums
iii.Business strategy
iv.Capital req and ret on capital

Question 22

Profit Criterion

3

Answer 22

• Premiums for MP set to produce profit required in aggregate w/o each MP being profitable (due to expenses)
• Cross subsidies between MP are also accounted for
• Once premiums det for MP, contract variations determined by interpolation

Question 23

Competitive premiums and business strategy

1,2

Answer 23

Competitive premiums:
* Contract Design,Distribution,Profit req are reconsidered due to competition.

Business strategy:
* Net CF from MP scaled up for expected NUB used in business model
* Assess impact on capital management

Question 24

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

3

Answer 24

• Take the cashflows from the pricing model and 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 25

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

Answer 25

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 26

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

Answer 26

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