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Modelling (Producing a solution (Finding a model (Commercial product could…
Modelling
Producing a solution
Approaches to solving actuarial problems
Need to develop a model
What is a model?
Finding a model
Commercial product could be purchased
Depend on
Accuracy required
In house expertise available
Times model will be used
Flexibility
Cost of each option
Existing model reused
New model developed
Existing models
Model and parameter error
Results only as good as the model and parameter values
Sensitivity Analysis
Varying individual assumptions and assessing the impact on the results
Scenario Testing
Changing many assumptions in combination, for example to look at the may assumptions that may change if the economy were to move into a recession
Small reasonable changes [1% up or down -small increments]
Goodness of fit
Can be used to reduce model error
Stress Testing
A stress test can be a sensitivity test (just change one thing) or a scenario test (change a bunch of things in a consistent manner)
Just an extreme version of a scenario test [e.g. 10% up or down]
Objectives and Requirements for Model Building
Why build a model?
Enable sound financial management
Checks and controls
Assists the day to day work of the provider
Requirements [VW PRC]
Parameters and values thereof should be appropriate
Profile of risk for business modelled
Rigorous
Valid
Well documented
Refinement should be possible
Robust
Communicable
Verifiable output
Complexity must be low
Type
Deterministic
Definiton
Parameter values are fixed at the outset of running the model
Result of the model is a single outcome
Sensitivity testing and scenario analysis can be used to test the potential variability of the results
Advtanges
More explicable to non-technical audiences
Clearer what economic scenarios have been tested
Easier to design
Quicker to run
Disadvantages
Stochastic
Definition
Estimates at least one of the relevant parameters by assigning a probability distribution
Run many times with the value of stochastic parameters being selected from their distribution on each simulation
Outcome is a range of values giving an understanding into the range of outcomes and their measures of certainty
Advantages
Tests a wider range of economic scenarios
Quality of result is higher
Better for assessing impact of financial guarantees [good at allowing for uncertainty involved]
Disadvantages
More computationally intensive
Degree of spurious accuracy introduced
False precision (also called overprecision, fake precision, misplaced precision and spurious precision) occurs when numerical data are presented in a manner that implies better precision than is justified
Harder to communicate
Choice of density functions may be wrong
Dynamism
Need to establish rules as to how parameters should interact in different scenarios
e.g. Interest and Inflation
Pricing
Model points
Representative policy
Smaller collection of policies that are representative of homogeneous underlying groups
Risk discount rate
Allows for return required by company
Allows for level of statistical risk
Can be stochastic
Single rate used to reflect average level of risk
Can allow for risk by including margins in parameter s values or using the risk discount rate
Marketability Considerations
Product Design
Distribution channels
Profit requirements
Market size
Green-lighting a product
Development
Purpose
Collect , group and modify data
Choose form of model
Identify parameters and variables
Ascribe values
Construct a model of expected cashflows
Check goodness of fit
Fit new model if fit is poor
2 more items...
Choose pdf for each stochastic variable
Specify correlations between variables