Requirements of a good model

A good model will:

- be valid, rigorous and well documented

- be communicable and the output verifiable

- not be overly complex or time consuming to run

- be capable of development and refinement

- be capable of being implemented in a range of ways.

- reflect the risk profile of the business being modelled

- allow for all the significant features of the business

being modelled

- have appropriate input parameters and parameter values

A model needs to allow for all the cashflows that may arise, including:

- guaranteed and discretionary benefits e.g.

reversionary and terminal bonuses

- cashflows arising from any supervisory requirement to

hold provisions

- the potential cashflows arising from options and

guarantees

Dynamic model

Allows for the interaction between the parameters and variables affecting the cashflows

Steps involved in running a deterministic model

- specify the purpose
- collect, group and modify the data
- choose the form of model
- identify the parameters and variables
- ascribe the parameter values
- construct a model based on expected cashflows
- check the goodness of fit is acceptable
- fit a new model if the first choice does not fit well
- run the model using selected values of the variables and values that will apply in the future
- sensitivity test the parameters

Steps involved in running a stochastic model

- specify the purpose
- collect, group and modify the data
- choose a suitable density function for each stochastic variable
- specify the correlations between the variables
- construct a model based on expected cashflows
- check the goodness of fit is acceptable
- fit a new model if the first choice does not fit well
- run the model many times using randomly generated values of the stochastic variables
- produce a summary of the results

Risk discount rate could allow for

- the return required by the company

- the level of statistical risk (assessed analytically or by sensitivity analysis or from a stochastic model)

Premiums resulting from the model may need to be considered relative to the market, which may require reconsideration of:

- product design
- distribution channels
- profit requirement
- size of the market
- whether to go ahead with the product

Define a model

A cut-down, simplified version of reality

…. that captures the essential features of a problem

…. and aids in:

—- understanding of the problem.

—- producing (potential) answers to the problem.

3 Approaches to obtaining a model

- a commercial modelling product could be purchased
- an existing model could be reused, possibly after modification
- a new model could be developed

The merits of the modelling approaches will depend on (5)

- the level of accuracy required
- the “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

The prime objective in building a model

To enable a provider of financial products to be run in a sound financial way.

Merits of a deterministic model

- more readily explicable to a non-technical audience, since the concept of variables as probability distributions is not easy to understand.
- it is clearer what economic scenarios have been tested
- the model is usually easier to design and quicker to run.

Disadvantage of a deterministic model

it requires thought as to the range of economic scenarios that should be tested.

Merits of a stochastic model. what are stochastic models particularly good at?

Tests a wider range of economic scenarios.

Stochastic models are particularly important in assessing the impact of financial guarantees.

Disadvantage of a stochastic model

The programming is more complex and the run time longer.

What is meant by a “dynamic” model

The asset and liability parts are programmed to interact as they do in reality

and the assumptions affecting assets and liabilities (for example inflation and interest rates) are consistent.

Model point

A representative policy.

It is usual to identify model points, which represent relatively homogeneous underlying groups of policies.

The risk discount rate could allow for (2)

- the return required by the company

- the level of statistical risk (assessed analytically or by sensitivity analysis or from a stochastic model)

Considering the resulting premiums from the model relative to the market requires consideration of (5

- product design
- distribution channel
- profit requirement
- size of market
- whether to go ahead with the product.

Statistical risk (3 parts)

Comprises:

- model risk
- parameter risk
- random fluctuation risk

The level of statistical risk could be assessed in 4 ways

- analytically, by considering the variances of the individual parameter values (this is a proxy to assess the possible magnitude of deviation from the model in reality)
- by using sensitivity analysis, with deterministically addressed variations in the parameter values.
- by using stochastic models for some, or all, of the parameter values and simulation
- by comparison with any available market data.

Why is a model necessary in the first place?

Some problems cannot be solved by closed-form solutions, they are too complex.

Need some simplification to get insight into the problem.

How would a model aid in understanding the problem? (4)

- What are the essential features
- Interactions
- What can happen (possible output)
- Often just the act of producing a model, highlights issues

A rigorous model

One that produces realistic (and hence useful) results under a wide range of circumstances and conditions.