Chapter 18: Modelling

Question 1

What is a model

Answer 1

A cut down, simplified version of reality that captures essential features of a proble and aims to aid in understanding

Question 2

Two main uses of models in actuarial work

Answer 2

• Pricing new products
• Valuing liabilities

Question 3

Sensitivity analysis

Answer 3

Varying individual assumptions and assessing the impact on the results

Question 4

Scenario analysis

Answer 4

Changing many assumptions in combination to assess the impact on the result

Question 5

Approaches to modelling

Answer 5

• Purchase a commercial model
• Make use of an existing model, after some modifications
• A new model can be developed

Question 6

What will be the merits of each approach to modelling depend on

Answer 6

• Flexibility desired from the model
• Accuracy required
• Cost of each option
• Expertise available
• Reusability

Question 7

Operational issues in constructing a model

Answer 7

Use by other staff
* The model used should be adequately documented - to understand assumptions and limitations
* Capable of redevelopment and refinement
* The outputs of the model should be capable of independent verification for reasonableness and should be communicable to those to whom advice will be given.
* Must not be overly complex such that:
1. The results are hard to interpret
2. Results are hard to communicate
3. Model becomes too long or expensive to run

Client
* The workings from the model should be easy to communicate and appreciate

Statistics
* The model should exhibit sensible joint behaviour of model variables
* A range of methods of implementation should be available to facilitate testing, parameterisation and focus of results

Computation
* The more frequently the cashflows are calculated, the more reliable the model
* The less frequently the cashflows are calculated, the faster the model can be run and results obtained

Question 8

Explain the use of model points

Answer 8

• A wide number of policies are brought together into relatively homogenous groups
• Such that each policy is expected to produce similar results when the model is run
• The model points are used to represent the whole underlying business

Question 9

How are model points chosen

Answer 9

Exisitng product - the profile of the existing business modified to allow for any expected changes in the future.
New business - the profile of any similar existing business with advice from the company’s marketing department

Question 10

What will the number of model points depend on ?

Answer 10

• The compiting power available
• Time constraints
• The heterogenity of the class
• The sensitivity of results to different model points
• The purpose of the excercise

Question 11

Statistical risk

Answer 11

model risk + parameter risk + random fluctuation risk

Question 12

How can statistical risk be assessed

Answer 12

• Analytically - By considering the variances of the paramters used.
• Using sensitivity analysis
• Using stochastic analysis for some, or all paramter values
• Comparison with any market data

Question 13

Merits of a deterministic model

Answer 13

Advantages
* Easily understood by a non-technical audience.
* It is clearer what economic scenarios have been tested
* Usually cheaper, easier to design and quicker to run
* Users can get blinded by science by complex models, assuming they must be working correctly, without veryfying or testing this

Disadvantages
* Requires thought as to the range of economic scenarios which are tested.
* Since these are limited, there is a danger of not testing scenarios which are dentrimental to the company
*

Question 14

Merits of a stochastic model

Answer 14

• Tests a wider range of scenarios.
• Programming is more complex and takes longer to run, but the benefit is in the quality of the result.
• It depends on the parameters used in any standard model.

Question 15

Considerations when choosing between a deterministic and stochastic model

Answer 15

• Does additional computation needed in a stochastic model justify the increase in information.
• Degree of spurious accuracy that may be introduced.
• Increased difficulty in intepreting and communicating the result
• Questionable accuracy of the distributions that are repalcing the deterministic values.

Question 16

Dynamism of the model

Answer 16

The asset and liability parts and all the assumptions are programmed to interact as they would in real life - rules for this would need to be determined

Question 17

Steps in developing a deterministic model

Answer 17

• Specify the purpose of the investigation
• Collect, group and modify data
• Choose the form of the model, identifying its parameters or variables
• Ascribe values to the paramters using past experience and appropriate estimation techniques
• Construct a model based on expected cashflows
• Test the model in order to dentify any build errors, and correct if necessary
• Check that the goodness of fit is acceptable
• Run the model using estimates of the values of the variables in the future
• Run the model several times to assess the sensitivity of the results too different parameter values

Question 18

Steps in developing a stochastic model

Answer 18

• Specify the purpose of the investigation
• Collect, group and modify data
• Choose the form of the model, identifying its parameters or variables
• Choose a suitable density function for each of the variables to be modelled stochastically
• Specify corelation between variables
• Construct a model based on expected cashflows
• Test the model in order to dentify any build errors, and correct if necessary
• Check that the goodness of fit is acceptable
• Run the model many times, each time using a random sample from the chosen density function(s)
• Provide a summary of the results that shows the distributionof the results after many simulations have been run

Question 19

Model error

How can it be tested

Answer 19

If the model developed is not appropriate for the financial product, contract, transaction or scheme being modelled

Tests of goodness of fit , taking expected changes in the future experie

Question 20

Parameter error

How can it be tested

Answer 20

Mis-estimation of paramter values

Sensitivity analysis

Question 21

Course of action if a model is overly sensitive to a parameter

Answer 21

• Redesign the product
• Increase margins into the assumptions

Question 22

When assessing premiums for marketibility (competitiveness), what reconsiderations might be made?

Answer 22

• The design of the product - adding or removing features to differentiate the product
• The distribution channel used - if it allows for revision of asuumption, higher premium without loss of marketibility
• The company’s profit requirement
• The size of the market
• Whether to proceed marketing the product