CHP 29

Question 1

1.3. What is a model?

Answer 1

Simplified version of reality that captures the essential features of a problem and helps understanding.
Modeling requires a balance to be struck between realism and simplicity.

Question 2

1.4. Finding a model

Answer 2

Various approaches to modeling:
• Commercial modeling product can be purchased
• Existing model could be reused (possibly after modification)
• Develop a new model

Question 3

Merits of each model choice will depend on:

Answer 3

• Level of accuracy required
• In-house expertise available
• Number of times the model is to be used
• Desired flexibility of the model
• Cost of each option
Make sure the model is fit for purpose. This is particularly important when purchasing a model externally or reusing an old model for a different purpose.

Question 4

1.5. Existing models

Answer 4

There are a large number of stochastic asset models in existence, e.g. Wilkie, log-normal
There are fewer models available for other variables, e.g. mortality and voluntary discontinuance – these are starting to be developed.

Question 5

2.1. Why build a model

Answer 5

Prime objective is to enable the provider of financial products to be run in a sound financial way.
Models will be used in the day-to-day work to provide checks and controls on the business.

Question 6

2.2. Requirements of a good model

Answer 6

Models will need to satisfy the following requirements:
1. Model must be valid, rigorous enough for the purpose and adequately documented.
2. Capable of reflecting the risk profile of what is being modeled accurately.
3. Parameters should allow for all features of the business being modeled that could affect advice given.
4. Inputs should be appropriate to the business and,
o Take into account special features of the provider
o Economic and business environment
5. Workings of the model should be easy to appreciate and communicate – display results clearly.
o Model should exhibit sensible joint behavior of model variables.
6. Outputs should be capable of independent verification and should be communicated to relevant parties.
7. Model must not be overly complex – results become difficult to interpret and model becomes too long and expensive to run. Avoid the impression that everything can be modeled.
8. Capable of development and refinement
9. A range of methods of implementation should be available to facilitate testing, parameterization and focus of results.

Question 7

Merits of a deterministic model

Answer 7

• More readily accessible to a non-technical audience, since the concept of variables as probability distributions is not easy to understand.
• It is clearer what economic scenarios have been tested
• The model is usually easier to design and quicker to run.

Question 8

disadvantages of a deterministic model

Answer 8

• It requires thought as to the range of economic scenarios that should be tested. Some detrimental scenarios may not be thought of.

Question 9

Merits of a stochastic model:

Answer 9

• Tests a wider range of economic scenarios.
• The programming is more complex and takes longer to run – benefit is quality of result.
• It depends on the parameters that are used in any standard investment model.
• Particularly important when assessing the impact of financial guarantees.

Question 10

2.5. Dynamism of the model

Answer 10

This is vital – it is the way assets and liabilities interact. This should be realistic.
Rules for how various features interact under different circumstances need to be developed.
These interactions are usually much more important than the type of model.
Actuarial judgment may be needed in choosing and using the model.
Also in setting the parameters and interactions between the different features.

Question 11

3.1. Cashflows to be modeled

Answer 11

An actuarial model must allow for all the cashflows that may arise.
These will depend on the nature of the financial products, schemes, contracts or transactions being modeled and any discretionary benefits they carry.
Also allow for any cashflows from a supervisory or commercial requirement to hold reserves and maintain adequate solvency capital.
Cashflows must allow for interactions – especially when assets and liabilities are modeled together.
Allow for cashflows from options and the take up of these (where applicable).
Some cases use stochastic models and simulation, e.g. financial guarantees.

Question 12

3.2. Appropriate time period

Answer 12

The time period in the projection must be chosen bearing in mind that:
• The more frequently the CF’s are calc’ed, the more reliable the output – danger is spurious accuracy.
• The less frequently the CF’s are calc’ed, the faster the model can be run and results obtained.

Question 13

3.3. Developing a deterministic model

Answer 13

1. Specify the purpose of the investigation
2. Collect, group and modify the data
3. Choose the form of the model, identifying its parameters and variables
4. Ascribe values to the parameters using past experience and estimation techniques
5. Construct a model based on expected cashflows
6. Check that the goodness of fit – could be done by running a past year and compare the model results with actual results
7. Attempt to fit a different model if the first choice does to fit well
8. Run the model using selected values of the variables
9. Run the model using selected values of the variables
10. Run the model using estimates of the values of variables in the future
11. Run the model several times to assess the sensitivity of the results to different parameter values.
12. Run the model under different scenarios to see the robustness of the results to many parameters changing at the same time

Question 14

3.4. Developing a stochastic model

Answer 14

1. Specify the purpose of the investigation
2. Collect, group and modify data
3. Choose a suitable density function of each of the variables to be modeled stochastically
4. Specify correlation between variables
5. Ascribe values to the variables not being modeled stochastically
6. Construct a model based on the expected cashflows
7. Check the goodness of fit – could be done by running a past year and compare the model results with actual results.
8. If it does not fit well, attempt to fit another model
9. Run the model many times, each time using a random sample from the chosen density function(s).
10. Produce a summary of results that shows the distribution of results after many simulations.

Question 15

4. The use of models for pricing

Answer 15

A model could be developed to determine a premium or charging structure for a new or existing product that will meet a life insurance company’s profit requirements.

Question 16

4.1. The use of model points

Answer 16

The underlying business will probably consist of a very wide variety of different policies, these will need to be reduced into a manageable number of relatively homogenous groups.
The groupings must be made such that each policy is expected to give the same results when the model runs.
It is then sufficient for a representative single policy to be run instead of the whole group – this result is then just scaled up.
This single representative policy is then the model point – a number of such model points will represent the business.

Question 17

4.2. Choosing model points

Answer 17

A number of model points will be chosen to represent the expected new business under the product.
In the case of existing business, the profile can be changed to allow for expected future changes.
For a new product, use a similar existing product, combined with advice from the marketing department.

Question 18

4.3. Rate for discounting cashflows

Answer 18

For each model point, CF’s will be projected on the basis of a set of base values for the parameters in the model. This is done also taking into account CF’s for reserving and solvency margin requirements.
The net CF’s will then be discounted at the risk discount rate.

Question 19

the discount rate could allow for

Answer 19

• The return required by the company, and
• Level of statistical risk attaching to the CF’s under the particular contract i.e. their variation about the mean as presented by the CF’s themselves.

Question 20

The level of statistical risk could be assessed:

Answer 20

• Analytically, by considering the variances of the individual parameter values used.
• Using sensitivity analysis with deterministically assessed variation in the parameter values
• Using stochastic models for some (or all) parameter values and simulation.
Alternatively a stochastic discount rate can be used.
In theory, a separate discount rate must be applied to each separate component of the CF’s as the statistical risk associated with each component will be different.
In practice a single risk discount rate is used, bearing in mind the average risk of the product.

Question 21

4.5. Competitive premiums

Answer 21

The premiums or charges produced must be considered for marketability.
This might lead to reconsideration of:
• Design of the product – either remove features that increase risk within the net CF’s, or include features that will differentiate the product.
• Distribution channel to be used – if this will permit either a revision of the assumptions or a higher premium / charges to be used without loss of marketability.
• The company’s profit requirements
• Size of the market
• Whether to proceed with marketing the product

Question 22

4.6. Business strategy

Answer 22

The net CF’s of the model points will be scaled up for the expected new business under the product and incorporated into a model of the business as a whole.
It’s possible for the profit requirement to be reached in aggregate without requiring every model point to be profitable.
In this case, the business is exposed to business mix risk – risk of mix and volume sold changes.
The impact on capital management of writing the product will be assessed by observing the modeled amount and timing of CF’s. If the capital is a problem, it could lead to reconsideration of the product design to reduce or amend the timing of its financing requirements.
Once premiums or charges have been determined for the model points, it can be done for all contract variations.

Question 23

4.7. Assessing the capital requirements and return on capital

Answer 23

Use the scaled up model point for the expected sales to see how much capital will be required from a regulatory or economic basis.
Add to this, any once off development costs to the extent that they are not amortised and included in the CF’s used. This can be added to the total capital requirement and be compared with the expected profits to determine the expected return on capital.

Question 24

5. The use of models for setting financing strategies

Answer 24

For a benefit scheme, the same modeling techniques can be used.
Existing members can be grouped into model points, similarly, new members can be presented by a single model point – e.g. average entry age and salary.
A potential financing strategy is determined, in terms of both the amount and timing of future contributions.
The CF’s of existing assets, future contributions and liability CF’s can be modeled. This must take into account all possible decrements.
Unlike an insurance company, a benefit scheme can show a deficit at a point in time – the value of the accumulated assets < value of accrued liabilities. This will only be allowed if there is a sponsor with a good enough covenant to make up the short fall.
However the scheme does need to be solvent to the extent that it has sufficient assets to meet benefit outgo as it falls due.
A well designed model will check this feature as well as determining the discounted value of assets and liability CF’s.
Considerations such as risk discount rate, need to test sensitivities to changes in conditions are similar to product pricing.

Question 25

6. The use of models for risk management

Answer 25

CF models are used to determine the amount of capital required to be held to support risks retained by the institution.
Models of specific risks can be used to determine the extent of a risk event that will occur at a given probability, even if a full stochastic model is too slow, too complex or otherwise not used.

Question 26

7. Valuing provisions on an individual basis

Answer 26

The normal procedure for determining life assurance or pension scheme liabilities is to value the benefits for each policy or scheme member individually. This may be required by legislation or regulation.
Because of this, there is little scope for using model points for published results.
However, before finalizing a published basis, many questions can be answered by running a model of the business.
For smaller schemes or sections of the company, this may entail running the whole business given the current computing power and thus eliminating model risk.
As part of assessing a realistic provision, it is necessary to consider the effect of changes in the economic scenarios.

Question 27

8. Pricing and valuing options and guarantees

Answer 27

Usually options and guarantees that are of concern are ones dependant on future investment returns, or investment value at some future point in time.
Because of the uncertain, a stochastic investment model should be used to assess the provisions necessary for such guarantees.

Question 28

9.1. Reliability of results

Answer 28

Results of a model depends on the model itself, consider the workings of the model.

Question 29

9.2. Understanding potential variability of experience

Answer 29

Stochastic model goes some way to illustrate the potential variability of experience, but the results that it produces are still dependant on the accuracy of the model and the parameter values.
Deterministic models the uncertainty of results is greater because of fewer scenarios being tested.
The re-running of a model (stochastic or deterministic) with different (but feasible) parameter values will produce alternative results. This may help to illustrate potential deviations.
The re-running using different sets of parameter values will help illustrate the likely range in which actual experience may lie. A probability distribution of this could be created.

Question 30

9.3. Model error

Answer 30

Happens when the model is not appropriate for the financial products, schemes, contracts or transactions being modeled.
Checks for goodness of fit will be needed to assess the suitability of the model.

Question 31

9.4. Parameter error

Answer 31

The effect of mis-estimation of parameter values can also be investigated by carrying out a sensitivity analysis. This involves assessing the effect on the output of the model of varying each of the parameter values.
When doing this, any correlation between different parameters should be allowed for.
In case of a model used for pricing, the results from sensitivity analysis will help assess margins that need to be incorporated into parameter values.
Where the models are used to assess return on capital and profitability of existing business, the results will quantify the effects of departures from the chosen parameter values when presenting the results of the model to the company.

Question 32

9.5. Alternative ways of allowing for risk

Answer 32

Statistical risk associated with the parameter values can be allowed for through the risk element of the risk discount rate.
Alternatively, use a predetermined discount rate and then assess the effect on results of the models of statistical risk.
Where a probability distribution can be assigned to a parameter, it may be possible to derive the variance of the profit or return on capital analytically.
A sensitivity analysis can be carried out. Whichever of these 2 is used, it will help to assess margins or quantify the effect of departures from the chosen parameter values when presenting the results of the model.