CH 18: Modelling Flashcards
What is a model?
3
- A model can be defined as a ‘cut-down, simplified version of reality that captures the essence of the problem and aids understanding
- It is important to be able to communicate the results effectively
- Can be purchased,reused,developed depending on costs,expertise and level of accuracy available
Where might a model come from and what factors affect the decision about where to get it
- A new model might be developed in-house
- An existing model might me modified
- A commercial model might be purchased externally
- The factors that need to be considered are:
- Fit for purpose
- Expertise available in-house
- Need for flexibility
- Cost of each option
- Expected number of times the model is to be used
- Desired level of accuracy
Developing a model
3
- Actuarial problems require assumptions about uncertain future events.
- Varibility of answers are important as assumptions vary.
- Assess variability using:
Sensitivity analysis: vary individual assumptions and assess impact
Scenaro testing: Combination of assumption changes and assess impact
What is the advantage of an actuarial model over a formula?
2
A model is better able to reflect uncertain future events by giving an indication of the effects of varying the assumptions.
This is important so that the client understands the uncertainty involved in the underlying assumptions
Outline the operational issues that need to be considered when designing and constructing a model
Simple, but retains key features, approx instead of model
Clear results
Adequately documented: Key assumptions, approx
Range of implementation methods
Communicable workings and output
Easy to understand
Refineable and developable
Frequency of cashflows (balance accuracy vs practicality)
Independent verification of results
Length of run not too long
Expense not too high
Sensible joint behavior of variables( linked variables)
SCARCER FILES
What are model points? Why are they used? How are they used?
4
- A model point is a representative single policy from a large homogeneous group that captures most important characteristics of the group
- The business being modelled may comprise a very large number of different policies and it may be too time consuming to run all of these through a model.
- The model point is run through the model and the output is then scaled up by the number of policies in the group to give the results of the whole group.
- For pricing purposes, model points are chosen to reflect the expected profile of future business to be sold. This could be based on the existing profile, or that of a similar product.
When are model points not used?
3
- Model points are not generally used when valuing liabilities for calculating reserves.
- The normal procedure for determining the value of life assurance or pension scheme liabilities is to value the benefits for each actual policy or scheme member individually.
- In many territories this may be a regulatory requirement However, model points may be required in order to answer various ‘what if’ questions
Risk discount rate and model points
2
- For each MP CF’s will be projected, allowing for reserving and solvency margins on base parameter values.
- Projected CF’s are then discounted@ discount rate
What factors make up the risk discount rate?
2,4
- The return required by the company
- The level of statistical risk attaching to the cashflows
NOTE: In theory a different discount rate should be used for each cashflow (as the risk is different); In practice a single rate is often used based on the average risk of the product
Assess Statistical risk:
* Analytically: variance of parameter values
* Sens analysis: assess variation or parameters
* Stoch models: simulate dbn of parameter values
* Compare: to Market data
Determinstic Models
1,3,3
- Model where parameter values are fixed and a single outcome is provided. Sens/Scen tests to check variability
Advantages:
- Cheaper, faster and easier to design, build and run
- Clearer what scenarios have been tested
- Results are easier to explain to a non-technical audience
Disadvantages:
* Results are highly dependant on assumptions
* Can lead to inaccurate results
* Test small range of scenarios
Stochastic Models
1,5,3
- Atleast 1 parameter is assigned a distribution. Model is run on multiple simulations and parameter values vary. Outcomes are a distribution.
Advantages:
- Allows naturally for the uncertainty of outcomes
- Enable better modelling of the correlations between variables more accurate results
- Test a wider range of scenarios
- Good at identifying extreme outcomes, which may not have been thought of under a deterministic scenario
- Important in assessing the impact of financial guarantees
Disadvantages:
* Large amt of info required
* Slower and more expensive to develop and run
* More difficult to explain
Combined model: High risk variable are stoch while others deterministic
eg Stoch for econ assumptions and det for demographic assumptions
Define what is meant by ‘dynamism’ of a model
1,1
- If a model is dynamic, then the asset and liability parts of the model and all the assumptions are consistent with each other and are programmed to interact under different scenarios as they do in reality.
- Interactions need to be determined using actuarial judgement. more NB than type of model.
For example:
- Inflation rates and investment returns
- Bonus rates and investment returns
- Withdrawal rates and economic conditions
Set out the steps involved in developing and running a deterministic model
- Specify the purpose of the investigation
- Collect, group and modify data
- Choose the form of the model and its parameters / variables
- Ascribe values to those parameters using past experience / estimations
- Construct a model based on expected cashflows
- Test the model and correct if necessary
- Check goodness of fit using past data, modify if poor
- Run using estimates of future values of variables
- Sensitivity tests (and maybe scenario test) using different parameter values
Additional / Alternative steps in a stochastic model
- Choose a density function for each of the stochastic variables
- Specify correlations between the variables
- Run model many times using a random sample from the chosen density function
- Produce a summary of results – a distribution (e.g. summarized at various confidence levels)
Outline how a deterministic model could be used to determine a set of new premium rates for a term assurance contract
- An objective would be set based on profit criterion and an appropriate time horizon
- Data relating to the existing profile of customers would be collected and model points created. It would be modified for any perceived future differences in the profile of customers
- Parameter values for key assumptions such as mortality, expenses, lapses and investment returns would be set based on past experience
- For each model point, the model would be run, projecting future cashflows and discounting the net profits at the risk discount rate (RDR). The premium would be varied until the required profit criterion is met.
