# 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