17 - Modelling Flashcards
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
