18. Modelling Flashcards
What is a model?
- A cut-down simplified version
- Of reality that captures the essential features of a problem
- And aids understanding
- It must communicate results effectively
What are the uses of a model?
5
- 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
What is a deterministic model?
- Parameter values are fixed at the outset and the result of running the model is a single outcome
What are the advantages and disavantages of deterministic models?
3/1
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
What are the steps in deterministic modelling?
- 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
What is a stochastic model?
- 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
What are the advantages and disadvantages of stochastic models?
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
What additional steps are involved in stochastic modelling?
- 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
What are the two things that modelling requires a balance to be struck between
- Realism → Complexity – may be able to capture more clearly
- Simplicity → Ease of use, verification, and interpretation of results
What is an alternative to modelling?
Using a formula to solve a problem.
What is the advantage of an actuarial model over a formula
- 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
Where might the model come from?
3
It may be:
* A new model developed in-house
* A modification of an existing model
* A commercial product purchased externally
What factors affect the decision about where to get a model?
6
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
What operational issues need to be considered when designing and constructing a model?
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
What two factors should be considered when choosing the time period (or frequency) for the projection of the cashflows in the model?
2
- 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
What is meant by dynamism in a model?
- 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
What is a model point?
A representative of a single policy.
Why are model points used?
- 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
How are model points chosen?
- 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
When are model points not used?
- 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
What should the rate used to discount the net cashflows in a model reflect?
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
What are the four methods of assessing statistical risk?
- 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
How can a deterministic model be used to determine a set of new premium rates for a TA contract
- 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
Identify important characteristics that should be captured by the model points for a without-profit critical illness insurance policy
- 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
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.
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.
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.
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(NPVofprofitstream)=capitalrequirement.
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.
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.
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.
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
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
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
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.
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.
