Chapter 18 - Modelling Flashcards
(18 cards)
What is a model?
A model can be defined as a cut-down, simplified version of reality that captures the essence of the problem and aids understanding
It is important to be able to communicate the results effectively
Modelling requires a balance to be stuck between which 2 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 model can be a:
Commercially produced product
Modified (reuse) existing model
New model
The merits of each of these approaches will depend on the following
**All Engineers Use Fine Calculators **
The level of Accuracy required
‘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
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
* Withdrawal rates and economic conditions
Outline the operational issues that need to be considered when designing and constructing a model
CHIC DENT
Be easily Communicable, with clearly displayed results
Have sensible joint behaviour of variables: The model should make allowance for variables that are linked to each other
Be capable of Independent verification and communicable to those receiving the advice
Not be overly Complex or time-consuming to run
Be well Documented: For understanding of assumption and usability by other members of staff
Expandable: Be capable of development and refinement
Numerous Implementations: Be capable of being implemented in a range of ways
Have an appropriate Time period between projected cashflows, balancing the reliability of the output with the speed of running the model
Set out the steps involved in developing and running model
SOSCCRO
Specify the purpose and key feature of the model
Obtain and adjust the data
Set the parameters/assumptions, including any dynamic links
Construct the model cashflows
Check the accuracy and fit of the model, and amend if necessary
Run the model as many times as required
Output and summarise the results
List 4 methods for 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, of the parameter values and simulation
By comparison with any available market data
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 the 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 differeces 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 woulld be varied until the required profit criterion is met.
What are the RELATIVE merits of deterministic vs stochastic models?
Deterministic:
* Quicker, cheaper and easier to design, build and run
* Clearer what scenarios 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
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
What are model points? Why are they used? How may they be chosen?
A model point is a representative single policy
The business being modelled may comprise a very large number of different policies and it may be too time consuming to run all of these through a model.
So, policies are classified into relatively homogeneous groups
A model point for each group is chosen that is representative of the whole group
The model point is run through the model and output is then scaled up by the number of policies in the group to give the results of the whole group.
For pricing purposes, model points are chosen to reflect the expected profile of future business to be sold. This could be based on the existing profile, or that of a similar product.
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 pollicy or scheme member individually.
In many teritories this may be a regulatory requirement
However, model points may be required in order to answer various “what if” questions
How can models be used in risk management?
Models can be used to determine:
* The extent of a risk event that will occur with a given probability
* The amount of capital that is needed to support such an event
Outline 5 factors that might be reconsidered, if the premium rates are not thought to be marketable/competitive
The design of the contract, to remove features that increase the riskiness of the net cashflows or to add differentiating features
The distribution channals (revision of assumptions, premium rates)
The profit criterion (company’s profit requirement)
The size of the market
The decision to market the contract in the first place
What are the different ways of allowing for risk in a model?
Statisitical risk associated with parameter values can be allowed for in the discount rate and/or by including margins in the parameter values
Alternatively, use a pre-determined discount rate but incorporate margins in the individual parameter values, e.g. mortality rates, expenses
Define model error and state how it can be assessed
The risk that the model is inappropriate for the contracts being modeled.
-It can be assessed using goodness of fit tests
Define parameter error and state how it can be assessed
The risk of mis-estimation of parameter values
-It can be assessed using a sensitivity analysis. The results of the analysis can help in assessing the margins to be incorporated into the parameter values or to quantify the effect of departures from the chosen parameter values.
Two model validation tools
Sensitivity analysis: vary individual assumptions and inputs to assess the impact on the results
Scenario Testing: changing assumptons in combination to represent an economic scenario such as a recession
