What is a model?

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

Ways to acquire a model:

- 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

The approach used to acquire the model depends on:

- 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

A good model will fulfill the following requirements:

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

Pros & cons of deterministic model:

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

Pros & cons of stochastic model:

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)

Steps to follow to make a deterministic model:

- 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

Steps to follow to make a stochastic model:

- 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

What is a model point?

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

Process followed to obtain model points & prices:

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

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

- 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

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

- 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

The number of model points used will depend on:

- 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

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:

- 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)

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

- 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

Considerations for premiums produced by the model for marketability:

- 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