Chapter 29: Modelling

Question 1

Requirements of a good model

Answer 1

A good model will:

• be valid, rigorous and well documented
• reflect the risk profile of the business being modelled
• allow for all the significant features of the business being modelled
• have appropriate input parameters and parameter values
• be communicable and the output verifiable
• 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.

A model needs to allow for all the cashflows that may arise, including:

• guaranteed and discretionary benefits
• cashflows arising from any supervisory requirement to hold provisions
• the potential cashflows arising from options and guarantees

Question 2

Dynamic model

Answer 2

Allows for the interaction between the parameters and variables affecting the cashflows

Question 3

Steps involved in running a deterministic model

Answer 3

• specify the purpose
• collect, group and modify the data
• choose the form of model
• identify the parameters and variables
• ascribe the parameter values
• construct a model based on expected cashflows
• check the goodness of fit is acceptable
• fit a new model if the first choice does not fit well
• rund the model using selected values of the variables and values that will apply in the future
• sensitivity test the parameters

Question 4

Steps involved in running a stochastic model

Answer 4

• specify the purpose
• collect, group and modify the data
• choose a suitable density function for each stochastic variable
• specify the correlations between the variables
• construct a model based on expected cashflows
• check the goodness of fit is acceptable
• fit a new model if the first choice does not fit well
• run the model many times using randomly generated values of the stochastic variables
• produce a summary of the results

Question 5

Risk discount rate could allow for

Answer 5

• the return required by the company

- the level of statistical risk (assessed analytically or by sensitivity analysis or from a stochastic model)

Question 6

Premiums resulting from the model may need to be considered relative to the market, which may require reconsideration of:

Answer 6

• product design
• distribution channels
• profit requirement
• size of the market
• whether to go ahead with the product

Question 7

Define a model

Answer 7

A cut-down, simplified version of reality
…. that captures the essential features of a problem
…. and aids in:
—- understanding of the problem.
—- producing (potential) answers to the problem.

Question 8

3 Approaches to modelling

Answer 8

• a commercial modelling product could be purchased
• an existing model could be reused, possibly after modification
• a new model could be developed

Question 9

The merits of the modelling approaches will depend on (5)

Answer 9

• 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 10

The prime objective in building a model

Answer 10

To enable a provider of financial products to be run in a sound financial way.

Question 11

Merits of a deterministic model

Answer 11

• more readily explicable 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 12

Disadvantage of a deterministic model

Answer 12

it requires thought as to the range of economic scenarios that should be tested.

Question 13

Merits of a stochastic model

Answer 13

Tests a wider range of economic scenarios.

Stochastic models are particularly important in assessing the impact of financial guarantees.

Question 14

Disadvantage of a stochastic model

Answer 14

The programming is more complex and the run time longer.

Question 15

What is meant by a “dynamic” model

Answer 15

The asset and liability parts are programmed to interact as they do in reality

and the assumptions affecting assets and liabilities (for example inflation and interest rates) are consistent.

Question 16

Model point

Answer 16

A representative policy.

It is usual to identify model points, which represent relatively homogeneous underlying groups of policies.

Question 17

The risk discount rate could allow for (2)

Answer 17

• the return required by the company

- the level of statistical risk (assessed analytically or by sensitivity analysis or from a stochastic model)

Question 18

Considering the resulting premiums from the model relative to the market requires consideration of (5)

Answer 18

• product design
• distribution channel
• profit requirement
• size of market
• whether to go ahead with the product.

Question 19

Statistical risk (3 parts)

Answer 19

Comprises:

• model risk
• parameter risk
• random fluctuation risk

Question 20

The level of statistical risk could be assessed in 4 ways

Answer 20

• analytically, by considering the variances of the individual parameter values
• by using sensitivity analysis, with deterministically addressed variations in the parameter values.
• by using stochastic models for some, or all, of the parameter values and simulation
• by comparison with any available market data.

Question 21

Why is a model necessary in the first place?

Answer 21

Some problems cannot be solved by closed-form solutions, they are too complex.
Need some simplification to get insight into the problem.

Question 22

How would a model aid in understanding the problem? (4)

Answer 22

• What are the essential features
• Interactions
• What can happen (possible output)
• Often just the ACT of producing a model, highlights issues

Question 23

A rigorous model

Answer 23

One that produces realistic (and hence useful) results under a wide range of circumstances and conditions.