17 - Modelling

Question 1

What is a model?

Answer 1

A simplified version of reality that captures the essential features of a problem to aid understanding

Question 2

Ways to acquire a model:

Answer 2

• Develop a new model to solve a specific problem using in-house expertise
• Buy the modelling product from an external company
• Could reuse an existing model by making changes to it

Question 3

The approach used to acquire the model depends on:

Answer 3

• Level of accuracy required
• Level of ‘in-house’ expertise available
• Number of times the model is to be used
• How flexible the model needs to be
  o Is it to be used in other circumstances?
• Relative costs of the different options

Question 4

A good model will fulfill the following requirements:

Answer 4

QUALITATIVE CHARACTERISTICS
- The model should be:
    o Valid
    o Fit for the purpose
    o Adequately documented

• A range of implementation methods should be available to test that the model is:
  o Easy to parameterise
  o Easy to test
  o Easy to review for sensibleness of results
• Model results should be easy to communicate to those being advised
• Model outputs should be capable of independent verification for reasonableness
• Model should NOT be so complex st. :
  o Results are difficult to interpret/communicate
  o Model becomes expensive/time-consuming to run
• Model should be capable of refinement/development

QUANTITATIVE CHARACTERISTICS
- Model should reflect the risk profile of financial products, schemes, contracts or transactions being modelled ie. timing, likelihood and value of cashflows

• Model parameters should reflect the business features that are most likely to affect advice given
• Values chosen for parameters should be appropriate to the business being modelled and take into account:
  o Economic and business environment
  o Special features of the provider
• Model should exhibit sensible correlations b/w variables

Question 5

Pros & cons of deterministic model:

Answer 5

Pros:

• Easier to design & run
• Simpler to explain to others
• The effect of modelling different economic scenarios can be shown clearly

Cons:

• Many economic scenarios may have to be run which takes time
• Care needs to be taken to make sure variables are sensibly related to each other

Question 6

Pros & cons of stochastic model:

Answer 6

Pros:

• Tests a wider range of scenarios
• Useful for assessing impact of financial options and guarantees - since it allows for uncertainties

Cons:

• Depends on accuracy of dbns and parameters chosen
  ie. more room for parameter/model error
• Slower to design and run
• Difficult to interpret and explain results
• May be harder to use
• More difficult to make (expertise required)

Question 7

Steps to follow to make a deterministic model:

Answer 7

• Specify the purpose of investigation
• Collect, group & modify data as appropriate
• Choose the model & identify parameters and variables within it
• Decide the values of parameters using past experience or appropriate estimation methods
• Construct full model based on expected cashflows
• Check the goodness of fit is satisfactory
• If non-satisfactory, fit a different model or fit different parameters until goodness of fit is acceptable
• Run the model using selected values of the variables
• Run the model using future estimates of variables
• Run the model several times to sensitivity test the model wrt different parameters

Question 8

Steps to follow to make a stochastic model:

Answer 8

• Specify the purpose of investigation
• Collect, group & modify data as appropriate
• Choose the model & identify parameters and variables within it
• Select suitable density functions for each of the variables being modelled stochastically
• Specify any correlations b/w the model variables
• Construct full model based on expected cashflows
• Check if goodness of fit is satisfactory
• If unsatisfactory, fit different model or different parameters/correlations/density functions until results are acceptable
• Run the model many times, each time sampling from all the density functions
• Produce a summary of results that shows the dbn of modelled results after running sufficient simulations
• If appropriate & time allows, conduct sensitivity tests with different parameters

Question 9

What is a model point?

Answer 9

A single policy with defined features which represents the risk associated in the homogenous group on which it is based.

Question 10

Process followed to obtain model points & prices:

Answer 10

MODEL POINTS:
- Break the anticipated business into groups of homogeneous risks
o The idea is that the ideal price is the SAME for risks within the homogeneous group
o Using larger number of (credible) groups makes pricing more accurate;
o But may require increased run-time + error checking + data
- Specify attributes for a single policy to represent the risks associated with the homogeneous group (MODEL POINT)

PRICES:

• Run the model point through the model to determine the price to charge these risks
• Discount these cashflows at a risk discount rate

Note: Results may need to be scaled up to allow for anticipated business volumes

Question 11

When running a model point through a model, what needs to be projected in the model?

Answer 11

• Premiums/contributions being paid
• Investment returns/interest rates
• Benefits being paid out
• Expenses
• Commission
• Cashflows required to establish reserves
• Cashflows from release of reserves
• Cashflows to and from and required solvency margin

Question 12

BONUS: How would you go about estimating how much new business you will get wrt to each model point?

Answer 12

• Speak to marketing department to determine which products are being promoted, to what extent are they being promoted, and which risk groups will find them attractive
• Speak to sales team to get their sense of where the greatest number of sales will take place
• Analysing the cost of the product wrt each of the model points and compare w mkt. prices
• Analyse past trends in respect of new business volume
• Analyse past trends in respect of business mix/split
• Consider changes in general economic/business environment that could impact business mix/volumes

Question 13

The number of model points used will depend on:

Answer 13

• The computing power available
• Time constraints
• The heterogeneity of the class
• The sensitivity of the results to different choices of model points
• The purpose of the exercise

Question 14

After projecting CFs for each of the model points, the CFs are discounted using a risk discount rate. The discount rate used can either be:

Answer 14

• Required rate of return by company + allowance for statistical risk attached to the CFs
  OR
• A stochastic discount rate can be used (in theory because each CF has diff. amt of risk attached)

Question 15

How can the level of statistical risk be assessed in models?

Answer 15

• Check the individual variances of parameters used
• Using sensitivity analysis using deterministically assessed variations of parameter values
• By using stochastic models for some/all parameter values and simulation
• By comparison with available market data

Question 16

Considerations for premiums produced by the model for marketability:

Answer 16

• Might reconsider the product design, st. either features that increase the risk in net CFs are removed or features are added to differentiate the product from competitors
• Dbn channel to be used, if a diff channel would permit revision of model assumptions/higher premiums/charges without loss of marketability
• Company’s profit requirement
• The size of the market
• Whether to proceed with marketing the product