Chapter 18: modelling

Question 1

What is a model

Answer 1

A model is a simplified version of reality that captures essential features of a problem and aids understanding. It should communicate results effectively

Question 2

Main uses of models

Answer 2

Pricing new products (or repricing old ones)
Valuing liabilities

Question 3

Sensitivity analysis

Answer 3

varying individual assumptions and assessing the impact on the results

Question 4

Scenario testing

Answer 4

Changing many assumptions in combination and assess the impact on the results

Question 5

Technical areas of model sign/Operational issues that need to be considered on a model

Answer 5

The model being used should be adequately documented.
The workings of the model should be easy to appreciate and communicate.
The results should be displayed clearly.
The model should exhibit sensible joint behavior of model variables.
The outputs from the model should be capable of independent verification for reasonableness and should be communicable to those to whom advice will be given.
The model, however, must not be overly complex so that either the results become difficult to interpret and communicate or the model becomes too long or expensive to run, unless this is required by the purpose of the model. I
The model should be capable of development and refinement – nothing complex can be successfully designed and built in a single attempt.
A range of methods of implementation should be available to facilitate testing, parameterisation and focus of results.
The more frequently the cashflows are calculated, the more reliable the output from the model, although there is a danger of spurious accuracy.
The less frequently the cashflows are calculated, the faster the model can be run and results obtained

Question 6

Model point

Answer 6

A representative single policy
Needs to represent the whole of the underlying business
Needs to capture the most important characteristics of the group

Question 7

Important characteristics that should be captured by the model points that would be used when modelling a without-profit term assurance product in order to set premiums.

Answer 7

term of the policy
sum assured payable on death
claim basis of policy (single life, joint life, last survivor
age of life / lives covered
gender of life / lives covered
smoker status of life / lives covered
health status of life / lives covere

Question 8

Level of statistical risk can be assessed by:

Statistical risk here is intended to encompass all types of risk, and comprises the model risk, parameter risk and random fluctuation risk

Answer 8

In some situations, analytically – by considering the variances of the individual parameter values used
by using sensitivity analysis, with deterministically assessed 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.

Question 9

Deterministic model

Answer 9

A deterministic model is one where the parameter values are fixed at the outset of running the model and the result of running the model is a single outcome.

Question 10

Merits of a deterministic model:

Answer 10

A deterministic model is more readily explainable 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 cheaper and easier to design
The model is quicker to run.
Disadvantage is that it requires thought as to the range of economic scenarios that should be tested

Question 11

Stochastic model

Answer 11

A stochastic model estimates at least one of the parameters by assigning it a probability distribution.
The model is run a large number of times, with the values of stochastic parameters being selected from their distributions on each run.
The outcome is a range of values, giving an understanding of the likely distribution of outcomes

Question 12

Merits of a Stochastic model:

Answer 12

Tests a wider range of economic scenarios.
Programming is more complex
It gives quality results.
It is good to model derivatives and options
The run time is longer.

Question 13

Steps for developing deterministic model

Answer 13

Specify the purpose of investigation
Collect, group and modify data
Choose the form of the model, identify its parameters or variables
Ascribe values to the parameters using past experience and appropriate estimation techniques
Construct a model based on expected cashflows
Test the model in order to identify any build errors and correct if necessary
Check that the goodness of fit is acceptable
Attempt to fit a different model if choice does not fit well
Run the model using estimates of the values of variables in the future
Run model several times to assess the sensitivity of the parameters to different parameter values

Question 14

Steps for developing stochastic model

Answer 14

Specify the purpose of investigation
Collect, group and modify data
Choose the form of the model, identify its parameters or variables
Choose a suitable density function for each of the variables to be modelled stochastically
Specify correlation between variables
Construct a model based on expected cashflows
Test the model in order to identify any build errors and correct if necessary
Check that the goodness of fit is acceptable
Attempt to fit a different model if choice does not fit well
Run the model many times, each time using a random sample from the chosen density functions
Produce a summary of results that shows the distribution of the modelled results after many simulations have been run
Run model several times to assess the sensitivity of the parameters to different parameter values

Question 15

Alternative ways of allowing risk

Answer 15

Statistical risk associated with parameter values can be allowed through the risk element of RDR.
Use risk-free return demanded by shareholders, quantify the variance of rate of return and allow for it appropriately, add that to the risk-free return.
A predetermined discount rate can be used and assess the effect on the results of models of statistical risk.
Discount cashflows using RFR but use more pessimistic parameter values instead of using best estimates.
Where a probability distribution can be assigned to a parameter, it may be possible to derive the variance of the profit or return on capital analytically.

Question 16

Common applications of models

Answer 16

Pricing
Set future financing strategies
Risk Management
Valuing liabilities
Valuing options and guarantees

Question 17

Model error

Answer 17

Model developed is not appropriate for the purpose being modelled

Question 17

Common applications of actuarial models

Answer 17

Pricing
Setting future financing strategies
Risk management models
Valuing liabilities
Valuing options and guarantees