Chapter 23: Capital Modelling - practical considerations Flashcards
How might a capital model be used to inform management decision making in:
reinsurance
optimising the purchase of reinsurance - this may involve deciding on the retention level that optimises the savings in reinsurance premiums and the capital required.
How might a capital model be used to inform management decision making in:
investment
assessing the impact of a change in the investment mix on the capital required and expected return.
How might a capital model be used to inform management decision making in:
pricing
assessing return on capital for pricing and performance measurement
How might a capital model be used to inform management decision making in:
reserving
quantifying the uncertainty in claims reserves - the capital model may be used to give a range of outcomes around a deterministic best estimate.
How might a capital model be used to inform management decision making in:
strategy
this could include assessing the capital implications of a proposed acquisition to determine whether the capital diversification benefits from some risks will outweigh the impact of increased aggregations in other risk areas
assessing the risks and diversification benefit of new strategies, eg assessing the capital implications of a proposed new class by analysing the diversification benefits and comparing this to the expected return on the class.
How might a capital model be used to inform management decision making in:
risk management
identifying key risks based on the model output and assessing the impact of mitigation.
Claims characteristics
Refer to the ways and speeds with which claims
- originate
- are notified
- are settled and paid
- and reopened.
Claim frequency and amount, as well as potential accumulations are relevant.
How are attritional claims modelled?
AGGREGATE DISTRIBUTION using a Lognormal/similar.
- Due to the high number of losses classified as attritional, the stability of the distribution means that the aggregate distribution is appropriate.
- The loss distribution can also be linked to premium income.
How are large losses modelled?
FREQUENCY-SEVERITY
allows more details of the available information to be used, expecially important where there is scarce data.
FREQUENCY ~ Poisson/Negative Binomial
SEVERITY ~ Pareto/LogNormal or other heavy-tailed distribution.
- The additional detail is worth the effort due to the larger values and will enable reinsurance limits to be tested more adequately.
- Need to decide on a threshold per class of business above which large losses will be modelled.
How will catastrophe losses be modelled?
- Catastrophe losses will be modelled using different approaches depending on the peril. Generally, historic data is not sufficient to model such perils. Proprietary CAT models are widely used by insurers.
Earthquake and natural cat events: may use proprietary catastrophe model which applies losses to the exposure base.
Factors which will affect the size of the loss include event magnitude and location.
Other perils such as hail/flood etc. may be modelled using a frequency-severity approach.
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Reasons why capital allocation is desirable:
Performance measurement
Capital has a cost. Therefore to accurately assess the performance of a particular class we need to calculate the profit/return as a percentage of the capital required to write that class, i.e. return on equity. This requires knowing the capital cost for each class.
Reasons why capital allocation is desirable:
Business planning and strategy setting
If the insurer can allocate capital to different areas of the business (and hence understand risk adjusted performance) then it can make decisions about which areas of the business to develop based on return and capital.
Reasons why capital allocation is desirable:
Pricing
Premiums charged should have a capital/profit loading to reflect the cost of capital held to write the business. Any pricing exercise should allow for diversification benefits between policies, which results in the total capital requirement being lower. This allows the insurer to charge more competitive premiums. The insurer will thus want to allocate capital to products or even policies so that premium rates can accurately take account of the risk of the product/policy.
Describe the process the company may follow in modelling earthquake risk
- The company will likely need to purchase model output from a company that is an expert in modelling earthquakes as this is different to the core business of employees of the insurer.
- The model output will include something along the lines of potential earthquake events with their associated locations, severities and frequencies.
- A simulation model would then be able to simulate whether each of the events happens or not in a particular year.
- The key modelling function is to then determine the cost to the insurer if each earthquake were to occur.
- This will be a function of the amount of exposure the insurer has (measured in terms of EML) at or within a near range of the location of the simulated earthquakes.
- For large buildings, the insurer may wish to model damage separately.
- The reinsurance model should be able to calculate recoveries on treaties.
- Key parameters should be sensitivity tested to understand model sensitivity to each factor and decide which factors are worth putting more time into estimating accurately, including more research.
How might the calculation of economic capital differ from the calculation of regulatory capital?
Economic capital is typically calculated using an insurer’s own internal model, whilst regulatory capital would usually be calculated using a prescribed model or formula.
Economic capital would use a DETAILED BREAKDOWN of assets and risk exposures, using an insurer’s own risk profile, whereas regulatory capital would use data which are summariesd to a degree, and applying market risk profiles/characteristics.
The economic capital requirement may be on a more REALISTIC BASIS, without any prudence which may exist on a regulatory basis. Even a regulatory basis which is on a best estimate basis may include a risk margin which represents an adjustment for uncertainty.
Economic capital may use a HIGHER LEVEL OF CONFIDENCE than the regulatory figure, especially if this is a published risk disclosure.
Risks and events may be correlated in a very complex manner in an economic setting, whilst this is normally more simply applied in a regulatory setting.
