Chapter 4 - Modelling Flashcards
Give an example of how Insurers may make a model for car insurance pricing
Might base model on answers in policy form. To price, insurers try to evaluate how likely each driver is to make a claim, and how big the claim might be.
Why might a car insurer base their pricing model on elasticity of demand?
Insurer then has to work out plus or minus a profit margin, Model may also be based on a model based on price elasticity of demand. Idea that people who are more price sensitive will get a more competitive price than those who are not as price sensitive (more wealthy).
How might insurance companies use models to get approval from the regulator of the change in product design and investment strategy?
To persuade the regulator that the switch leaves policyholders no worse off, one could model the fact that the new investment has historically provided superior investment returns compared to the old one.
How might the regulator use models to enforce regulation of corporation tax insurer must pay
No two insurance policies are the same, so finding a fair price for insurance is difficult. Model is needed to decide if corporation tax is reflecting the full profit the insurer is making - company may be understating its profit if the model demonstrate insurance premiums are insufficient for the risks covered.
How might an actuary use models to calculate the value a member leaving a DB pension scheme early is entitled to?
The pension plan retains an actuary who confirms that the cash value offered is fair compensation for the lost pension entitlement, using a model that describes the cost of the benefits foregone.
How might a model assist to decide between paying out dividends vs reinvesting into the firm
They build a model to describe the likely effect of dividend policy on share prices over the medium term, to support the decision.
How might a firm make a model for mortality if they were worried about the effect of mortality improvements? Who else would use this model?
The firm constructs a model for pensioner mortality analysing past data to quantify the effect of mortality improvements int he past- can be used as input into pricing and underwriting decisions.
Givernment would also use ismilar models - find out what services are needed etc.
Define a model
A model is a mathematical representation of a real-world phenomenon. Models enable analysts to reduce complex problems to manageable terms. Models invariably involve making simplified assumptions about the real world. Computation tool is not a model and a theoretical hypothesis of what the world might look like is also not a model.
Both of these become a model when it is implemented in formulas and calibrated by reference to the real world phenomena that the model is attempting to represent.
What are some simplifying assumptions often in a model?
Assuming:
A quantity is constant over the period
We know the statistical distribution of a quantity
Some aspects of the model are not influenced by (or are independent of) other aspects.
Aspects of the real world have an insignificant effect on what is being modelled
All financial instruments are priced to preclude risk free arbitrage profits
What are two collections of data often assumed independent by isnurers. And when was this proved wrong
Assumption usually that longevity and returns are independent, covid 19 ruins this.
What are the biggest causes of death today?
Biggest causes of death are now diet and pollution
How is the structure and complexity of a model determined?
Structure of a model sets out the relationship between the variables modelled (inputs) so as to determine the functioning of the system (outputs).
Complexity of model is determined by the number of variables modelled and the form of relationship posited between them.
What are the three approaches to building a model in terms of setting it up.
A commercial modeling product could be purchased;
An existing model could be reused, possibly after modification; or
New model could be developed.
What will determine if an actuary will re use or build anew a model
the level of accuracy required;
the ’in-house’ expertise available;
the number of times the model is to be used;
the desired flexibility of the model; and
the cost of each option.- If model will be used multiple times you will not want to be paying license fees to the third party
Give advantages of modelling
Modelling can claim all the advantages of the scientific programme over any other logical, study of phenomenon that builds to a body of knowledge.
You’re not relying on re-inventing everything the first time. Building on knowledge that’s come before
Complex systems can be studied.
It is quicker, and less expensive than alternatives.
Consequences of different policy actions can be assessed, good for optimisation - trial and error bears no consequences
We can reduce variance of model as we can better control experimental conditions.
Drawbacks of modelling?
Investment of time, money and expertise.
Often time consuming to use many simulations needed and results analysed.
Not especially good at optimising outputs (better at comparing results of input variations)
Human pride - Impressive looking models can lead to overconfidence in model.
Model only as good as parameter inputs quality and credibility of data. - garbage in garbage out
Must understand model limitations
Sometimes can be difficult to interpret output
Model will become obsolete because of changes
Automation can result in reduction of scrutiny. Something to watch.
What is a static model?
Static: later stages of a model can be forecast independent of what has happened earlier in the model - no feedback loops
Each model point can be computed in parallel
with other model points, and then assembled in a final step.
May be able to project with more or less
objective assumptions.
Simpler to code, aggregate and analyse.
What is a dynamic model?
Dynamic: output from one variable affects the future trajectory of other variables. Example: path of interest rates or investment returns affect lapse rates;
Decisions affecting any model point can be
based on the results across all model points at an earlier point in time.
Dynamic aspects may arise from future
decisions by management/policyholders or by third parties. Anticipating these decisions may involve a large subjective element.
More model complexity arising from complex
feedback loops.
Explain profit sharing policies and how it would need a dynamic model?
Profit sharing, participating or with profits policies: means there is some pooling of risk between policyholders. For example for term assurance policies where there is lighter than expected mortality. This could lead to policy holders getting some sort of refund or bonus increase to the sum assured. Will pay a higher premium at first and then profit is redistributed.
Profit sharing agreement needs a dynamic model so at the end of each year/month you have the aggregate policies and then distributed the bonuses, and next year starts then.
So you cannot forecast one policy in isolation from others so cannot be a static mod
Describe how a DB pension plan could be made into a dynamic model
Dynamic model DB pension plan, dynamic decisions for a pension plan could include sponsor contributions(how much contributing annually), investment decisions (in surplus we can seek higher returns, greater capacity to take investment risk). Also DB Pension scheme is one big pool of assets , these decisions will be taken at pool level so cannot look at each individual benefit and add up.
