Ch 18: Modelling

Question 1

List 10 areas of a life insurance company’s activities that might require a model. (10)

Answer 1

Life insurance company activities that might require a model include:
> calculating provisions
> setting premium rates
> assessing reinsurance requirements
> estimating future investment returns
> estimating future mortality improvements
> estimating future discontinuance levels
> estimating future expense levels
> determining future capital requirements
> estimating future new business levels
> valuing guarantees and/or options

Question 2

What is a model?

Answer 2

A ‘cut-down’, simplified version of reality that captures the essential features of a problem and aids understanding.

Modelling requires a balance to be struck between realism (and hence complexity) and simplicity (for ease of application and interpretation of results).

Question 3

Name 3 modelling approaches.

Answer 3

One of the following approaches can be followed:
> a commercially produced product can be bought
> an existing model can be modified
> a new model can be developed

Question 4

List the criterion that should be considered before choosing a modelling approach. (5)

Answer 4

The following needs to be considered:
> the level of accuracy required
> the ‘in-house’ expertise available
> the number of times the model is to be used
> the desired flexibility of the model
> the cost of each option

Question 5

List the operational issues of a model that should be taken into consideration.

Answer 5

The model should:
> be well documented
> be easily communicable, with clearly displayed results
> have sensible joint behaviour of variables
> be capable of independent verification
> not be overly complex or time-consuming to run
> be capable of development and refinement
> be capable of being implemented in a range of ways
> have an appropriate time period between projected cashflows, balancing the reliability of the output with the speed of running the model.

Question 6

What is a deterministic model?

Answer 6

It is a model 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 7

Name the advantages and disadvantages of a deterministic model.

Answer 7

Advantages:
> The model is much easier to explain to a non-technical audience
> It is clearer what economic scenarios have been tested
> The models is usually cheaper and easier to design and quicker to run
> Users can get blinded by complex models assuming that they must be working correctly

Disadvantage:
> It requires thought as to the range of economic scenarios that should be tested

Question 8

What is a 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 the stochastic parameters being selected from their distribution on each run.

The outcome is a range of values, giving an understanding of the likely distribution of outcomes.

Question 9

Name the advantages and disadvantages of a stochastic model.

Answer 9

Advantages:
> It tests a wider range of economic scenarios
> It may produce better quality result than a deterministic model.

Disadvantages
> Involves more complex programming
> The model takes longer to run
> It depends on that parameters used in any standard investment model

Question 10

What does it mean for a model to be dynamic?

Answer 10

The asset and liability parts of the model and all the assumptions are programmed to interact as they would in ‘real life’.

Question 11

Name the key steps involved in developing and running a model. (7)

Answer 11

1) Specify the purpose and key features of the model
2) Obtain and adjust the data
3) Set the parameters/assumptions, including the 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 possible
7) Output and summarise results

Question 12

Define a model point.

Answer 12

A model point is a representative policy used in pricing to try and mirror the key characteristics in all policies

Question 13

What is the purpose of the risk discount rate?

Answer 13

The purpose of the discount rate is
> to allow for the return required by the company and
> to allow for the level of statistical risk

Question 14

What is statistical risk and how is it assessed?

Answer 14

Statistical risk represents all types risk and includes model risk, parameter risk and random fluctuation risk.

It is assessed:
> analytically by considering the variances of the individual parameter values
> by using sensitivity analysis
> by using a stochastic model
> by comparison to market data

Question 15

Name items that needs to be considered after a model has produced the resulting premium/charges.

Answer 15

The following needs to be considered:
> product design
> distribution channel(s)
> the profit requirement
> the size of the market
> company’s business strategy
> capital requirements
> whether to go ahead with the product

Question 16

Name ways in which statistical risk can be allowed for.

Answer 16

Statistical risk can be allowed for:
> in the discount rate
> by including margins in the parameter values

Question 17

Name methods that can be used to reduce/spot model and parameter error.

Answer 17

> Sensitivity analysis can be used to illustrate the possible impact of mis-estimation of parameter values

> Scenario testing involves changing many parameters in combination

> Goodness of fit tests can be used to reduce model error