Chapter 18: Modelling Flashcards
What does the modelling approach depend on?
Approaches to solving actuarial or financial problems
- Approach taken will be driven by purpose of the exercise and nature of the problem
- E.g. far more detailed approach will be required to determine provisions for life insurer’s statutory returns than provide interim update to the provisioning level for internal management purposes during year
- Simple problems can have simple solution that is arrived at by straightforward mathematics
Why do we need to develop a model?
The need to develop a model
- Most problems that require actuarial skills involve taking view on uncertain future events
- Possible to take view on various parameters and produce single answer that is appropriate in these best estimate conditions
- If this is done, then the communication of the solution to client needs care as there are uncertainties in underlying assumptions
- I.e. client likely to wish to know the variability of answer provided, should circumstances not be as estimated
- To assess effects of varying assumptions used in producing the answer – necessary to use actuarial model of future events
- The variability of answer might be assessed by carrying out:
Sensitivity analysis – varying individual assumptions and assessing the impact on results
Scenario testing – changing many assumptions in combo e.g. to look at the many assumptions that may change if economy were to move into a recession
What is a model?
What is a model?
- Cut-down, simplified version of reality that captures the essential features of problem and aids understanding
- Important to be able to communicate results effectively
- Modelling requires balance between realism and simplicity for ease of application, verification and interpretation of results
When finding a model what are the various approaches to modelling and what will the merits of each of these approaches depend on?
Finding a model
- Various approaches to modelling when faced with actuarial/financial problem:
Commercial modelling product could be purchased
An existing model could be reused – possibly after modification
A new model could be developed
- Merits of each of these approaches 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 model
The cost of each option
What are the two types of existing models ?
Existing models
- Existing deterministic or stochastic models can be used
Stochastic models
- Many stochastic asset models in existence – in public and private domains
- Fewer models available for other variables, such as mortality and voluntary discontinuance, but these are starting to be developed
What are the key objectives of construction of an actuarial model?
Key objective
- Any model should be fit for purpose for which it is being used
- This is very relevant when model is being purchased from external provider or when existing model is being reused for different purpose (after modification)
- Even with new purpose-built models there is risk of model error – model that replicate past results may still be unreliable in projecting future results
What are the operational issues of construction of an actuarial model?
Operational issues
- Model being used should be adequately documented
So that key assumption and approximations made are understood and so it can be run by other members of staff and improvements introduced over time
- The workings of model should by easy to appreciate and communicate – results should be displayed clearly
- Model should exhibit sensible joint behaviour of model variables
So model needs to make allowance for variables that are linked to each other: relationship between them need to have been modelled in appropriate way
Assumption should also be consistent – assumed rate of investment return should be consistent with assumed rate of inflation
- Outputs from model should be capable of independent verification for reasonableness and should be communicable (to whose getting advice)
- Model must not be overly complex = so that results become difficult to interpret and communicate or too expensive and long to run – unless necessary
- Model should be capable of development and refinement
- Model should be capable of being implemented in a range of different ways – to facilitate testing, parameterisation and focus of results
- More frequently the cashflows are calculated, the more reliable the output from the model – but danger of spurious accuracy
- Less frequently the cashflows are calculated, the faster the model can be run and results obtained
- Argument for having shorter time period between cashflows in early years – given that starting points for model should be known with fair degree of certainty and thus early result are most meaningful
- Time period chosen so that it captures key areas of experience
- Decision must be made about how many years into the future the results will be projected
How are model points used in the construction of an actuarial model?
The use of model points
- Underlying business being modelled will comprise very wide range of different policies
- These will need to be brought together into manageable number of homogeneous groups
- Groupings need to be made in way that each policy in a group is expected to produce similar results when the model is run
- It is then sufficient enough for a representative single policy in each group to be run through the model and for result to be scaled up to give total set of policies in the group
- Model point – the representative single policy in a group and set of such model points can be used to represent whole of underlying business
- Model point needs to capture most important characteristics of the group of policies it represents
How are model points chosen in the construction of an actuarial model?
Choosing model points
- Set of model points will be chosen to represent expected new business under the product
- For an existing product – profile of existing business, modified to allow for expected changes in future, used to obtain model points
- For new product – profile of any similar existing product combined with advice from company’s marketing department would be used
- Number of model points will depend on number of model points that can be handled by the model
- Number of model points used will depend on:
Computing power available
Time constraints
Heterogeneity of the class
The sensitivity of the results to different choices of model points
Purpose of the exercise
What discount rate is used in the construction of an actuarial model?
Rate for discounting cashflows
- For each model point – cashflows projected, allowing for reserving and solvency margin requirements, on the basis of set of base values for parameters in model
- Net projected cashflows will then be discounted at rate of interest = risk discount rate
- Could be rate that allows for:
Return required by company
Level of statistical risk attaching to cashflows under particular contract i.e. variation about the mean as represented by the cashflows
- Statistical risk is intended to encompass all types of risk – comprises the model risk, parameter risk and random fluctuation risk
- The level of statistical risk could be assessed:
Analytically – by considering the variances of individual parameter values used
By using sensitivity analysis – with deterministically assessed variations in parameter values
By using stochastic models for some, or all, of the parameter values and simulation
By comparison with any available market data
- Stochastic modelling approach achieved by:
varying the important parameter values in model according to their assumed probability function
and recalculating the rate of return for each new scenario
- by running many simulations, a good idea of variance of the rate of return can be found
- OR, stochastic discount rate could be used
- IN THEORY, separate risk discount rate should be applied to each separate component of cashflows – as statistical risk of each component will differ
- IN PRACTICE, single risk discount rate is commonly used, bearing in mind the average risk of the product
- This keeps it simple
- And difficult (time and data requirements) to analyse accurately the variability of different cashflow components
A deterministic or stochastic model?
A deterministic or stochastic model?
- Deterministic model – parameter values are fixed at the outset of running the model and result is a single outcome
- Sensitivity analysis and scenario testing can then be carried out to assess variability of results
- Stochastic model – estimates at least one of the parameters by assigning it a probability distribution
- Run a large number of times and values of stochastic parameters selected from distributions on each run
- Outcome is a range of values giving understanding of likely distribution of outcomes
Merits of a deterministic model
Advantages:
- More readily explicable to a non-technical audience
- Clearer what economic scenarios have been tested
- Cheaper and easier to design
- Quicker to run
Disadvantages:
- Requires thought as to range of economic scenarios that should be tested
Limited economic scenarios testes = danger that certain scenarios are not identified
- Users can get blinded by science by complex models – assuming they must work but without verifying or testing this
Merits of stochastic model
- Tests wider range of economic scenarios
- Programming is more complex and run time longer but benefit is quality of the result
- Depends on parameters used in any standard investment model
- Actuary must decide if increase amount of info provided by model justifies significant additional computations
- Other NB considerations:
degree of spurious accuracy introduced,
increased difficulty in interpreting and communicating results
and questionable accuracy of distribution functions that are replacing the deterministic values
- stochastic models are important in assessing impact of financial guarantees or to allow for investment mismatching risks – because good at allowing for uncertainty involved
How can a combination of deterministic and stochastic modelling be used?
A combination of deterministic and stochastic modelling
- In many cases problem solved by combining the two
- Variables whose performance is unknown and risk associated with them is high might be modelled stochastically
- While other variables can be modelled deterministically
- Stochastic approach usually limited to economic assumptions
- Demographic assumptions modelled deterministically
Discuss the dynamism in the model.
Dynamism of the model
- In all cases dynamism of model is vital
- Means that asset and liability parts of the model and all assumptions are programmed to interact as the would in real life
- E.g. inflation and interest rates are consistent
- Rules need to be determined as to how various features would interact in different circumstances
- Actuarial judgement may be required in choosing and using model and in setting parameters and interactions between different features
- Interactions important when assets and liabilities are being modelled together
How is a deterministic model developed?
Developing a deterministic model
- Specify the purpose of investigation
- Collect, group and modify data
- Choose form of the model – identifying its parameters or variables
- Ascribe values to parameters using past experience and appropriate estimation techniques
- Construct model based on expected cashflows
- Test model in order to identify any build errors and correct if necessary
- Check that goodness of fit is acceptable – attempt to fit another model if first choice doesn’t fit well
- Run model using estimates of values of variables in the future
- Run the model several times to assess the sensitivity of the results to different parameter values
- Model might be run under different scenarios to test the robustness of the results to many parameters changing at the same time
How is a stochastic model developed?
Developing a stochastic model
- Stochastic modelling would involve same process, with additional or alternative steps:
- Choose suitable density function for each of the variables to be modelled
- Specify correlation between variables
- Run the model many times – each time using random sample from chosen density function
- Produce summary of results that shows distribution of the modelled results after many simulations
What should the sensitivity analysis look at?
Reliability of the results
Understanding potential variability of experience
Model error
Parameter error
Alternative ways of allowing for risk
What should the sensitivity analysis look at? - Reliability of results and model error
Reliability of the results
- Results from model depend on model itself and values assigned to the parameters
- Output should not be assumed correct
Model error
- If model developed is not appropriate for the financial products, schemes, contracts or transactions being modelled – possibility of model error
- Checks of goodness of fit needed to assess the suitability of the model
What should the sensitivity analysis look at? - Understanding the potential variability of experience
Understanding potential variability of experience
- Stochastic model tries illustrating the potential variability of the experience – but results that it produces are dependent on accuracy of model and its parameter values
- For deterministic model potential for uncertainty is greater since fewer scenarios are tested
- Re-running with different but feasible parameter values will produce alternative results and help illustrate potential deviations
- Re-running with series of different sets of parameter values (chosen from PDF for such values) will help illustrate range in which actual experience may lie or even creating probability distribution for this experience
- Extent to which this can be achieved will depend upon:
confidence with which probabilities can be assigned to different sets of parameter values used
time it takes to run the model
the associated costs
- running the model on different sets of assumptions is useful in highlighting errors in a model
What should the sensitivity analysis look at? - Parameter error
Parameter error
- Effect of mis-estimation of parameter values can be checked by carrying out a sensitivity analysis
- Involves assessing effect on output of model of varying each of the parameter values
- Any correlation between different parameters should be allowed for
- When model used for pricing, results from sensitivity analysis will help assess the margins that need to be incorporated into parameter values
- E.g. consider steps actuary takes if they identify that product is unduly sensitive to withdrawal rates and mortality rates
- If product profitability is sensitive to any factor the results may indicate need to redesign the product OR increase margins in assumptions
- If product is too sensitive to increasing withdrawal rates, then reduction in surrender values should be considered
- If too sensitive to mortality, then reinsurance programme could be revised
- OR, additional margins could be included in pricing basis to reflect increased risk
- When models used to assess return on capital and profitability of existing business – results enable actuary to quantify effect of departures from chosen parameter values when presenting results
What should the sensitivity analysis look at? - alternative ways of allowing for risk
Alternative ways of allowing for risk
- Statistical risk associated with the parameter values – can be allowed through the risk element of the risk discount rate
- Alternative would be to use predetermined discount rate and then assess the effect on results of the model of statistical risk
- Predetermined discount rates – means discount rate arbitrarily set by shareholders (perhaps based on return on risk-free assets)
- We discount cashflows at risk-free rate and used more pessimistic parameter values instead of best estimate parameter values
- Degree of pessimism should correspond to risk margin introduce in first approach
- Where a PDF can be assigned to a parameter – may be possible to derive variance of profit or return on capital analytically
- BUT, difficult to objectively assign a PDF to value of any parameter
- A sensitivity test can be carried out
- They will both help in assessing margins or in quantifying the effect of departures from chosen parameter values
- Using sensitivity analysis is a pragmatic, transparent and informative way of understanding the parameter risk without difficulty of deciding upon some arbitrary PDF to represent the uncertainty
What are some of the common applications of actuarial models?
Using models in pricing
Setting future financial strategies
Risk management models
Valuing liabilities
Valuing options and guarantees
What are some of the common applications of actuarial models? - Using models in pricing
Using models in pricing
- Model could be developed to determine a premium or charging structure for new or existing product that will meet insurance company’s profit requirement
- A model will be needed to set the premium
- For pricing purposes model points are used to represent profile of business expected under a product
- Company will use model to monitor the appropriateness of premium rates at regular intervals, to:
Check that business is profitable
Check that rates are appropriate for all groups
Ensure the rates remain competitive
Using models in pricing - Meeting profit requirements
Meeting profit requirements
- Premium or charges for model points can be set so as to produce profit required by company
- Difficult to achieve for all model points – in particular for small policies
- Because element of expenses incurred in relation to each policy will be fixed – allowing for fixed costs makes it difficult to achieve adequate profitability
- May instead focus on total profitability resulting from group of model points
- Group chosen to represent the expected new business mix and volume for product – there will be a degree of cross-subsidy within the group of model points
- Introducing cross-subsidies generates risk that actual business mix is not as assumed (insurer must be aware)
Using models in pricing - Competitive premiums
Competitive premiums
- Premium or charges need to be considered for marketability
- Might lead to reconsideration of:
Design of product – either remove features that increase the risks within net cashflows or include features that differentiate products from competitors
Distribution channel used – revision of assumptions used in model or higher premium or charges used without loss of marketability
Company’s profit requirements
Size of the market
Whether to proceed with marketing the product
