Chapter 14: Best estimate reserves Flashcards
Important issues when reserving
- be clear by what is meant by a single point estimate (or best estimate) of an outstanding reserve
- attempt to quantify the degree to which the eventual outcome may diverge from the point estimate and likelihood of divergence.
Best estimate reserve
A point estimate reserve.
In statistics, we take this to mean the expected value of the outstanding liabilities, after allowing for all the areas of uncertainty (model, parameter and process uncertainty)
Under SAM, the key characteristics of a best estiamte are:
It is:
- a point estimate
- not inherently pessimistic or optimistic
- based on sound and appropriate actuarial or statistical techniques
- based on current and credible information
The requirements say nothing about the skewness of the underlying distribution or its inherent volatility
Data required for reserving
- dates of reporting and occurrence
- paid claims (gross and net of recoveries)
- case estimates
- premiums
- number of claims
- other measures of exposure
- expenses (direct and indirect)
Case estimates for use in reserving
These are the latest estimates of the cost of each claim of which the insurer is aware. A history of case estimates is usually required
Case estimates may be easy to determine for some classes of business, but complex for others:
- may be easy to determine these case estimates if the benefit is fixed
- when the estimation process is not so straingthforward, a mechanical approach may be used, or the judgement and experience of a claims handler or legal adviser may be used.
Data required:
Paid claims and case estimates
Checks
- check whether data has been adjusted for recoveries and decide whether to make the adjustments - need accurate information gross and net of reinsurance
- check whether data net of any recoveries is consistent with data gross of such recoveries
- claims data for reserving should be reconciled with accounts and general ledger to ensure two sources are consistent
- compared to historical data to check for unusual movements and understand why such movements have occurred
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
- office premium is most appropriate
For the purpose of claims analysis, the data can be grouped into cohorts of common origin:
- year of accident
- year of reporting
- year of underwriting
Overriding principle of all claims analyses
The need to determine the basic characteristics, values and trends of past data.
During a claims analysis, consideration needs to be given to:
- materiality
- homogeneity of data
- how to deal with large/catastrophic losses
- how to deal with latent claims
Relative merits of grouping claims data by accident year
Advantages
- all claims will stem from the same exposure cohort and therefore have been subject to the same risk environment
- might have arisen from policies written under different ratng and policy terms
Disadvantage
- full number or amount of claims in the cohort is not known until the last claim is reported
- relies on detailed claims records being maintained (e.g. date of loss, date reported, payment date, etc.)
Relative merits of grouping claims data by underwriting year
Advantages
- can follow the total outcome of all policies written in each year
- 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 premiums
- terms, rates and conditions are more stable by underwriting year
Disadvantages
- takes more than one year before all claims under that cohort have occurred - reporting delays, including IBNER will extend this further
Relative merits of grouping claims data by reporting year
Advantages
- no further claims will be added to the cohort after the end of the origin reporting period
Disadvantages
- projection methods based on this cohort will not allow for IBNR. A seperate allowance will 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’s difficult to find an exposure base that would correspond to the definition of risk under the claims being developed - possibilities include average premium and current year’s premium
Development period
The period/frequency at which each claim cohort is tracked over time . Annual and quarterly periods are the most common
What elements of the claim reserve does the following triangle estimate?
Claims grouped by reporting year
- RBNS
- IBNER
What elements of the claim reserve does the following triangle estimate?
Claims grouped by accident year
- RBNS
- IBNER
- pure IBNR
What elements of the claim reserve does the following triangle estimate?
Claims grouped by underwriting year
- RBNS
- IBNER
- pure IBNR
- URR
Methods of estimating the outstanding claims reserve
- case-by-case basis
- statistical methods
- exposure-based reserving
Methods for deriving estimated ultimate values for large losses
- claims development methods
- expposure-based methods
Considerations in deriving ultimate values for catastrophe losses
- catastrophe losses tend to develop more quickly than attritional claims
- main reason for this is the increased focus on these claims from the claims adjusters and poicyholders due to the magnitude of the loss
- once claims experience starts to emerge, the development pattern of similar catastrophes in the past may assist the actuary in refining initial estimates
Approaches to exposure-based methods of reserving for large losses
- bottom-up approach
- top-down approach
Bottom-up approach to esposure-based methods for estimating reserves for 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 assesses the extent of any claim on that policy
Top-up approach to esposure-based methods for estimating reserves for 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.
If the insurer has written less than 100% of a particular risk, the reserving/claims staff will also reflect a proportion of that particular risk that the insurer has agreed to insure.
At the very early stages of development where there is very little information available to derive estimates then the insurer may estimate its losses as the product of an estimated total market loss and its estimated market share.
Considerations in deriving ultimate values for latent claims
Many latent claims have a “calendar year” development effect, that is, a similar claims development pattern for a particular year rather than a development year.
- publicity in the media may lead to influencing the rates at which claims develop
- group of underwriting years can show development that results from the same underlying latent claims = earlier underwriting years cannot easily be used as a guide to how later underwriting years might develop
Bases on which business is written
- losses occurring basis
- claims made basis
- risks attaching basis
Losses occurring basis
The policy provides cover for losses occurring in the defined policy period, no matter when they are reported.
Consistent with an accident year approach
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 (or “made”) during a certain period rather than claims arising out of occurrences during that period (“losses-occurring”)
Not a common approach
Covers losses reported during a the policy year (in some cases also during an extended reporting period, esp on renewal of coverage).
Used to reduce tail on liability business by removing the development caused by late reporting
Risks attaching basis
Basis under which reinsurance is provided for claims arising from policies incepting during the period to which the reinsurance relates. For reinsurance policies, it ensures they collectively match the inwards business.
Consistent with an underwriting year approach.
Ways in which to apply benchmarks
- age-to-age development factors
- ultimate to paid or incurred factors
- ultimate loss ratios
- IBNR as a percentage of paid: outstanding or incurred
- IBNR as a percentage of premium
Age-to-age development factor
The development factor as calculated in the standard basic chain ladder method approach. Here we adjust the factors obtained from our own data by comparing them with the corresponding benchmark data
In what ways may the benchmarks differ from the business being analysed?
They may refer to different:
- classes of business
- Ts&Cs
- allowance for reinsurance
- time periods
- excesses
- geographical location
- mix of business
- coverage
- reserving basis
- inflation allowance
Issues that may affect the stability of the claims development pattern
- changes in terms and conditions
- changes in the mix of business
- distortions in the data
- changes in claims handling processes
- market wide initiatives
- claims reviews
- seasonaility
- changes in commencement of writing policies
- changes in average policy length
- changes in reserving policy
- developments in the business, economic and legal environment
Issues affecting claims development stability:
Changes in the mix of business
Changes in the mix of business will increase the heterogeneity in the data. There may not be enough data to analyse the data at a level where the mix of business is relatively stable from one period to the next.
If there’s been a change in the business mix over time, it’s important to estimate the impact of this change on the claims development pattern.
Incurred claims might mean:
- paid claims plus estimates for outstanding reported claims
- paid claims plus estimates for all outstanding claims (including an appropriate loading for IBNR). This is the accident year accounting definition of incurred claims.
Examples of changes in claims handling procedures which might affect claims development
- 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
- a new claims process is implemented that speeds up the processing of newly notified claims
- the case reserving philosophy is changed. E.g. from best estimate to realistic worst case
- delays in making claim payments, whether deliberate or due to circumstances
- the failure to mark claim records as settled on a consistent basis
How might market-wide initiatives affect the claims development pattern?
A major issue may arise that the market is keen to quantify as quickly as possible.
Where such initiatives are take, it is important that the chain ladder model that is fitted to the data recognises that claims development will be different to what it has been in the past.
How does seasonality affect the claims development pattern?
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.
Noting levels
Also known as notification levels, i.e. the claims level above which claims should be referred to a reinsurer.
Re-underwriting
Sometimes an insuer will state that they have “re-underwritten” a class of business. This may be for:
- a generally poor performing class of business
- a class which has suffered material losses from a single event which led to claims from a large number of policies.
Chain ladder method
A statistical method of estimating the ultimate value of a set of development data, whereby a weighted average of the past development is projected into the future.
The projection of successive periods of future development is based on the calculation of ratios of cumulative past development.
This method can be applied to premium and claim development data.
Basic chain ladder method assumption
It assumes that the future pattern of claims development derived from the past experience will remain stable.
It also implicitly assumes that past inflation will continue into the future. Inflation adjusted chain ladder can be used if explicit inflation assumptions are needed.
Method for carrying out a basic chain ladder calculation is:
- tabulate claims on a cumulative basis by development year/origin year
- calculate the development ratios
- apply these ratios to complete the table
- from the cumulative results, find the amounts expected to be paid in each future development year/origin year cell
Issues arising when using the basic chain ladder method
- analysis and selection of link ratios (development factors)
- mechanical generation of standard link ratio models for initial modelling - judgement is needed
- case reserve, paid and incurred modelling
- paid vs incurred modelling
- link ratios with values less than one
Examples of reasons why the paidand incurred claims don’t converge on the same ultimate claim amount
- payments are made after claims are incurred, so for early development periods the paid claims can be very sparse and hence unreliable for projection, leading to potentially different paid and incurred projections
- large complex claims usually take longer to settle and there may be significant case reserves at later development periods
- disputed claims may be slow to settle and more subject to change
- one pattern may be more volatile than the other, which makes projection difficult
- at later development periods there may only be a small number of open claims remaining, with the remaining claims all settled. It may appear by looking at the paid claims development, that there’ll be no future development and hence a paid link ratio model is likely to give different answer to incurred link ratio model
- changes to case reserving procedures over time
Subrogation recoveries
If an insurer indemnifies a policyholder against a loss, it may be entitled to attempt to recover some or all of that loss from a third party.
Key strengths of the chain ladder method
- method can be applied to a wide variety of sets of data
- provided the data can be arranged into a development triangle, the chain ladder method can be used to project it to ultimate
- the basic method can be easily modified to allow for data distortions
- the method is conceptually straightforward and it is easy to relate results back to the pattern of development
- the method can be developed to serve as a starting point for a number of other methods
Key weaknesses of the chain ladder method
- results can be distorted by unusual experience (e.g. very good or very bad past claims experience)
- limited use for recent cohorts, particularly for long-tailed classes
- considerable care is needed in applying the method to prevent unusual features in the data having a significant impact on the results
Methods relating to the chain ladder method
- The Berquist-Sherman method
- Curve fitting
- Trend analysis
Methods related to the chain ladder method:
The Berquist-Sherman method
Suggest techniques that produce adjusted development patterns that are consistent with the current reserve levels and settlement rates that are thought to apply at the time of the latest diagonal.
We derive these adjusted development patterns by restating the historical development data to be on the current reserving or settlement basis.
Methods related to the chain ladder method:
Curve fitting
Using regression techniques, we can fit curves to premium/claim development data. We can fit a number of different distributions, e.g. Weibull, inverse power ir exponential.
This would involve estimating a best fit to cohort development data. We can also use curve fitting to smooth development patterns.
Loss ratio
The cost of claims per unit of exposure
Expected loss ratio method
Requires a measure of exposure. Historic loss ratios based on the company or industry-wide data are applied to current premiums to obtain future claims estimates.
Expected loss ratio method
When to use the method
It is useful when the data is scanty, unreliable or missing all together.
Advantages of the expected loss ratio method
- it is not distorted by anomalous data. This can particularly have an impact in longer tailed business and at early durations if claims experience to date is particularly heavy or light
This is provided the assumptions about the loss ratios are correct
Disadvantages of the expected loss ratio method
- it ignores the pattern of claims development to date
- it is difficult to adjust for large claims
- if loss ratios are derived from past years, the method will replicate past biases
- the benchmarks used may not be appropriate as the business written may be different from that to which benchmarks relate
- when used, the ultimate loss ratios for previous years may be understated or overstated because of fluctuations in experience. Any changes in the underwriting or claims environment may make them unsuitable for use, although it may be possible to make appropriate adjustments
- the underlying assumptions can be subjective, particularly when based on information such as the underwriter’s opinion. Aim to understand business written to form a view on the reasonableness of the underwriter’s assumptions
- where premium rate changes are introduced, these are often only for renewed business and not for new business
Bornhuetter-Ferguson method
A credibility estimate, based on a weighted average of an expected level of claims as estimated by the loss ratio method, and a projection of the ultimate claims based on the experience to date as estimated by the chain ladder method.
Can apply method to paid or incurred claims
Bornhuetter-Ferguson method
When to use it
Very useful where the available data for the particular cohort is sparse. This is often the case with more recent cohorts, cohorts from longer tailed portfolios or where premium volumes are so small that claims activity is expected to be extremely volatile.
Unusual to use this method after the first few development years. May still be used at longer durations if the development is slow.
Advantages of Bornhuetter-Ferguson method
Can be used when the claims data is at a very early stage of development.
Disadvantages of Bornhuetter-Ferguson method
It can be difficult to gather the information for the prior estimate for the claims. The result, particularly at the early stages of development, can be heavily dependent on this prior estimate
Average cost per claim (ACPC) method
In general, we estimate two seperate components for each origin year, the claims frequency and the claims severity.
If severity used is the average ultimate claim, we calculate estimated claims by multiplying the estimated ultimate number of claims and extimated average claim size. The claims reserve is estimated by subtracting the paid claims to date from the estimated ultimate claims.
If average claim size used in the method is the average of future payments, we estimate the claims reserve directly by multiplying the estimated number of future claims and estimated average claim size
Average cost per claim (ACPC) method
When to use it
Need more data dor the ACPC method than for other methods. Can only apply method if appropriate data is available. Need information on claim numbers and amounts.
Not use method where the claim count or an average claim size is not meaningful, e.g. in a subscription market where insurers write different shares on each of the policies they underwrite
Average cost per claim (ACPC) method
Issues arising
Claim numbers:
- reported claims projections can provide a short-tailed projection of the ultimate number of claims as claims are often reported more quickly than settled
- settled claims - consider the definition of a settled claim
- reopened claims - define carefully how reopened claims are treated
Claim amounts:
- can apply to data adjusted for claims inflation
- consider the allowance for inflation and whether inflation varies by origin year/calendar year
- allow for large claims
Strengths of the average cost per claim (ACPC) method
- easy to understand and communicate
- provides information on how claim numbers and claim amounts are expected to develop in future
- for direct business in particular, the data required is generally available
- can be used in conjnction with other projection techniques
- helps explain volatile data and results when the data contain only a small number of claims
- can be applied to settled claims when claims reserving protocals have changed over the development history, making some other methods invalid
- if used in the correct way, can be useful as a basis for estimating latent claims because we can make explicit assumptions about the average claim size, the long-term effect of inflation and the expected number of claims.
Weaknesses of the average cost per claim (ACPC) method
- can be distorted by reopened claims, nil claims or partial payments
- assumes the distribution of claims is the same for each origin year or settlement year
- needs more detailed information, which may or may not always be available
- small data samples may lead to volatile results, this is in common with other projection techniques
Statistical methods of estimating outstanding claims might be impaired by distortions which invalidate the underlying assumptions. Problems might be caused by:
- errors in the data
- large claims
- inflation
- latent claims
- catastrophes
- changes in procedures
- changes in the mix of business
- lack of data
Communication of the best estimate
- results should be explained clearly and effectively to key stakeholders
- highlight that best estimate is just an estimate
- highlight key assumptions and comment on the main restrictions or shortcomings in analysis
Examples of distorting effects on the loss ratio
- catastrophes
- change in premium rates
- the insurance cycle
