C17 Modelling Flashcards
What is a ‘model’?
Definition:
- Cut down, simplified version of reality that captures essential features of a problem and aids understanding
- Important to be able to communicate results effectively
Modelling – a balance:
- Realism (and hence complexity)
- Simplicity (for ease of use, verification and interpretation of results)
Advantages of Actuarial Model v Formula approach:
Actuarial Model v Formula approach:
- Better able to reflect uncertain future events by assessing the impact of of varying the assumptions
- So client understands the uncertainty involved in underlying assumptions
Three approaches to obtaining a model
Decision criteria in choosing a model
Sources: (PEN)
1. Purchased externally
2. Existing model modified
3. New model developed in house
Decision will depend on: CU FLIP
1. Cost of each option
2. Usage of the model (Frequency)
3. Flexibility desired
4. Level of accuracy required
5. In house level of expertise
6. Purpose of the model
Requirement of a good model
Requirement of a good model
CLERICAL ADVISORS
Capable of refinement
Length/expense of run not too long/high
Easy to understand
Rigorous
Independent verification of outputs
Clear results
Adequately documented
Large range of implementation methods (testing, parameterizing of results)
All significant features allowed for
Developable
Valid
Inputs to parameter values appropriate
Sensible joint behaviour of variables
Output and workings are communicable
Reflects risk profile
Simple whilst retaining key features
Deterministic vs. Stochastic
Deterministic models:
+ Quicker/easier to design, build and run
+ Clearer what scenarios have been tested
+ Results are easier to explain
+ Less risk of model and parameter error
+ Cheaper
- Judgement on range of scenario to be tested
Stochastic models:
+ Allow explicitly for “real world” uncertainty of outcomes
+ Allows for correlations between variables
+ Test a wide range of scenarios
+ Good for identifying extreme outcomes
+ Good for assessing cost of guarantees and options
- Complex and Longer run time
- Expensive
Outline with an example how a model can be made ‘dynamic’
Dynamism: Assumptions are consistent and interact with each other under different scenarios
e.g. Lapse rates in economic conditions
Explain the use of ‘model points’
How suitable model points can be obtained for pricing
Using model points
- Representative single policy
- May be too time consuming to run every single policy through a model
- So policies are classified into relatively homogeneous groups
- Model point for each group is chosen
- Output is scaled up to give results of whole group
- Are chosen to reflect expected profile of future business
- Could be based on existing profile or that of a similar product
When is it not appropriate to use model points?
Not using model points
- Not used generally used when valuing liabilities for calculating provisions
- Normal procedure for determining value of life assurance or pension scheme liabilities is to value benefits for each policy or scheme member individually
- In many territories this may be a regulatory requirement
Outline how risk discount rate for the model can be determined
Discount rate should reflect:
1. Return required by the company
2. Level of statistical risk attaching to cashflows (i.e. their variation about the mean level)
In theory, a different discount rate should be used for each cashflow (as the risk is different); in practice, a single a rate is often used based on the average risk of the product
How to assess the level of statistical risk attached to the cashflows
The level of statistical risk could be assessed: MASS
1. by comparison with any available market data
2. in some situations, analytically - by considering the variances of individual parameter values used
2. by using sensitivity analysis,
3. by using stochastic models for all or some of the parameter values and simulation
Changes needed in modelling if product is not deemed marketable
If not marketable then you could change: (DAD PD)
1. Design of contract to remove risky features
2. Add differentiating features
3. Distribution channel (revision of assumptions or higher premium/charges)
4. Profit criterion
5. Decision to market contract in first place
How to develop a stochastic model?
- Specify the purpose
- Collect the data, group and modify it
- Choose a distribution for each stochastic variable, with parameter values
- Specify correlations between variables
- Construct the model based on the expected cashflows
- Check goodness of fit against past data, modify fit if poor
- Run it may times using a random sample from the chosen distribution
- Produce a summary of results showing the distribution of the modelled results
How to develop a deterministic model?
- Specify the purpose
- Collect data, group and modify it
- Choose the form of the model
- Identify parameters and variables
- Ascribe values to those parameters
- Construct a model based on expected cashflows
- Check goodness of fit against past data, modify fit if poor
- Run the chosen model using selected values of variables
- Run using estimates of future values of variables
- Sensitivity test using different parameters
