18. Modelling Flashcards
1
Q
What is a model?
A
- A cut-down simplified version
- Of reality that captures the essential features of a problem
- And aids understanding
- It must communicate results effectively
2
Q
What are the uses of a model?
5
A
- To set premiums and charges for insurance products
- To value options and guarantees (stochastic model)
- To determine the financial strategy for a benefit scheme
- To aid risk management and determine capital requirements
- To understand the potential variability of experience (sensitivity and scenario testing)
Sensitivity analysis - varying individual assumptions and assessing the impact on the results Scenario testing - changing the assumptions in combination
3
Q
What is a deterministic model?
A
- Parameter values are fixed at the outset and the result of running the model is a single outcome
4
Q
What are the advantages and disavantages of deterministic models?
3/1
A
Advantages:
* More readily explainable to a non-technical audience
* Clearer what economic scenarios have been tested
* Easier to design and quick to run
Disadvantages:
* Requires a wide range of different economic scenarios to be tested
5
Q
What are the steps in deterministic modelling?
A
- Specify the objective of the model
- Collect, group (into model points), and modify data
- Choose the form of the model, identify its parameters and variables
- Ascribe value to the parameters using past experiences and appropriate estimation techniques
- Construct a model based on expected cashflows
- Test the model for any errors and correct if necessary
- Check the goodness of fit and modify if the fit is poor
- Try to fit a different model if the first does not work or change parameters
- Run the model using selected values of the variables
- Run the model using the estimates of the values of variables in the future
- Perform sensitivity tests
- Summarise the results
6
Q
What is a stochastic model?
A
- Model that estimates at least one of the parameters by assigning it a probability distribution
- Run simulations and assign probability of each scenario, making it possible to have a distribution of outcomes
7
Q
What are the advantages and disadvantages of stochastic models?
A
Advantages:
* Tests a wider range of scenarios
* Allows naturally for the uncertainty of outcomes
* Enables better modelling of correlations between variables
* Can assess the impact of financial guarantees
Disadvantages:
* Programming is more complex
* The time to build and run the model is longer
8
Q
What additional steps are involved in stochastic modelling?
A
- Specify the objective of the model
- Collect, group (into model points), and modify data
- Choose suitable density functions for stochastic variables
- Specify correlation variables
- Ascribe value to the non-stochastic parameters using past experiences and appropriate estimation techniques
- Construct a model based on expected cashflows
- Check the goodness of fit
- Try to fit a different model if the first does not work or change parameters
- Run the model using a random sample from the chosen density functions
- Perform sensitivity tests (deterministic variables)
- Summarise the results showing their distributions
9
Q
What are the two things that modelling requires a balance to be struck between
A
- Realism → Complexity – may be able to capture more clearly
- Simplicity → Ease of use, verification, and interpretation of results
10
Q
What is an alternative to modelling?
A
Using a formula to solve a problem.
11
Q
What is the advantage of an actuarial model over a formula
A
- Better able to reflect uncertain future events
- By giving an indication of the effects of varying the assumptions
- NB: Client understands the uncertainty involved in the underlying assumptions
12
Q
Where might the model come from?
3
A
It may be:
* A new model developed in-house
* A modification of an existing model
* A commercial product purchased externally
13
Q
What factors affect the decision about where to get a model?
6
A
The decision will depend on: (FENCED)
* Fit for purpose
* Expertise available in-house
* Need for flexibility
* Cost of each option
* Expected number of times the model is to be used
* Desired level of accuracy
14
Q
What operational issues need to be considered when designing and constructing a model?
A
SCARCER FILES
- Simple but retains key features
- Clear outputs
- Adequately documented
- Range of implementation
- Communicate workings and results
- Easy to understand
- Refinable and developable
- Frequency of cashflows (balance accuracy and practicality)
- Independent verification of outputs
- Length to run not too long
- Expense not too high
- Sensible joint behaviour of variables
15
Q
What two factors should be considered when choosing the time period (or frequency) for the projection of the cashflows in the model?
2
A
- The more frequently the cashflows are calculated, the more reliable the output from the model → DANGER of spurious accuracy
- The less frequently the cashflows are calculated, the faster the model can be run and results obtained
16
Q
What is meant by dynamism in a model?
A
- Dynamic model → Asset & liability part of the model + all assumptions are consistent with each other
- And programmed to interact under different scenarios as they do in reality
- E.g. Inflation, investment returns, bonus rates, withdrawal rates
17
Q
What is a model point?
A
A representative of a single policy.
18
Q
Why are model points used?
A
- Business being modelled comprises a very large number of different policies
- Too time-consuming to run all these through the model
- Policies are classified into relatively homogeneous groups
- A model point from each group is chosen → representative of the whole group
- Model point is run through the model
- The output is scaled up by the number of policies in the group → results for the whole group
19
Q
How are model points chosen?
A
- Pricing purposes: Model points chosen to reflect the expected profile of future business to be sold
- Based on the existing profile
- Or that of a similar product
20
Q
When are model points not used?
A
- Valuing liabilities → calculating provisions
- Normal procedure for valuing life assurance or pension liabilities
- Value the benefits for each actual policyholder or scheme member individually
- Might be a regulatory requirement
- Model points used to answer “what-if” questions
21
Q
What should the rate used to discount the net cashflows in a model reflect?
A
The discount rate should reflect:
* Return required by the company
* The level of statistical risk attached to the cashflows (variance of cashflows/risk)
* Different discount rates used for each cashflow → risk is different
* A single rate is used in practice → average risk of the product
22
Q
What are the four methods of assessing statistical risk?
A
- Analytically → considering the variances of the individual parameter values used
- Sensitivity analysis → varying individual assumptions and assessing the impact of the results
- Stochastic model → for some or all of the parameter values and simulation
- Comparison with any available market data
23
Q
How can a deterministic model be used to determine a set of new premium rates for a TA contract
A
- The objective is to set premiums based on a profit criterion (e.g., NPV 2% of NPV premiums).
- Data on the existing customer profile is collected, model points are created, and future changes are considered.
- Assumptions for mortality, expenses, lapses, and investment returns are set based on past experience.
- For each model point, the model is run to project and discount cashflows, adjusting the premium until the profit criterion is met
24
Q
Identify important characteristics that should be captured by the model points for a without-profit critical illness insurance policy
A
- Term of the policy
- Duration in-force or date of issue
- Sum assured payable on the occurrence of a critical illness
- Claim basis of policy (single life, joint, last survivor)
- Age of life/lives covered
- Gender
- Health status (whether covered on standard or rated terms)
- Smoker status
25
Why might a life insurance company decide that the profit criterion does not need to be met for all model points?
* If all model points were profitable in their own rate, it would result in a set of premiums that is:
1. Not smooth between different types of policyholders (e.g., age and sum assured).
2. Not competitive.
* More useful to ensure that the profit criterion is met in aggregate.
* Net cashflows in respect of the model points are scaled up by the expected volumes and mix of new business under the product → incorporated in a model of the whole company.
* Profitability of the class of business as a whole can then be assessed to determine if the profit criterion is met in aggregate.
* Set of premium rates varied until this is the case.
* Marketability considerations also play a role.
26
What factors should be considered if the premium rates (or charges) are not thought to be marketable?
* Design of the contract → remove features that increase riskiness of net cashflow or add differentiating features.
* Distribution channel.
* Profit criterion.
* Size of the market.
* Decision to market the contract in the first place.
27
Other than profitability and marketability, what is another consideration in determining a suitable set of premium rates?
* Capital requirement of the contract.
* Return on capital.
28
How can a model be used to assess the capital requirements and returns on capital when writing a new contract?
* Net cashflows from the pricing model → gross up for the expected volumes of new business.
* Capital requirement = New business strain + one-off development costs not amortized and already included in the cashflows used.
* Expected return on capital:
E(NPV of profit stream)=capital requirement.
29
How can models be used in risk management?
Models can be used to determine:
* Extent of a risk event that will occur with a given probability.
E.g., size of an equity market crash that occurs with a 1 in 200 probability.
* The amount of capital needed to support such a 1 in 200 probability event.
30
Why is it more appropriate to model contracts with variable risk factors such as interest rates with a stochastic model rather than a deterministic model?
Deterministic model:
* Changing the variable rate could be done to calculate the cost of risk using sensitivity testing and estimate the variability of the cost of risk.
* BUT the model will not take into account the probability of the cost.
Stochastic model:
* A probability distribution is assigned to a variable risk factor.
* Simulations can be run to calculate the cost of risk in each case.
* Provides the expected cost and its variability as many simulations are run.
* Takes into account the probability and likelihood of each outcome.
31
What might a stochastic model illustrate about the complete variability in results?
Results of a stochastic model are dependent on:
* Probability distribution for the stochastically modelled assumptions.
* Parameter values of the distribution.
* Correlation between assumptions.
* Not all assumptions are modelled stochastically; some deterministic parameters may be uncertain.
To understand additional volatility → Re-run the model using different probability distributions, parameters, and correlations.
32
What is model error and how can it be assessed?
* The risk that the model is inappropriate for the contracts being modelled.
* Assessed using goodness of fit
33
What is parameter error and how can it be assessed?
* Risk of mis-estimation of parameter values.
* Assessed using sensitivity analysis.
**Results can help in**:
* Assessing margins incorporated into parameter values (if pricing).
* OR quantify the effects of departure from the chosen parameter value
34
What are the different ways to allow for risk in a model?
* Risk element in the discount rate.
* Use of a pre-determined discount rate, incorporating margins into individual parameter values (e.g., mortality rates, expenses).
* If probability distribution is assigned to a parameter → Derive analytically the variability of profit or capital requirement.
* Use a stochastic model or sensitivity analysis to show variation in results
35
Explain, with an example, why it is more important to use a stochastic model than a deterministic model to assess the provisions required for a contract with a guaranteed minimum investment return of 5% pa
If Deterministic model is used:
* Assumes a fixed investment return
* Example scenarios:
1. 7% return => guarantee does not bite => cost = 0
2. 3% return => guarantee bites => costs incurred
* Limitation:
1. Sensitivity testing can estimate cost variability under different assumptions.
2. Does not indicate the likelihood of the guarantee biting.
If stochastic model is used:
* Models investment return as a random variable with a specified density function.
* Uses multiple simulations to calculate the guarantee cost in each case.
*Advantages over deterministic models:*
* Provides expected cost of the guarantee.
* Better estimates variability of the cost.
* Indicates the likelihood of the guarantee biting.
36
Why a stochastic model does not completely illustrate variability
Dependence on Assumptions:
* Results rely on chosen probability distributions for stochastic assumptions.
* Parameter values of these distributions affect outcomes.
* Correlations between assumptions impact results.
Not All Assumptions Are Modelled Stochastically:
* Some parameters remain deterministic and may still be uncertain.
Model Variability Can Be Tested Further By:
* Using different probability distributions.
* Adjusting parameters of the distributions.
* Changing correlation coefficients.
* Modifying deterministically modelled assumptions.
