Sensitivity analysis and types of risks

Question 1

Sensitivity analysis

Answer 1

• Reliability of the results
  o The results of the model depend on the model itself and the values assigned
  to the parameters in the model
• Understanding potential variability of experience
  o The use of stochastic modelling goes some way to illustrating the potential
  variability of the experience ( sensitiveness of assumptions )
  o But the results that it produces are still dependent on the accuracy of the
  model and parameters
  o The potential uncertainty of the results is greater with the deterministic
  model because few scenarios are tested
  o Re-running both the models with different but feasible parameter values will
  produce alternative results and help in illustrating potential deviations
  ▪ The re-running might also happen with creating a probability
  distribution for this experience
  ▪ However the extent of this will depend on
• Running time
• Associated costs
  ▪ Re-running the model on different assumptions also helps in
  highlighting errors in the model
  o Helps in coming up with a risk margin

Question 2

Types of risks

Answer 2

o Model error
▪ There is a possibility of model error if the model developed is not
appropriate for financial products, schemes , contracts or transactions
being modelled
▪ Checks of goodness of fit will be needed to assess the suitability of
the model but taking account of expected changes in experience into
the future
o Parameter error
▪ There is risk and effects of mis-estimation of parameter values
▪ These effects of mis-estimation of parameter values can be
investigated by carrying out sensitivity analysis
▪ It involves assessing the effect on the output of the model varying
each of the parameter values
▪ Need to also consider the correlation between different parameters
should be allowed for
o Courses of action that the actuary may take having identified an
unacceptable potential impact of certain assumptions when designing and
pricing a new product
▪ Redesign the product
* Where an assumption is uncertain and would have financial
material financial impact
The product may be redesigned to try reduce the financial
sensitivity to that assumption
▪ Increase margins in prudence
* If it is impossible to redesign product , then it may be
appropriate to include higher margins for that uncertain
assumption
* The margins may be assessed using sensitivity analyses that
should be incorporated
▪ Examples of assumptions were they could be overly sensitive
* Withdrawals rates
o Further step could be for the company to reduce
surrender values
* Mortality rates
o Put reinsurance measures in place

Question 3

Alternative ways of allowing for risk

Answer 3

ernative ways of allowing for risk
▪ Can allow for statistical risk through the risk discount rate
* Determine the risk free return demanded by shareholders
* Use the methodology above to quantify the variance of rate of
return and allow for it properly
* This would give us the risk margin to add to the risk free rate
* The model can be assessed using best estimate parameter
values
▪ Use a predetermined discount rate and then assess the effect on the
results of the models of statistical risk
* Involves using the pre-determined discount rate which was
arbitrary selected by shareholders
* May be based on risk free assets
* We discount the cashflows at the risk free rate , and use more
pessimistic values
* Degree of pessimism introduced here corresponds to the risk
margin

Question 4

Benefits of using sensitivity analysis

Answer 4

Pragmatic
➢ Transparent
➢ Informative way of understanding of parameter risk without difficulty and
spurious accuracy