What is a Model?
A model is an imitation of a real world system
Explain the benefits of modelling.
Compressed timeframe (e.g. for financial planning, real world figures unfold over a lifetime, need to test over a shorter period)
Ability to incorporate randomness
(in stochastic models)
Scenario testing (Can combine parameters in realistic scenarios - e.g. relating to interest rate rises)
Greater control over experimental conditions
Cost control
(upstream testing cheaper than assessment after implementation)
Explain the limitations of modelling.
Time and cost
complex models are expensive to create
Multiple runs required
for stochastic models, gives an indication of the dbn of outputs, but shows the impact of changes to inputs, rather than optimising outputs
Validation and verification
Complex models are hard to relate back to the real world in sanity checking
Reliance on data input
rubbish in, rubbish out
Inappropriate use
Scope and purpose of model must be understood by client to avoid misuse
Limited scope
models can’t cover all future eventualities, such as changes in legislation
Difficulty intepreting outputs
results usually useful only relative to other results, not in absolute real-world terms
Describe is a stochastic model.
- A stochastic model is one that recognizes the random
nature of the input components. - The inputs to a stochastic model are random variables
and hence for a given set of inputs the output is an
estimation of the characteristics of the model. - Several independent iterations of the model are
required for each set of inputs. - The output of a stochastic model gives the distribution
of relevant results for a distribution of scenarios.
Describe a deterministic model.
- A deterministic model is a model which does not
contain any random components. - The output is determined once the fixed inputs and the
relationships between inputs and outputs have been
defined. - The output is only a snapshot or an estimate of the
characteristics of the model for a given set of inputs.
How do you determine the suitability of a Model?
- Objectives of the modelling exercise.
- Validity of the model for the purpose to which it is to be put.
- Validity of the data to be used.
- Possible errors associated with the model or
parameters used not being a perfect
representation of the real world situation being
modelled. - Impact of correlations between the random variables
that “drive” the model. - Extent of correlations between the results produced
from the model. - Current relevance of models written and used in the
past. - Credibility of the data input.
- Credibility of the results output.
- Dangers of spurious accuracy.
- Ease with which the model and its results can be
communicated. - The time and cost of constructing and maintaining the
model.
Factors to consider when assessing the suitability of a Model.
- Objectives of the modelling exercise.
- Validity of the model for the purpose to which it is to be put.
- Validity of the data to be used.
- Possible errors associated with the model or
parameters used not being a perfect
representation of the real world situation being
modelled. - Impact of correlations between the random variables
that “drive” the model. - Extent of correlations between the results produced
from the model. - Current relevance of models written and used in the
past. - Credibility of the data input.
- Credibility of the results output.
- Dangers of spurious accuracy.
- Ease with which the model and its results can be
communicated. - The time and cost of constructing and maintaining the
model.
Explain the difference between the short-run and long-run properties of a model, and
how this may be relevant in deciding whether a model is suitable for any particular
application.
Individual variables may behave differently, for example a model over 50 years may be more
sensitive to differences in the input values of certain variables than one over the short term.
A variable which has an ignorable effect in the short term may have a non-ignorable effect
over 50 years.
Over the short term, it may be reasonable to assume the values of some variables to be
constant or to vary linearly, whereas this would not be reasonable over 50 years.
For example, growth which is exponential may appear linear if studied over a short time frame.
The interaction between variables in the short-term may be different from that over the longterm.
Higher order relationships between variables may be ignored for simplicity if modelling over
a short time frame.
The time units used in the model might be shorter for a model projecting over a short time
frame, so that the total number of time units used in each model is roughly the same.
Over 50 years, regulatory changes and other “shock” events are more likely to occur, and the
model design may need to consider the circumstances in which the results or conclusions may
be materially impacted (e.g. in the short term the tax basis may be known, but in the long run
it is likely to change).
Describe, in general terms, how to decide whether a stochastic model or Deterministic model is suitable for any particular application.
If the distribution of possible outcomes is required then stochastic modelling would be needed, or if only interested in a single scenario then deterministic.
Budget and time available stochastic modelling can be considerably more expensive and time consuming.
Nature of existing models.
Audience for the results and the way they will be communicated.
The following factors may favour a stochastic approach:
The regulator may require a stochastic approach.
Extent of non-linear variation for example existence of options or guarantees.
Skewness of distribution of underlying variables, such as cost of storm
claims.
Interaction between variables, such as lapse rates with investment
performance.
The following may favor a deterministic approach: Lack of credible historic data on which to fit distribution of a variable.
If accuracy of result is not paramount, for example if a simple model with deliberately cautious assumptions is chosen so as not to underestimate costs.
