Ch18: Modelling

Question 1

Model definition

Answer 1

Defined as a cut-down simplified version of reality that captures the essential features of a problem and aids understanding. Requires a balance being struck between realism (complexity) and simplicity for ease of application, verification and interpretation of results.

Question 2

When model required, three approaches:

Answer 2

• Commercial modelling product could be purchased
• Existing model could be reused, possibly after modification
• A new model could be developed

Question 3

Merits of three approaches of modelling will depend on the following: (5) (Commercial vs create in-house model vs existing)

Answer 3

• The level of accuracy required
• The ‘in-house’ expertise available
• Number of times the model is to be used
• Desired flexibility of the model
• Cost of each option

Question 4

Operational issues surrounding modelling that need to be considered: (8)

Answer 4

• Model being used should be adequately documented
  + Key assumptions and approximations made are understood as models are often run by different staff
• Workings of the model should be easy to appreciate and communicate, the results should be displayed clearly
• Model should exhibit sensible joint behavior of model variables
  + Allowance for variables linked to each other , and should be consistent
• Outputs from the model should be capable of independent verification for reasonableness and should be communicable to those to whom advice will be given
• Model should not be overly complex or time-consuming to run
  + Avoid difficulty in interpretability or expensive to run, unless required by purpose
• Model should be capable of development and refinement
• A range of methods of implementation should be available to facilitate testing, parameterization and focus of results
• Appropriate time period between projected cashflows
  + Reliability vs speed
  + Argument for shorter time period between cashflows in the early years, given that the starting inputs for the model should be known with a fair degree of certainty. Later on longer time periods, to avoid spurious accuracy.

Question 5

Key steps in developing and running an actuarial model (7)

Answer 5

• Specify the purposes and key features of the model
  + Valid for purpose: (simple vs complex; Deterministic vs stochastic)
• Obtain and adjust the data
• Set the parameters and assumptions, including dynamic links
  + List assumptions applicable
  + Consult experts available
  + Consideration of factors that could influence assumptions
  + Assumptions should be consistent
  + Should exhibit sensible joint behavior of model variables
• Construct the model cashflows
  + Expenses; tax; investment income; premiums; provisioning
• Check accuracy and fit of model and amend if necessary
  + Sensitivity analysis or scenario testing
  + Assumptions changed if necessary
  + Should be easy to develop and refine over time
• Run model as many times as required
• Output and summarize the results
  + Should not be overly complex to understand and explain
  + Check if output seems sensible

Question 6

Deterministic and stochastic models definitions

Answer 6

Deterministic:
- A model where the parameter values are fixed at the outset of running the model and the result of running the model is a single outcome.
- Sensitivity analysis and scenario testing can be carried out to assess the potential variability of the results

Stochastic:
- Model estimates at least one parameter 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 7

Advantages and disadvantages of deterministic models (3&3)

Answer 7

Advantages:
- Easy to communicate output and process to a non-technical audience since it does not involve explanation of probability distributions
- Clearer which economic scenarios have been tested
- Usually cheaper and easier to design and quicker to run

Disadvantages
- Difficult to determine the range of economic scenarios that should be tested
- Danger that certain scenarios, which could be detrimental to the company are not identified
- Not good for valuing options and guarantees as it is difficult to model variability in take-up rates or guarantees biting

Question 8

Advantages and disadvantages of stochastic models: (7&4)

Answer 8

Advantages:
- A wide variety of simulations can be run
- May due to random nature, identify valuable scenarios to consider which may not have been thought of as a scenario to test under a deterministic model
- Takes into account variability of model parameters and covariances between them
- Output forms a probability distribution from which valuable statistics such as mean and variance of output can be calculated
- Aids in understanding of the risks inherent in the project
- Useful for valuing options or guarantees, since likelihood of option being taken up or guarantee biting can be allowed for
- May be more accurate

Disadvantages:
- Time consuming to run and is more expensive to develop
- More complex design, leading to increased operational risk
- Output difficult to communicate and interpret for senior management
- Output only as good s input, and depends on choice of probability distributions and parameters for stochastic variables (and data)