Chapter 18: Modelling Flashcards
(24 cards)
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’.
The final phrase in this definition recognises the importance of being able to communicate the results effectively.
Modelling requires a balance to be struck between which two things?
- Reality, and hence complexity
- Simplicity, for ease of use, verification and interpretation of results
Where might a model come from and what factors affect the decision about where to get it?
- A new model could be developed in-house
- An existing model might be modified
- A commercial model might be purchased externally
- The factors that need to be considered are:
* 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
What is the advantage of 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
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
- Refinable 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 behaviour of variables
Define what is meant by “dynamism” of a model
If a model is dynamic, then the asset and liability parts of the model and all the assumptions are consistent with each other and are programmed to interact under different scenarios as they do in reality.
For example:
* Inflation rates and investment returns
* Bonus rates and investment returns
* Wtihdrawal rates and economic conditions
What is a model point?
The underlying business being modelled will typically comprise a very wide range of different policies, and these will need to be brought together into a manageable number of relatively homogeneous groups. The groupings need to be made in a way that each policy in a group is expected to produce similar results when the model is run. It is then sufficient for a representative single policy in each group to be run through the model, the result to be found, and for this result to be scaled up to give the result of the total set of policies in the group.
The representative single policy in a group is termed a “model point” and a set of such model points can then be used to represent the whole of the underlying business.
The number of model points used will depend on:
* the computing power available
* time constraints
* the heterogeneity of the class
* the sensitivity of the results to different choices of model points
* the purpose of the exercise
When are model points not used?
Model points are not generally used when valuing liabilities for calculating reserves.
The normal procedure for determining the value of life assurance or pension scheme liabilities is to value the benefits for each actual policy or scheme member individually
In many territories this may be a regulatory requirement.
However, model points may be required in order to answer various ‘what if’ questions
Set out the steps involved in developing and running a deterministic model
- Specify the purpose of the investigation
- Collect, group and modify data
- Choose the form of the model and its parameters / variables
- Ascribe values to those parameters using past experience / estimations
- Construct a model based on expected cashflows
- Test the model and correct if necessary
- Check goodness of fit using past data, modify if poor
- Run using estimates of future values of variables
- Sensitivity tests (and maybe scenario test) using different parameter values
Additional / alternative steps in a stochastic model
- Choose a density function for each of the stochastic variables
- Specify correlations between the variables
- Run model many times using a random sample from the chosen density function
- Produce a summary of results - a distribution (e.g. summarised at various confidence levels)
Outline the 2 factors to consider in choosing the time period (or frequency) for the projection of the cashflows in a model
- The more frequent the cashflows are calculated the more reliable the output from the model, although there is a danger of spurious accuracy
- The less frequent the cashflows are calculated the faster the model can be run, and results obtained.
What are the relative merits of deterministic vs stochastic models?
Deterministic:
* Quicker, cheaper and easier to design, build and run
* Clearer what scenario have been tested
* Results are easier to explain to a non-technical audience
Stochastic:
* Allows naturally for the uncertainty of outcomes
* Enables 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.
Outline how a deterministic model could be used to determine a set of new premium rates for a term assurance contract
- An objective would be set based on profit criterion and an appropriate time horizon
- Data relating to the existing profile of customers would be collected and model points created. It would be modified for any perceived future differences in the profile of customers
- Parameter values for key assumptions such as mortality, expenses, lapses and investment returns would be set based on past experience.
- For each model point, the model would be run, projecting future cashflows and discounting the net profits at the risk discount rate (RDR). The premium would be varied until the required profit criterion is met.
List 4 methods of assessing statistical risk
- In some situations, analystically - 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 the 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 practce a single rate is often used based on the average risk of the product
Explain why even a stochastic model does not illustrate the complete variability of results
The use of a stochastic model goes some way to illustrating the potential variability of the experience, but the results that it produces are still dependent on the accuracy of the model and its parameter values.
In the case of a deterministic model, the potential uncertainty of the results is greater, because fewer scenarios are tested.
The re-running of a model with different, but feasible, parameter values will produce alternative results and hence help to illustrate the potential deviations.
The re-running with a series of different sets of parameter values, perhaps chosen from a probability distribution for such values, will help to illustrate the likely range in which actual experience may lie, perhaps as far as creating a probability distribution for this experience.
Define model error and stat how it can be assessed
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 for goodness of fit will be needed to assess the suitability of the model, but taking account of expected changes in experience into the future.
Define parameter error and state how it can be assessed
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.
What are the different ways of allowing for risk in a model?
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.
More generally, a sensitivity analysis, can be carried out. Whichever of these two is used, they will help in assessing margins or in quantifying the effect of departures from the chosen parameter values when presenting the results of the model.
Other than profitability and marketability, what is another big consideration in determining a suitable set of premium rates?
To check that the rates are appropriate for all groups, i.e. the rates are not inappropriately low or high for certain types of policyholder.
Explain why a life insurance company may decide that the profit criterion does not need to be met for all model points
It will be difficult to achieve this for all model point, especially for small policies. This is because an element of the expenses incurred in relation to each policy will be fixed. Allowing for these fixed costs makes it difficult to achieve profitability on small policies.
It is possible for the desired level of profitability to be reached in aggregate, without requiring every single model point to be profitable in its own right.
Outline five factors that might be reconsidered, if the premium rates are not thought to be marketable / competitive
- The design of the product, so as either to remove features that increase the risks within the net cashflows, or to include features that will differentiate the product from those of competing companies
- The distribution channel to be used, if that would permit either a revision of the assumptions to be used in the model, or a higher premium or charges to be used without loss of marketability
- The company’s profit requirement
- The size of the market
- Whether to proceed with marketing the product
Explain briefly how a model could be used to assess the capital requirements and the return on capital when writing a new contract
The net cashflows for the model points described in the section on pricing above can be grossed up for the expected new business and used to assess the amount of capital that will be required to write the product, either on a regulatory or an economic basis.
Any one-off development costs can be added, to the extent that they are not amortised and included in the cashflows used.
This gives the total capital requirement and can be compared with the profits expected to emerge from the product so as to determine the expected reutrn on that capital.
How can models be used in risk management?
Cashflow models are commonly used in risk management to determine the amount of capital that it is necessary to hold to support the risks retained by a financial institution.
As well as the full corporate model to assess capital requirements, models of specific risks can be used to determine the extent of a risk event that will occur at a given probability, even if a full stochastic model is too slow, too complex or otherwise not used.
A standard equity market stochastic model can be used and calibrated to historical performance of the market beign considered. By running the model several thousand times and ranking the results, the equity fall that gives the one in a thousand worst result can be found.
