Chapter 15: Triangulation methods (Best estimate reserves) Flashcards
2 Important issues when presenting reserves
We should:
- clearly define what we mean by our single point (or best) estimate
- attempt to quantify the likely divergence from this estimate
From another card (related):
- explain WHAT HAS BEEN ALLOWED FOR the best estimate, and WHAT HAS NOT
- ensure stakeholders understand the LEVEL OF UNCERTAINTY
- comment on the UNCERTAINTY IN THE CONTEXT AND SCOPE and purpose
- focussing on the most SIGNIFICANT ISSUES, given the purpose of the exercise
- emphasise the unusual issues
- avoid MISUNDERSTANDINGS
- be consistent with VOCABULARY used by other professionals, and explain terms
Best estimate reserve
• It is a point estimate, in other words a single number, not a range of outcomes.
* the expected value of the outstanding liabilities, after allowing for all the areas of uncertainty, (ie model, parameter and process uncertainty)
• It is unbiased, ie the underlying assumptions used do not take a deliberately prudent or optimistic view.
• It is meant to be the actuary’s impartial view of the reserves with no margins, implicit or explicit, for prudence or optimism.
• It is based on sound and appropriate actuarial or statistical techniques.
• It is based on current and credible information.
• The Solvency II requirements say nothing about the skewness of the underlying distribution or its inherent volatility.
In SAM the best estimate is characterised as (4)
- a point estimate
- not inherently optimistic or pessimistic
- based on sound and appropriate actuarial or statistical techniques
- based on current and credible information
nothing is said in the requirements about the skewness of the underlying distribution or its volatility
Data required for reserving: (7)
- premiums
- number of claims
- dates of reporting and occurrence
- case estimates
- paid claims (gross and net of recoveries)
- other measures of exposure
- expenses (direct and indirect)
Case estimates (for use in reserving)
Latest estimates of the cost of each claim of which the insurer is aware.
Case estimates may be easy to determine for some classes of business, but complex for others:
- It may be easy to determine these case estimates if the benefit is fixed, such as the compensation offered for the loss of a limb under a personal accident policy.
- When the estimation process is not so straightforward, a mechanical approach may be used, or the judgement of an experienced claims handler or legal advisor may be used.
Claims analysis:
3 cohorts of common origin
- year of accident
- year of reporting
- year of underwriting
Data required:
Premiums
- Earned premiums are appropriate for an accident year cohort.
- Written premiums are appropriate for an underwriting year cohort.
- A reporting year cohort would be very difficult to use in a loss ratio calculation, since premiums and claims would have to be found with the corresponding exposure.
The overriding principle of all claims analyses
The need to determine the basic
- characteristics
- values, and
- trends of past data.
Consideration needs to be given to
- materiality
- homogeneity of data
- how to deal with large/catastrophic losses
- how to deal with latent claims
Main ADVANTAGE of grouping claims data by ACCIDENT YEAR
All claims will stem from the same exposure cohort.
The claims will therefore have been subject to the same risk environment, although they might have arisen from policies written under different rating and policy terms.
Main DISADVANTAGE of grouping claims data by ACCIDENT YEAR
- The full number or amount of claims in the cohort is not known until the last claim is reported.
- This relies on detailed claims records being maintained. (eg date of loss, date reported, payment date etc). DOL can be difficult to determine in some cases.
- Claims may arise from different premium rates or terms
ADVANTAGES of grouping claims data by UNDERWRITING YEAR
- We can follow the total outcome of all policies written in each year. Follows funded year accounts.
- Similarly we can follow claims that arise from a particular group of policies that are subject to the same set of premium rates and
- use the results to test the adequacy of the premiums.
- A further advantage is that the terms, rates and conditions are often more stable by underwriting year.
- IBNR and clams from unearned exposures are automatically included in the projection.
DISADVANTAGE of grouping claims data by UNDERWRITING YEAR
It will take more than one year before all the claims under that cohort have occurred.
Reporting delays, including IBNER, will extend this further.
Thus takes longer to gather data.
ADVANTAGE of grouping claims data by REPORTING YEAR
No further claims will be added to the cohort after the end of the origin reporting period.
DISADVANTAGES of grouping claims data by REPORTING YEAR (3)
- Projection methods based on this cohort will not allow for the IBNR. A separate allowance will therefore be needed for IBNR claims.
- Claims will have come from several different exposure periods, each of which may have differed in respect of volumes of business, cover applying, claim settlement patterns and claim environments.
- It is difficult to find an exposure base that would correspond to the definition of risk under the claims being developed.
Development period
The period or frequency at which each claim cohort is tracked over time.
Annual and quarterly periods are the most commonly used.
3 Methods of estimating the outstanding claims reserves
- case-by-case basis
- statistical methods
- exposure based reserving
2 Methods for deriving estimated ULTIMATE VALUES for LARGE LOSSES
- claims development methods
eg. chain ladder methods, but project from the date of actual loss and allow for different speed of development - exposure based methods
Bottom up
Top down
Considerations in deriving ultimate values for catastrophe losses
Catastrophe losses often tend to DEVELOP MORE QUICKLY than attritional claims.
The main reason for this is the increased focus on these claims from claims adjusters and policyholders due to the magnitude of the losses.
Once claims experience starts to emerge, the development pattern of similar catastrophes in the past may assist the actuary in refining initial estimates.
2 approaches to Exposure based methods for estimating ultimate values of large losses
- Bottom-up approach
- Top-down approach
BOTTOM-UP APPROACH to exposure-based methods for estimating the ultimate values of large losses
Examine on a policy by policy basis to determine the likelihood of whether each policy is exposed to the loss event.
If they decide the underlying insured is exposed to the relevant event, a claims expert needs to assess the extent of any claim on that policy.
TOP-DOWN APPROACH to exposure-based methods for estimating the ultimate values of large losses
We attribute the total market loss from an event to an individual insurer or policy level, based on the policy terms, excesses and limits.
3 Bases on which business is written
- Losses occurring
- Claims made
- Risks attaching
Losses occurring basis
The policy provides cover for losses occurring in the define policy period, no matter when they are reported.
This is consistent with an accident year approach.
Such policies are thus subject to potential problems in defining the date of loss which may be established as a result of legal action.
Claims made basis
The policy covers claims reported during a certain period.
It is used to reduce the tail on liability business by removing the development caused by late reporting.
Risks attaching basis
A basis under which reinsurance is provided for claims arising from policies incepting during the period to which the reinsurance relates.
This is consistent with an underwriting year approach.
5 ways in which to apply benchmarks
We can apply benchmarks in different ways, including:
- incremental development factors
- paid or incurred to ultimate factors ultimate loss ratios
- IBNR as a percentage of paid, outstanding or incurred
- IBNR as a percentage of premium.
An age-to-age development factor is just the development factor as calculated in the standard basic chain ladder method approach. But here we would adjust the factors obtained from our own data by comparing them with the corresponding benchmark data.
Age-to-age development factor
The development factor as calculated in the standard basic chain ladder approach.
But here we would adjust the factors obtained from our own data by
… comparing them with the corresponding benchmark data.
Issues that affect the stability of the claims development pattern (11)
- distortions in the data
due to changes in (administration) processes can affect the normal claims development.
Such changes could involve stricter claims underwriting or a new system to speed up the claims processing. Such changes affect the size and speed of the run-off respectively. - claims reviews
It is common for companies to undertake periodic claims reviews to ensure that the case reserves being held accurately reflect all currently known information relating to the claim. If such reviews are carried out regularly then it might be reasonable to assume that the historical development reflects the average impact that such reviews have, and that the future development may follow a similar pattern.
However, if such reviews are infrequent, or if a large ‘one-off’ review has been carried out, or if the company undertakes the reviews more frequently than it has in the past, it may be necessary to adjust the development pattern derived from the data. - market wide initiatives
For example, a market-wide initiative was put in place to speed up the reporting of energy losses arising from damage to oil rigs, following hurricanes in the southern US and Gulf of Mexico during 2005.
If such initiatives are taken, it is important that any chain ladder model that is fitted to the data recognises that the claims development may be different from what may be typically expected for the type of business or loss in question. - seasonality:
Seasonality can affect the claims development pattern, both within a cohort and for one cohort relative to another where the exposure period is not the same. Seasonality is the tendency for certain types of policy to have more claims at certain times of the year. For example, motor policies usually have more claims in winter when the weather conditions are more hazardous and household insurers receive more subsidence claims in the autumn / winter following a hot summer. Seasonality may not have a bearing on annual development factors but quarterly factors may appear less than smooth.
Seasonality can also impact the speed at which claims are processed – for example, fewer claims may be processed during December when there are a greater number of bank holidays. - developments in the business, economic and legal environment.
changes in:
- terms and conditions
- mix of business
- claims handling processes
1. Changing practices regarding the point at which a notified loss is formally accepted as a claim by the company and is marked as such on the claim file.
2. A new claims process is implemented that speeds up the processing of newly notified claims.
3. The case reserving philosophy is changed. For example, from ‘best estimate’ to ‘realistic worst case’, or if the initial standard case reserve is changed for certain types of claim.
4. A change in the period before non-active claims are reviewed – either to chase for outstanding information or to close the claim as a nil claim.
5. Delays in making claims payments, whether deliberate or due to circumstances.
6. The failure to mark claim records as settled on a consistent basis.
One way to deal with the first three examples might be to base the chain ladder link ratios only on development data from after the new procedures came into effect. Alternatively, we may make subjective adjustments to allow for the fact that the future development is expected to be different from that suggested by the historical data.
We may deal with the last two examples by excluding the affected link ratios.
- commencement of writing policies
- average policy length
- reserving policy