Pillar III – Market discipline
4 Technical liabilities
4.6 Summary of the main statistical methods used to determine outstanding provisions in practice
4.6.1 Below we discuss the more common statistical methods applied by insurance companies together with an assessment of their strengths and weaknesses. New techniques are being developed all the time to cope with specific issues so it is not possible to give a categorical listing.
4.6.2 Some companies tend to use more straightforward methods such as “loss ratio” or average claims methods for short tail business with largely homogeneous claims costs such as short tail accident and sickness or property. More sophisticated triangulation techniques are used for longer tail business such as liability classes.
4.6.3 Examples of techniques which have been developed to deal with areas where there is significant uncertainty such as asbestos claims and claims arising from the World Trade Center disaster are dealt with below.
Triangulation techniques
4.6.4 Triangulation methods are the most common. However, there are many variations. Other methods discussed below, such as the Bornhuetter-Ferguson method and numbers and averages approach rely on triangulation techniques in some way.
4.6.5 Data is generally presented in an array known as a “triangulation” (so called as the data is presented in the form of a triangle). This format shows, for a group of policies, how the item under review (such as the number of reported claims, cumulative claims paid, cumulative claims incurred etc) develops from one accounting period to another through to its latest or ultimate value. Data is commonly grouped by accident year, the calendar year in which a loss occurs, or by underwriting year, the financial year in which the risks incept. The intention is to model the way in which cumulative claims develop over time.
Having set out the basic claims data, the next step is to calculate the “development factor”
(the rate at which the cumulative claims increase from year to year). This is the factor that relates one year to the next. The development factors to be applied to each year are then determined based on an averaging method (chain ladder, basic link ratio (simple average), weighted chain ladder, restricted diagonals etc). The strengths and weaknesses of using more complicated methods of determining the development factors such as weighted chain ladder, restricted diagonals and the inflation adjusted chain ladder method are considered in the table below. Having established typical development factors, historical claims data is projected forward to determine an estimated ultimate position.
4.6.6 Most typically the approach is applied to cumulative paid or incurred claims both of which generate an ultimate claim amount. The required outstanding claims provision (notified plus IBNR) is then determined by deducting claims paid to date from projected ultimate claims.
4.6.7 The basic assumption underlying triangulation methods is that the data develops in a consistent manner and therefore, development patterns derived from historical data can be used to project the ultimate outcome for cohorts which are not fully developed.
Bornhuetter-Ferguson method
4.6.8 The Bornhuetter-Ferguson (BF) method is a combination of the loss ratio and triangulation methods.
4.6.9 The starting point is the information from other sources which is used to construct an
“initial expected ultimate loss ratio”. This could be, for example, information obtained from the underwriter who supplies his planned loss ratio when he wrote the business or from market knowledge as to the expected out-turn of a particular year.
4.6.10 The claims pattern is the percentage of expected claims at a point in time, based on the link ratios and is calculated using a triangulation method. The claims pattern is used to calculate, based on the ultimate loss ratios, how much future development is expected for each year being projected. These future developments can be added to actual claims development to date in order to estimate the projected ultimate development for each year. Future claims are calculated by multiplying the expected loss ratio by the ultimate premium for a cohort and then applying the claims pattern to apportion the ultimate losses between future and current claims.
Loss ratio method
4.6.11 The loss ratio method uses the ultimate loss ratio (ULR) to estimate the ultimate cost of claims, usually for a class of business. The ultimate cost of claims is calculated as ULR multiplied by earned premiums. The IBNR is then calculated as the ultimate cost of claims less claims notified to date.
4.6.12 For short tail classes it may be appropriate to consider the actual loss ratio for one or more years immediately preceding the current year, since these will be almost fully developed. The loss ratios for these years should be adjusted for any unusually large claims so that the ULR reflects the actual expected out-turn of the business. Adjustments will also be required for the effects of inflation.
4.6.13 This method is extremely subjective and would generally be seen as a reasonableness check for the results of other methods rather than the key method being used.
Average claims method
4.6.14 The ultimate cost of claims can be estimated by multiplying the average cost of claims by the ultimate number of claims. The ultimate number of claims is usually estimated using a triangulation method. Once the numbers of claims for each accident or underwriting year have been estimated then the appropriate average values (preferably based on monthly rather than annual rates) can be applied.
4.6.15 The averages are calculated using the average cost of claims for underwriting and accident years which are almost fully developed. Allowances will need to be made for the effects of inflation (using an appropriate index) and other changes that will affect claims costs. For example, changes in policy conditions, superimposed claims inflation over and above the movement in the index and impact of nil claims need to be taken into account.
4.6.16 The projection of claims numbers usually shows a more consistent development pattern than claims costs since the variation that comes from the size of individual claims is excluded from the development. This can be very useful in examining the incidence of pure IBNR large claims. However, the selection of the average claims costs to apply can be very subjective.
4.6.17 Some variations of the “averages” method project the pure IBNR only and in these cases separate consideration on IBNER needs to be made.
Curve fitting
4.6.18 An alternative to triangulation methods is to use a mathematical curve to describe the development pattern. The idea is to estimate the shape of the curve from past claims data and then use this shape to project the progress of incompletely developed years.
4.6.19 Curve fitting can be used in several different ways:
■ to fit a curve directly to the claim data;
■ to fit the link ratio development factors in order to project future development – fitting the “tail” of the development;
■ to fit a curve to the link ratio development factors already obtained to smooth them.
4.6.20 In order to fit a curve to any set of data (the raw claims data, the link ratios etc) it is necessary to:
■ select a mathematical model of the right shape to represent the data;
■ decide which points are to be fitted (which is not necessarily all the data);
■ find the appropriate parameters for the curve which give “best fit” to the data.
4.6.21 Curve fitting is often used to extrapolate claims where a tail factor is needed. It is very subjective but is not uncommon.
Benchmarking
4.6.22 An important alternative often used where there is limited development history is to use a benchmark development pattern from another similar book of business. In this case assumptions are made that the nature of claims development will be consistent.
Exposure based analysis
4.6.23 Catastrophe events pose different difficulties of estimation. For example, there may be little actual claims development at the accounting date. A common method is to work from a top-down estimate of the total cost of an event. By making assumptions as to the total cost of an event, the extent of the cost that is insured and the company’s market share, it is possible to derive a broad estimate of the company’s exposure from which a provision can be estimated. The range of the resulting provision is likely to be extremely wide.
4.6.24 Another variation of exposure analysis, particularly for reinsurance companies, is to consider the impact of an event on a contract-by-contract basis. In the first instance those contracts not exposed (due for example to the period or geographic region of risk exposure) are excluded. For those contracts remaining it may be possible to identify the maximum cover provided and in this manner get an early indication of the upper range of the impact of the event (and hence provision required). Such methods are being used to assess the impact of the World Trade Center event which is discussed in more detail below.
4.6.25 The following table summaries the main statistical methods used by companies to determine their outstanding claims provisions (reported outstanding claims plus IBNR).
Strengths and weaknesses of different statistical methods
Method Key Assumptions Strengths Weaknesses Data
Triangulation techniques
Past claims experience can be used as a guide to future claims development.
Basic assumption underlying triangulation methods is that the data being analysed is developed in a consistent manner, and that development patterns derived from historical data can be used to project the ultimate outcome of years not fully developed.
Commonly the factors selected are adjusted in some manner. This allows greater flexibility in application but introduces incurred and / or claims paid) by accident or underwriting year.
Data needs to be subdivided into a reasonable number of
homogeneous classes of data and produced in a consistent basis.
(a) Chain ladder Applies more importance to years with higher values by using values of the original data to weight the development factors.
Gives more weight to those years with higher claims experience.
Development factors used in projection place less reliance on those derived from small volumes of data, and more on those from large volumes of
(simple average) The average value of the link ratios are used to project forward those cohorts which are not yet fully developed.
All years are given equal weight
in determining the loss pattern. Distortions in the underlying data particularly arising from cohorts with low values, may be magnified.
As for Chain ladder.
Method Key Assumptions Strengths Weaknesses Data
(c) Weighted chain ladder
Refines the basic link ratio model to attach more importance to recent years.
Gives more weight to the more recent link ratios.
Choice of weight is subjective. As for Chain ladder.
(d) Restricted diagonals
Weights link ratios by only including the most recent diagonals.
(e) Inflation adjusted Future inflation rates are required. The projection of the ultimate cost of claims allows for an estimate of future inflation which is specific and does not have to depend on past inflation.
Requires use of an inflation index, which may be generic, or out of date, and therefore may not give an accurate indication of future inflation.
Requires an inflation index which may or may not reflect the true inflation within the claims data.
Bornhuetter- Ferguson
Uses triangulation, but instead of calculating the future development as a multiple of the current position. BF and Cape Cod methods add the estimated future development to the current position in order to reach the ultimate position. by selected loss ratios for years where very little has been reported to date.
Starting point is estimated initial ultimate loss ratio.
Claims pattern is percentage of expected claims at a point in time based on link ratios and calculated using triangulation methods.
Method Key Assumptions Strengths Weaknesses Data
Loss Ratio Ultimate loss ratio can be predicted from historical data or reliable estimates.
Ultimate losses can be calculated as ULR multiplied by premiums.
IBNR is calculated as ultimate losses less any claims notified to date.
Choice of loss ratio can be very subjective, and therefore needs to be carefully considered.
Underwriting year: losses arising on all policies incepting within the year.
Accident year: all losses arising in a calendar year as a
percentage of premiums earned in the year.
Adjustments for large and unusual claims and also to update them to allow for the effects of inflation and rating changes.
Average claims or
“formula claim”
Suitable for large number of similar claims which tend to be reported and settled quickly.
Ultimate loss = average cost x ultimate number of claims.
Simple and efficient.
Often a stable and at least visible base for the projection of large claims.
Can be adjusted for inflation and other changes affecting claims costs such as changes in policy conditions.
Assumes that the population is homogeneous.
Method Key Assumptions Strengths Weaknesses Data
Curve fitting Claims data can be fitted to a curve in order to project future development and link ratios in order to smooth them.
Assumes that future claims development can be predicted from historical claims data, by fitting historical data to a curve.
Can be used to project link ratios.
Method requires a number of subjective decisions, such as which model is appropriate to use, which data points to fit to the curve, and which to exclude.
Mathematical model of the right shape to represent the data.
Decide which data points are to be fitted.
Find appropriate parameters for the curve which give “best fit” of the data.
Benchmarking Assumes development of benchmark line of business is appropriate to apply to the business being projected.
Simple to use. Does not require a large history of loss
development.
Very difficult to verify the key assumption that the benchmark
That it is possible to build a model that sufficiently accurately models the process that generates a loss for each given class of business. data depends on the model used.
Summary of the main statistical methods applied in selected countries
4.6.26 The table below summarises, based on a questionnaire sent to KPMG member firms, the main statistical methods which are applied within the EU. Triangulation methods appear to be the most popular method throughout the EU. As noted above companies should be applying a variety of methods and comparing the results of these.
Statistical methods applied in practice
Country Methods most commonly used in practice
Denmark Actuarial methods are used to determine IBNR and IBNER. Large companies apply a variety of techniques and compare results with expectations. In small companies less sophisticated techniques are used.
France Except for motor, for which there is a requirement to use several statistical calculations (loss ratio and average claims cost), there is freedom to use statistical methods. In practice the most common methods used are triangulation techniques, including chain ladder on paid claims, loss ratios, and Bornhuetter-Ferguson.
Germany Many companies use the loss ratio method recommended by the supervisory authority. There is also a trend towards chain ladder methods.
Companies that draw up financial statements under US GAAP or IAS use a variety of techniques and compare the results.
Italy Triangulation methods are used but other actuarial models are not typically used except where companies prepare US GAAP financial statements.
Netherlands In general non-life actuarial techniques are not well developed / applied in the Netherlands and if adopted are only applied by large companies / groups. A lot of chain ladder techniques are used and some more advanced methods. Others apply average claims and experience.
Portugal Triangulation methods based on paid claims, in particular chain ladder, basic link ratio and separation method.
Spain Triangulation methods, in particular different weightings of the chain ladder method are the most commonly used. Some undertakings use a considerable variety of methods.
It is a regulatory requirement to apply at least two different statistical methods over a five year period and take the higher figure.
Sweden Triangulation based on paid claims is the most commonly used method with the method based on incurred claims also being used. Smaller companies with small and volatile business use loss ratio / average claims methods.
The results of different techniques are often blended together or a simple average taken.
United Kingdom Triangulation based on paid claims is the most commonly used method with the method based on incurred claims also being used. It is common to compare the results of different methods.
Smaller companies with small and volatile business use loss ratio / average claims methods.
Source: KPMG
4.6.27 The companies we visited as part of this study emphasised both the importance and difficulty of obtaining reliable data, ensuring that data used for projections is homogenous, and the difficulties presented by latent claims. Larger companies tended to use a variety of methods and compare the results. Some companies actually determine
“best estimate” provisions for management reporting purposes but then set up more prudent provisions for statutory reporting purposes.
4.6.28 Companies use a variety of methods to assess their provisions for outstanding claims and no single method is likely to be appropriate in isolation. Companies should use several methods and compare and explain the differences between the various methods before deciding on the most appropriate method to use. The methodology applied should be continuously reviewed and amounts provided compared with the actual experience. The tracking of the accuracy of past results is a key element of data that should be maintained to support this continuous review.
4.6.29 Disclosure to the prudential supervisor of the level of prudence which has been included in the provisions, the range of outcomes and their likely probability, the assumptions underlying the calculation and impact of changes in these assumptions is as important as the point estimate that is actually chosen. Disclosure to the supervisor should not necessarily lead to public disclosure. It is important that supervisors are informed of the degree of prudence, and the basis for judgemental decisions in setting provisions.
Chapters 8 and 9 deal with recommendations on the benefits of enhanced disclosure in financial reporting.
4.6.30 In practice, assessing the probability of various outcomes is subjective. For personal lines classes there may be sufficient volumes of data to employ statistical techniques such as the Thomas Mack method. For less homogenous and/or classes where the volumes of data available are smaller then reprojection of the data using assumptions with greater or lesser degrees of conservatism is the only practical approach. Even though rigorous statistical analysis is not possible for many classes of business, there is great benefit to be gained by giving regulators a feel of how sensitive the provisions are to changes in key assumptions.
4.6.31 In Australia the supervisory authority has recently implemented a system of requiring discounted best estimate provisions to be held along with an explicit provision for adverse deterioration (PAD). The main criticism has been in the implementation of the system rather than the system itself. There can be an over reliance on statistical techniques to set ranges of outcomes and their associated probabilities. These are sometimes applied without sufficient understanding of the risks surrounding the underlying business. In most cases, producing a reasonably accurate estimation of the range of probable outcomes requires considerable investment in modelling techniques (as well as sufficient data).
4.6.31 In Australia the supervisory authority has recently implemented a system of requiring discounted best estimate provisions to be held along with an explicit provision for adverse deterioration (PAD). The main criticism has been in the implementation of the system rather than the system itself. There can be an over reliance on statistical techniques to set ranges of outcomes and their associated probabilities. These are sometimes applied without sufficient understanding of the risks surrounding the underlying business. In most cases, producing a reasonably accurate estimation of the range of probable outcomes requires considerable investment in modelling techniques (as well as sufficient data).