Construction of an actuarial model Flashcards
(19 cards)
Key objective
o model should be fit for the purpose for which it is being used
▪ particularly important for external purchases or usage of existing
model that was used for another purpose
Operational issues that need to be considered
o model should be adequately documented
▪ ensures that key assumptions and approximations made are
understood
▪ also means that it can be run by other members of the staff
▪ allows for improvements introduction over time
o workings should be easy to appreciate and communicate
o the results should be displayed clearly
o the model should exhibit sensible joint behaviour of model variables
▪ model needs to make allowance for variables that are linked
▪ relationship between them has to be modelled in appropriate way
▪ assumptions should also be consistent
o outputs of the model should be capable of independent verification for
reasonableness
o the outputs of the model should be communicable to those to whom advice
will be given
o the model must not be overly complicated
▪ so that either the results become difficult to interpret and
communicate or ▪ model becomes too long or expensive to run unless required by the
purpose of model
o model should be capable of development and refinement
▪ nothing complex can be successfully designed and built in one
attempt
o a range of methods of implementation should be available to facilitate
testing , parametrisation and focus of results
Frequency of cashflows
▪ the more frequently calculated 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 run and results can be obtained
▪ these refer to chosen time period between projected cashflows e.g.
monthly , quarterly or annually
▪ the time period chosen should be chosen such that it captures key
areas of experience
* modelling class where claims are seasonal
* it makes sense to look at business monthly or quarterly
▪ decision needs to be made on the time horizon for the model
* how many years into the future we will project results
Summary of requirements of a model
- adequately documented
- Workings should be easy to communicate
- Results should be displayed clearly
- Look at sensible joint behaviour between variables of the model
- Output
o Capable of independent verification for reasonableness
o Easy to communicate to end user of results - Not overly complex, to avoid
o Hard interpretation and communication
o Expensive to maintain and run - Capable of development and refinement
- Range of methods of implementation should be available
o To facilitate testing , parametrisation and focus on results - Frequency of cashflows should be considered
Factors influencing model complexity
- Business significance of the problem
- How results will influence decision making ( materiality)
- Availability of data and ability to parametrise data – more data, more complexity
- Extent of uncertainty
The use of model points
- the business will typically have a wide range of different policies and these will need
to be brough together into manageable number of relatively homogenous groups - this needs to be made in such a way that each policy in a group is expected to
produce similar results when the model is run - the representative single policy in a group is termed a model point and a set of such
model points can be used to represent the whole of the underlying business
o the model points need to capture the most important characteristics of the
group policies it represents - Important characteristics that should be captured by the model points that would
be used when modelling a without- profit term assurance product to set premiums
o Term of policy
o Sum assured payable on death
o Claim basis ( single life, joint life , last survivor )
o Age of life/lives covered
o Gender of life /lives
o Smoker-status of life/ lives covered
o Health status of life/ lives covered
Choosing model points
o A set of model points will be chosen to represent the expected new business
under the product
o Factors influencing the number of model points that can be handled by the
model :
▪ Computing power available
▪ Time constraints
▪ Heterogeneity of the class business
* Also dependent on the risk factors
* Characteristics of the class of business – sum assured, term
▪ Sensitivity of the model to different choices of model points
▪ The purpose of the exercise
Rate of discounting cashflows
- For each model point, cashflows should be projected , allowing for reserves and
solvency requirements - The net projected cashflow will then be discounted at a rate of interest ,the discount
rate - This rate could allow for
o Return required by the company ( shareholders )
o Level of statistical risk attached to the cashflow under particular contract
▪ Variation about the means as represented by cashflows themselves
▪ This risk is meant to encompass all types of risk , and comprises - Model risk
- Parameter risk
- Random fluctuations risk
Ways of assessing the level of statistical risk include:
- Analytically – considering the variance of the individual
parameter values used - Sensitivity test analysis – assess variation in values
deterministically - Stochastic models for the parameter values and simulation
o Varies the important parameter values in the model
according to their assumed pdf and
o Recalculate the rate of return for each new scenario
o Through that variance of return can be found
o Numerical equivalent of first method - Comparison with any available market data
o Stochastic rate could be used
▪ Where separate risk discount rate should be applied to each separate
component of the cashflows as the statistical risk associated with
each component is different
Advantages of deterministic model
- more easily understood by non-technical people
- it is clearer what economic scenarios have been tested
- cheaper and easier to design
- quicker to run
- easier to parametrise
Disadvantages of deterministic models
- only limited number of economic scenarios can be tested
- can lead to overconfidence is answer as one answer is given
Advantages of stochastic modeling
- tests a wider range of economic scenarios
- quality of results (becareful of spurious accuracy)
- provides further information (distribution of results, tails)
- good for allowing uncertainty
- good at allowing parameters to vary together
Disadvantages of stochastic modeling
- programming is more complex
- run time is normally longer
- greater parameter risk (needs high level of expertise)
- can increase difficulty in interpretation and communication to end user
-greater model risk
-can be expensive to build
Both determinisic and stochastic models
Normally , modelling entails using both the deterministic and stochastic modelling
o Variables whose performance is unknown and risk associated with them
might be modelled stochastically
o Economic assumptions – normally modelled using stochastic approach (
investment model returns)
o Demographic assumptions- normally modelled using deterministic approach
( mortality rates )
Dynamism of model
Dynamism of model is essential
o This ensures that the model asset and liability parts of the model and all
assumptions are programmed to interact as they would in real life
o inflation and interest rates should be consistent
o interaction of various features should be determined
Use of deterministic model
- when parameter variance us not crucial
- valuations
- no detailed asset modeling
- simple problems \
- limited time/resource
Uses of stochastic modeling
- asset or liability models
- options and guarantees
- investment returns
- allowing for mismatch risk
-interest rates models
Developing a deterministic model
- deterministic model should involve the following steps (11)
o Specify the purpose of investigation
o Collect, group and modify data
o Choose the form of model
o Identify its parameters or variables
▪ These are the inputs to the model and include - Current policies on the book
- Past Investment returns
- Future new business
- Mortality rates
- Mortality improvements
- Discontinuance rates ( withdrawals)
- Future expenses
- Claim frequency and amounts
- Premium rates
- Commission
- Past inflation
- Profit loading
- Risk margins
o Ascribe the values of the parameter using past experience and appropriate
estimation techniques
o Construct a model based on expected cashflow
o Test the model in order to identify any build errors and correct if necessary
o Check that the goodness of fit is suitable – attempt to fit another model if
first choice doesn’t fit well
o Run model using estimates of the values of variables in the future
o Run the model several times to assess the sensitivity of the results to
different parameter values
o Run the model under different scenarios to test robustness of the results (
quality of the results must be good )
Developing a stochastic model
o Same as deterministic but differs with that
▪ Choose a suitably density function for each stochastic parameter
▪ Specify correlations between variables
▪ Run the model many times using random sample from the chosen
probability density function
▪ Produce summary of results that shows the distribution of the
modelled results after many simulations have been run
* Examples include
o Various confidence levels
o Expected values
