Chapter 18: Modelling Flashcards
What is a model?
A model can be defined as ‘a cut-down, simplified version of reality that captures the essential features of a problem and aids understanding’.
It is important to be able to communicate the results effectively.
Modelling requires a balance to be struck between realism and simplicity.
What is the advantage of using an actuarial model over a formula?
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
What are the various approaches to modelling and the factors influencing the merits of each?
When faced with an actuarial or financial problem, there are various approaches to modelling:
* A commercial modelling product could be purchased
* An existing model could be reused, possibly after modification
* A new model could be developed
The merits of each of these approaches will depend on the following:
* 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.
Outline the operational issues that need to be considered when designing and constructing a model
SCARCER FILES
Simple, but retains key features
Clear results
Adequately documented
Range of implementation methods
Communicable workings and output
Easy to understand
Refineable and developable
Frequency of cashflows (balance accuracy vs practicality)
Independent verification of outputs
Length of run not too long
Expense not too high
Sensible joint behavior of variables
What is a deterministic and stochastic model?
A deterministic model is one where the parameter values are fixed at the outset of running the model and the result of running the model is a single outcome.
A stochastic model estimates at leaast one of the parameters by assigning it a probability distribution. The model is run a large number of times, with the values of stochastic parameters being selected from their distributions on each run.
What are the relative merits of deterministic and stochastic models?
Deterministic models are:
* Easier to explain to non-technical audiences
* Clearer as to which economic scenarios have been tested
* Usually cheaper and easier to design, and quicker to run.
Stochastic models are:
* Allows naturally for the uncertainty of outcomes
* Enable better modelling of the correlations between variables
* 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
What are the disadvantages of deterministic and stochastic models?
Deterministic model:
* Requires thought as to the range of economic circumstances that should be tested.
Stochastic model:
* Programming is more complex and the run time is longer
Define what is meant by ‘dynamism’ of a model
A model is dynamic if the assets and liability parts of the model and all the assumptions are programmed to interact as they would in reality.
Rules need to determine as to how the various features would interact in different circumstances.
These interactions are usually much more important than the type of model.
What are the steps involved in creating a deterministic model?
- Specify the purpose of the investigation
- Collect, group and modify data
- Choose the form of the model, identifying its parameters or variables
- Ascribe values to the parameters using past experience and appropriate estimation techniques
- Construct a model based on the expected cashflows
- Test the model in order to identify any build errors, and correct if necessary
- Check that the goodness of fit is acceptable
- Run the model using estimates of the values of variables in the future
- Run the model several times to assess the sensitivity of the results to different parameter values
What additional steps are needed to develop a stochastic model?
- Choose a suitable density function for each of the variables to be modelled stochastically
- Specify correlation between variables
- Run the model many times, each time using a random sample from the chosen density function
- Produce a summary of the results that shows the distribution of the modelled results after many simulations have been run.
List four methods of assessing statistical risk
- In some situations, analytically – by considering the variances of the individual parameter values used
- By using sensitivity analysis, with deterministically assessing variations in parameter values
- By using stochastic models for some, or all, if the parameter values and simulation
- By comparison with any available market data
What should the rate used to discount the net cashflows in model reflect?
- 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
Discuss model and parameter error
There is a possibility of model error if the model developed is not appropriate for the financial products, schemes, contracts or transactions being modelled.
Checks of goodness of fit will be needed to assess the suitability of the model, but taking account of expected changes in experience into the future.
The effect of mis-estimation of parameter values can also be investigated by carrying out a sensitivity analysis. This involves assessing the effect on the output of the model of varying each of the parameter values. When doing this, any correlation between different parameters should be allowed for.
Discuss alternative ways of allowing for risk
The statistical risk associated with the parameter values can be allowed through the risk element of the risk discount rate.
An alternative would be to use a predetermined discount rate and then assess the effect on the results of the models of statistical risk.
Where a probability distribution can be assigned to a parameter, it may be possible to derive the variance of the profit or return on capital analytically.
The main problem with this is the difficulty of objectively assigning a probability distribution to the value of any parameter.
List the common applications of actuarial models
- Using models in pricing
- Meeting profit requirements
- Competitive premiums
- Business strategy
- Assessing the capital requirements and the return on capital
- Setting future financing strategies
- Risk management models
- Valuing liabilities
- Valuing options and guarantees
What should be reconsidered when premiums or charges produced need to be considered for marketability?
- The design of the product, so as either to remove features that increase the risks, or to include features that will differentiate the product from those of competing companies
- The distribution channel used, if that would permit either a revision of the assumptions to be used int he model, or a higher premium or charges to be used without loss of marketability
- The company’s profti requirements
- The size of the market
- Whether to proceed with marketing the product
