Part 7 Flashcards
Definition of a model
Cut-down, simplified version of reality that captures the essential feature of a problem and aids understanding
- 3 approaches to modelling
- considerations to chose approach
- Purchase commercial modelling product
- Reuse exisiting model (possibly after modification)
- Develop new model
- Level of accuracy required
- In-house expertise available
- Number of times the model is to be used
- Desired flexibility of the model
- Cost of each option
Explain “valid” in terms of a model
“valid” means that we should e.g. not use a stochastic investment model which has been developed for projecting assets proceeds over periods of 30 or more years, if we are only interested in cashflows over the next 5 years
Definition of a “rigorous” model
A model that produces realistic (and hence useful) results under a wide range of circumstances and conditions
Dynamic model
Allows for interaction between the parameters and variables affecting the cash flows
Cash flows to consider when modelling a final salary occupational pension scheme
Inflows:
- Contributions made by the employer and possibly members
- Investment income on assets
- Capital gains on any asset redeemed
- Transfer values into the scheme
Outflows:
- Pension payments
- Transfer values out of the scheme
- Any othe benefit payment (e.g. death benefit)
- Administration expenses
- Tax if applicable
Developing a deterministic model
- Specify the purpose of the investigation
- Collect, group and modify data
- Choose the form of the model (identify parameters and variables)
- Ascribe values to the parameters
- Construct a model based on the expected cash flows
- Check that the goodness of fit is acceptable (e.g. running a past year and comparing the model with the actual results)
- Fit a new model if the first choice did not fit well
- Run the model using estimates of the values of variables in the future
- Run the model several times to assess sensitivity of the results to different parameter values
Developing a stochastic model
- Specify the purpose of the investigation
- Collect, group and modify data
- Choose a suitable density function for each of the variables to be modelled stochastically
- Specify correlation between variables
- Construct a model based on the expected cash flows
- Check that the goodness of fit is acceptable (e.g. running a past year and comparing the model with the actual results)
- Fit a new model if the first choice did not fit well
- Run the model many times, each time using a random sample from the chosen density function(s)
- Produce a summary of the results that shows the distribution of the modelled results after many simulations have been run
Definition of “model point”
Representative single policy in a group. This policy can be used to represent the whole of the underlying business
What important characteristigs would you expect the model point to capture when modelling a without-profit term assurance product
- Term of the policy
- Sum assured, payable on death
- Basis of policy (single life, joint life, last survivor)
- Age of life/lives covered
- Gender of life/lives covered
- Smoker status of life/lives
- Health status of life/lives
3 factors that influence the number of model points used
- Heterogeneity of the class
- Sensitivity of the results to different choices of model points
- Purpose of the exercise
Risk discount rate for model points could allow for
- the return required by the company
- the level of statistical risk
Assessing the level of statistical risk
- Analytically (consider variances of the individual parameters)
- Sensitivity analysis
- Stochastic models
- Comparison with available market data
Decrements of a benefit scheme
- Death before retirement
- Death after retirement
- Withdrawal from active service
- Transfer out
- Ill-health retirement
- Normal/early/late retirement
- Other options, e.g. exchanging some pension for a cash lump sum
Use of models for risk management
Determine the amount of capital that is necessary to hold to support the risks retained by a financial institution
Mitigating model error
Checks of goodness of fit to assess the suitability of the model
Limitations of models and mitigations
- Prone to model error (results are only as as good as the underlying model)
- Consider losts of potential models
- Employ suitable expertise to identify the most appropriate model
- Level and timing of cash flows is uncertain
- Use stochastic moel
- Risk of data error (results will depend upon the data used=
- Ensure data is regularly updated
- Prone to parameter error (results depend upon the suitability of the assumptions used)
- Carry out sensitivity testing to identify the key assumptions, pay careful attention to the setting of those financial assumptions which are most important
Two main sources of data
- Publicly available data
- Internal data
Poor data can be due to … (2)
- Poor management control of data recording or its verification process
- Poor design of the data systems
Good quality data could mean
- Complete (i.e. no ommissions)
- accurate
- up-to-date
- consistent with previous data
- Necessary level of details
- Audit trail
Checks on data
- Detailed audit
- Resaonability tests:
- Averages
- Impossible values
- Outliers
- Consistency over time
- Check asset data vs. liabilities
- Spot checks
- In particular on the large items
- random
Assertions to be examined for data
- That a liability or asset exists on a given date
- That a liability is held or an asset is owned on a given date
- That when an event is recorded, the time of the event and the associated income or expenditure are allocated to the correct accounting period
- That data is complete, i.e. no unrecorded liabilities, assets or events
- That the appropriate value of an asset or liability has been recorded
4 causes for the lack of ideal data
- Data have not been captured at a sufficient detailed level
- There may be insufficient data to provide a credible result (e.g. new product)
- Poor systems
- Practically difficult/impossible to get good data
Main aim of risk classification
- Obtain homogeneous data
- Reduction of heterogeneity in the data makes the experience in each group more stable
- Therefore enables the data to be used more appropriately for projection purposes
Common economic assumptions
- Investment returns (e.g. bond yields, equity returns)
- Discount rate (for valuing liabilities)
- Earnings inflation
- Price inflation
- Pension increases
- Expenses
Demographic assumptions for pension scheme
- Rates of retirement in good health (early, normal late)
- Rates of ill-health retirement
- Rates of withdrawal (for reasons other than retirement or death)
- New entrant rates
- Rates of mortality before and after retirement
- Proportion married
- Average age of spouses
- Spouses’ mortality
- Salary scale
Historical data may be obtained from … (4)
- National statistics (published by government bodies and economists)
- Indistry data
- Tables compiled by actuaries
- Past information relating to the particular contract being considered
Where a cashflow model is being used to price a product, the risk to the provider from adverse future experience could be allowed for by
- Adjusting the risk element of the risk discount rate
- Using a stochastic discount rate
- Applying margins to the expected values
Features that increase risk in a product design
- Lack of historical data
- High guarantees
- Policyholder options
- Overhead costs
- Complexity of design
- Untested market
Classification of expenses
-
Fixed vs. variable
- Example of variable expenses: Commissions, postal costs, legal expenses
-
Direct (directly belonging to a particular class of business) vs. indirect (no direct relationship to any one class of business)
- Example of direct expenses: Underwriting costs, contract administration claims settlement expenses
- Example of indirect expenses: Computing, human resources, general management
Expenses need to be allocated between …
- Classes of business
- Functions (=activity, operation)
- Securing new business
- Maintaining existing business (renewal and investment)
- Terminating business (including claims)
Types of loading for expenses in contracts (3)
- Fixed amount per contract
- Percentage of the premium charged
- Combination of the above
Two elements of inflation adjustment needed to detemine an appropriate expense loading for premium rating
- Historic (bring expense data up-to-date)
- Prospective (inflate the expense data to the time when the expenses are expected to be incurred)
Calculation of premium or contribution
value of future premium(s) =
- value of benefits
- value of expenses
- contribution to profit
value of benefits = “risk premium”
total premium = “office premium”
Scenarios to test premium for robustness
- Economic scenarios (e.g. investment returns being higher or lower than expected)
Examples of distribution systems in the UK
- Independent intermediaries who select products for their clients from all or most of those available on the market
- Tied agents, who offer the products of one provider or a small number of providers
- Own sales force, usually employed by a particular provider to sell its products direct to the public
- Direct marketing, via press advertising, over the telephone, internet or mailshots
Approaches to financing benefits
- Unfunded approach
-
Pay-as-you-go (PAYG)
- Does not tie up funds
- Low transaction costs
-
Pay-as-you-go (PAYG)
- Funded approach
-
Lump sum in advance
- Ties up excessive funds
- Terminal funding (payment is made whenever a benefit start to be paid)
- Regular contributions
- Just-in-time funding (Funds are set up as son as a risk arises in relation to the future financing of the benefits (e.g. bankruptcy or change in control))
- Smoothed PAYG (funds that are set up to smooth the costs under a pay-as-you-go approach)
-
Lump sum in advance
