Chapter 29: Modelling Flashcards
What is a model?
A cut-down, simplified version of reality that captures the essential features of a problem and aids understanding.
A model is a small representation of the real thing, designed to show all the important features of the real thing - consistent with the model’s scale and use.
Where might the model come from and what factors might affect the decision?
It may be
- a new model, developed in house
- a modification of an existing model
- or a commercial product purchased externally.
The decision will depend on ● the level of accuracy required ● the “in-house” expertise available ● the number of times the model is to be used ● the desired flexibility of the model ● the cost of each option. - expertise, - the usage of the model, - whether the model is fit for purpose.
9 Requirements of a good model
A good model will
- be valid, rigorous and well documented
- reflect the risk profile of the business being modelled
- allow for all the significant features of the business being models
- be easy to appreciate and communicate
- have appropriate input parameters and parameter values
- have output that can be verified independently
- not be overly complex or time-consuming to run
- be capable of development and refinement
- be capable of being implemented in a range of ways
What is a dynamic model?
By dynamic we mean that the asset and liability parts are programmed to INTERACT AS THEY DO IN REALITY and the assumptions affecting assets and liabilities, for example inflation and interest rates, are consistent.
Which cash-flows should a model allow for?
All cashflows that may arise.
In particular:
- cashflows relating to both guaranteed and discretionary benefits
- cashflows arising from the requirement to calculate provisions
- cashflows relating to options
Advantages of deterministic models
- quicker to design, build and run
- clearer what scenarios have been tested
● more readily explicable to a non-technical audience, since the concept of variables as probability distributions is not easy to understand.
10 Steps involved in using a deterministic model
- Specify the purpose
- Collect, group and modify the date
- Choose the form of the model
- Identify the parameters and variables
- Ascribe the parameter values
- Construct a model based on expected cashflows
- Check if the goodness of fit is acceptable
- Fit a new model if the first choice does not fit well
- Run the model using estimates of the values of the variables, in the future
- Sensitivity test the parameters
9 Steps involved in using a stochastic model
- Specify the purpose
- Collect, group and modify the data
- Choose a suitable density function for each stochastic variable
- Specify the correlations between the variables
- Construct a model based on expected cashflows
- Check that the goodness of fit is acceptable
- Fit a new model if the first choice does not fit well
- Run the model many times using randomly generated values of the stochastic variables
- Produce a summary of the results
Specifying the purpose of a model, involves setting an overall time horizon and a time period for the output of cashflows.
How should the time period be chosen?
The time period should be frequent enough that the output is reliable that there is spurious accuracy or that the model takes too long to run.
What is a model point and why are they used?
A model point is a representative single policy.
It may be too time consuming to run every actual policy through a model, so policies are classified into relatively homogeneous groups.
A model point for each group is chosen. The output is then scaled up to give the results for the whole group.
How are model points chosen?
Model points are chosen to reflect the expected profile of future business.
This could be based on the existing profile or that of a similar product.
What should the discount rate used in a model reflect?
The return required by the company.
The level of statistical risk attaching to the cashflows.
In theory, a different discount rate should be used for each cashflows. In practice, a single rate is often used.
4 Ways in which the level of statistical risk attaching to the cashflows is ascertained.
- analytically, by considering the variances of the individual parameters used
- by using sensitivity analysis
- by using a stochastic model
- by comparison with any available market data.
When using a model to set premiums, what questions should be asked about the resultant premiums?
- Are the premiums marketable?
- Is the contract profitable on aggregate, when scaled up for expected new business volumes and built into a model of the whole company?
- What are the capital requirements of the contract?
If the contract is not marketable, what might need revising?
The design of the contract to remove risky features or to add differentiating features.
Alternatively, reconsider the sales channel, the profit criterion, or the decision to market the contract in the first place.
How would you assess the capital requirements of a contract using a model?
Scale up the capital requirements for individual model points by the expected new business volumes.
Add in the one-off contract development expenses.
Why are model points not generally used for calculating provisions?
Regulations often require that provisions be calculated separately for each individual contract, which means that model points can not be used.
For a benefit scheme, modelling can be used to set the future financing strategy.
What might be true of the relation between the asset and liabilities for a pension fund that would not be true for an insurer?
The benefit scheme can show a deficit at a point in time, as long as the scheme sponsor will be able to make up that shortfall over an appropriate time period.
What type of model should be used for valuing options and guarantees?
A stochastic model
What errors are involved in running models?
- Model error
- Parameter error
What are the different ways of allowing for risk margins and assumptions?
- Through the risk element of the risk discount rate.
- Alternatively, use a predetermined discount rate but incorporate margins in the individual experience assumptions,
- Or use a stochastic model.
2 Disadvantages of a deterministic model
It REQUIRES THOUGHT as to the range of economic scenarios that should be tested.
Since only a limited number of economic scenarios will be tested, there is a danger that certain scenarios, which could be particularly detrimental to the company, are not identified.
What should be the focus for data?
Quantity and quality together
What reasons are there for poor quality data?
Systems - poor design of data system
Recording - poor control of data recording
Good processes implemented, time lag in enough data
What are the consequences of poor quantity of data?
Non-homogeneous grouping
Low credibility of grouping
What is the consequence of poor quality data?
Unreliable results
Why is the proposal form important for data?
Prime information source
Well designed/unambiguous questions
Ratings factors/underwriting to be included
Cross checking and validity of claims possible
Updating policy information
Historical data gathered from it
What is risk classification?
Splitting data into homogeneous groups
Why do risk classification?
Appropriate use of data Experience of group stable Inaccurate provisions if didn't do it Sensitivity testing needs to be done If group contains few model points, need to group with more at cost of homogeneous
What historical data should be used in basis in general?
Investment return, benefit growth, demographic assumptions, changes in a persons life
What parts of past investment return would you look at?
dividend yield
returns on asset classes
inflation data
What parts of historical benefit growth would you use?
Salary levels for country/industry/company
inflation index
What demographic assumptions would you look at historical data for
Mortality for decrements
What changes in a persons life would you look at in using past historica data?
Leaving employment illness retiring regulation past price inflation
Why wouldn’t you use past averages in your basis?
Social and economic changes
Use what effect the changes caused in the past for your future predictions
What are unsuitable uses of un-adjusted historical data?
Economic Inflation Nominal data Dividend levels Mortality data
Why shouldn’t you use past inflation in your basis?
linked to past conditions, better to use current govt bonds and projections
Why not use past nominal data for econ assumptions?
Price inflation will strip out fluctuations
What historic economic data is unsuitable for using un-adjusted in your basis
Investment returns
salary
dividend growth
How would you adjust past dividend levels for use in basis
Adjust for tax changes on dividend income
How would you adjust mortality data (historic) for use in basis
for medical advances and tends
focus on more recent data more
What are the problems with grouping past data in homogeneous groups?
Information desired unlikely to be available
Available data small so non credible results
The balance in the homogeneous group may change over time, with workers shifting
adjust it in a subjective way
What are the problems with getting data from the state or groups of companies?
Stats recorded may change
Errors are possible, especially in older records
Census data has people who can’t afford or buy insurance
Correct mortality table should be used and adjusted
What factors determine accuracy of assumptions use in basis
Purpose of assumption
Sensitivity of result to assumption
Best estimate or MAD
Individual cash flows important (use accurate)
Capital value only important (not accurate is allowed)
Consideration of financial consequences
Expert witnesses must use same assumptions type (BE /MAD)
Awareness of implicit assumptions in model like mortality not changing in open pens scheme
How would you use historical economic data in your basis
Strip out fluctuations caused by fiscal changes
How do you allow for risk in assumptions?
Change risk discount rate
Stochastic discount rate
Apply MAD’s to expected values
What are the 3 main profit criterion?
NPV, IRR, DPP
What factors increase risk in a new product?
Historical data lacking Guarantees that are high Options that are risky Costs of overheads Complexity of design
What 2 things do you compare when deciding whether to invest?
Risk vs return
What does monitoring the experience entail?
Interpret modelling results Determine proposed solution Examine if current models can be adapted Select most appropriate model or new one Proposal formalise Alternative solution considerations and effects Implication of model Result on overall problem Stakeholder implications of results
Why monitor actual experience?
Method of financing benefits appropriate Assumptions to finance benefits correct Updating assumptions for future experience Management info providing Adverse trends, notice and correct
Is grouping suitable in an experience investigation, why?
Large/stable/consistent data Too few data makes groups non credible Data may be few due to model points or infrequent/volatile Might group data into larger year bands Grouping should be same as before
How do you compare mortality experience?
Actual deaths/Exposed to death vs assumed deaths
How do you compare withdrawal experience?
Lapses/Exposed to lapse vs assumed lapses
How do you compare interest rates experience?
Actual vs Estimate
Put actual in model and note difference to results
How do you compare investment returns experience?
Actual vs expected
Do out performance analysis of change
What do you need to take into account when looking at Actual vs Expected and deciding whether to change assumption
Abnormal period or permanent change
Would trend likely to continue
Are the people we’re looking at homogeneous with the group effected by future experience
May choose new assumptions based on our experience and adjust them for our uncertainty about the experience
Why review investment strategy regularly?
Liability structure changes New business Mergers and acquisitions Legislation Free assets/surplus changes Performance significantly out of line with other funds
What should you do in assessing investment performance?
Compare target return to actual return of an indexed fund
Index fund having maintained the asset proportions set in the benchmark
What constraints may effect performance of investment strategy
Shortage of cash flow
restriction of funds for investment
forced sale of investments at unsuitable time
What things shouldn’t you do in assessing investment strategy performance?
Set the performance targets too generally, if your investment restriction high on assets and classes
Compare return to valuation discount rate due to year on year volatility of returns
What current data can we use in basis setting?
Inflation index - fixed and IL current yields
Policy statements - by government for economic factors
Scheme sponsor - Info on salary increases and likely future rate of withdrawal
