PREAMBLE ... 3
1. Specific problems... 5
1.1. Model used ... 5
1.2. Problems relating to data... 6
1.2.1. Nature ... 6
1.2.2. Break elements ... 8
1.3. Discounting reserves ... 9
2. Approximate methods (Proxies) ... 10
2.1. No market references available ... 10
2.2. Market references available ... 10
2.2.1. Based on average market costs... 11
2.2.2. Based on market frequencies... 11
2.2.3. Based on development factors by type of cover ... 11
2.2.4. Based on loss ratio by occurrence or underwriting year ... 12
2.2.5. Based on exceptional market claims ... 12
2.2.6. Based on the development of claims management costs by type of cover ... 13
2.3. Factoring in the discount ... 13
2.4. Factoring in reinsurance ... 13
3. Applicable methods by risk category ... 14
3.1. Motor Third Party Liability... 15
3.2. Third Party Bodily Injury Auto... 16
3.3. Transport ... 18
3.4. Fire / Property... 20
3.5. Third Party Liability... 21
3.6. Assistance... 22 3.7. Legal Protection ... 23 3.8. Construction ... 24 3.9. Natural Events ... 26 3.10. Credit / Surety ... 27 3.11. Reinsurance / Acceptance ... 29
APPENDIX I: Supplementary material ... 30
PREAMBLE
Context
1. In a letter dated 11 August 2006, the European association of actuaries, Groupe Consultatif Actuariel Européen, suggested that groups of experts be set up at national level to determine approximate methods (proxies) to calculate the best estimate of non-life insurance technical provisions. Actuaries, industry representatives and the supervisory authority would participate in these groups.
2. These approximate methods provide companies which do not have adequate resources to calculate the best estimate (actuarial expertise, inadequate information system, lack of data, insufficient portfolio size, etc.) with assessment methods compatible with the requirements of the future Solvency 2 Directive. These proxies are temporary and can be used as a provisional substitute for the statistical methods required in the future Directive.
Objectives of the working group
3. The working group decided to expand its original objective and present more general ideas about the calculation of the best estimate for technical provisions in property and casualty insurance. It is worth noting that bodily injury risks are not included in this report.
4. In the section on proxy methods, the objective is to define the methods that will be acceptable to calculate the best estimate. We must, however, insist that methods of this kind can only be a temporary solution until all the insurance companies in the European Union possess sound actuarial knowledge and sufficient information.
The valuation of insurance liabilities in the context of Solvency 2
5. The current Directive Proposal indicates that the value of technical provisions will be equal to the sum of the best estimate and a risk margin. The methods of calculating the risk margin are outside of the scope of this report.
6. The concept of best estimate is defined in the following extract: "The best estimate equals the expected present value of future cash flows, using the relevant risk free yield curve, based upon current and credible information and realistic assumptions.
7. The best estimate may be determined by using both stochastic methods and deterministic methods provided these ones produce consistent results with those obtained using stochastic approaches."
8. We shall begin by describing the possible approaches to calculate the best estimate for technical provisions. We shall only deal with insurance provisions, relating to premiums and claims (including claims management expenses).
9. The methodological considerations included in this paper presuppose that, in accordance with usual practice on the French market, most lines of business are
managed by reference to the year in which the loss occurred1 and that the distribution per year of the available statistical data is compatible with the management of the line of business.
10.In order to ensure consistency in the analysis of changes in premiums and claims expenses, it may however be necessary to reprocess the distribution per year (loss occurrence, underwriting or other) of the statistical data in certain cases, in particular when the portfolio undergoes rapid changes or includes a significant proportion of atypical contracts (e.g. multi-annual).
11.The Directive Proposal states that technical provisions should be valued at "current exit value", which would require, inter alia, future cash flows to be estimated by underwriting year.
12.Issues relating to data quality will be highlighted. We shall refer to the nature of the data (claims, gross and net reinsurance premiums) and to changes, trends and missing data.
13.We shall then deal with one of the main changes introduced by the Directive Proposal, discounting of technical provisions.
14.Approximate methods will then be suggested, depending on how well-known is the portfolio, as well as, in each case, their main advantages and drawbacks.
15.In conclusion, we shall propose summaries for each risk category in the form of tables by line of business.
16.An Appendix aims at expanding on certain issues mentioned in the first part in a pedagogical manner .
1
Except for certain lines of business that are managed by underwriting or reported claims in Construction, Transport, Credit, Surety insurance and Professional general coverage and legal protection, and specific aspects of reinsurance acceptances.
1. Specific issues
1.1.
Model used
17. As mentioned previously, the definition given in the Directive Proposal states that "The best estimate equals the expected present value of future cash flows, using the relevant risk free yield curve, based upon current and credible information and realistic assumptions.
18.The best estimate may be determined by using both stochastic methods and deterministic methods provided these ones produce consistent results with those obtained using stochastic approaches."
19.In other words, technical provisions are the expected discounted future payment flows. The calculation may be carried out using the following methods:
- Stochastic: it involves assessing the distribution of future cashflows, whose discounted average leads to the above definition of the best estimate;
- Deterministic: on the assessment of the ultimate loss ("average" or "most likely" loss), are applied “cadences” and the yield curve, which allows to deduce the discounted value of future flows.
20.Due to their simplicity and reliability, deterministic methods are often favoured in determining the espérance. For this reason the recommendations made in this paper mainly deal with deterministic methods.
21.It must be underlined that the analyses carried out in order to determine the best estimate elements do not derive from simple mathematical calculations but require numerous additional studies, under a real risk-based approach. In other words, it is necessary to adapt the methods to the specific features of the line of business under study and to understand the methods and changes relating to the elements below in order to understand fully the behaviour of the various elements over time:
‐ Underwriting: changes in price or in the structure of the portfolio, changes in underwriting terms (nature of coverage, excess clause, etc), changes in the level of procedures for risk selection, etc;
‐ Claims management: type of assessment methods used throughout the life of the claim, assessment of changes in Case-by-case funding methods, etc;
‐ Reinsurance: changes in the reinsurance programme over time (new clauses or changes to clauses);
‐ External factors: changes in precedent, regulatory and economic changes (inflation, exchange rate, etc).
22.There are numerous deterministic methods. They are applied to various underwriting entries in order to estimate projections:
‐ Development of claims charges and payment in instalments, along with a separate analysis of recoveries received;
‐ Approach based on the number of claims / average costs;
‐ Analysis distinguishing between attritional claims and serious claims; ‐ Loss ratio approach or projection of exposure ratios.
23.The assessment models proposed below make it possible to assess most of the technical provisions in property and casualty insurance on the French market. They are principally based on the study of incurred loss triangles (premiums, payments, claims charges, numbers, recoveries, etc). Models based on a claim-by-claim projection of payments, while appropriate to assess reserves on certain exceptional claims, are not dealt with in this paper.
1.2.
Data issues
24.The nature and features of best estimate calculations can be assessed for each line of business. However, certain problems are general and apply to all risk categories.
25.Every insurer should set up data management tools to provide a sufficient history of reliable data for the lines of business it deals with (the depth of the histories required is indicated in the tables by type of cover). This point is particularly crucial for companies which outsource some or all of their management, for newly created entities, for newly launched business sectors or for acquired/merged portfolios. This can often lead to the coexistence of heterogeneous data which can be difficult to process.
1.2.1.Nature
26.As far as possible, the company should reconstitute data histories in order to understand the category’s development and integrate all break elements. The necessary data are the following (the necessary data’s history depends on the category’s duration):
‐ Premiums: history of earned and issued premiums by year;
‐ Claims: payments, recoveries received, claims charges, number of claims, average cost distinguishing between serious and attritional claims (incurred loss triangles); ‐ Costs: claims management expenses (unallocated2), fixed and variable
commissions, management and other expenses.
27.Only the best estimate relative to premiums provisions and loss provisions is dealt with. However, problems related to the reserve for claims management expenses are mentioned in Appendix 2.9.3 and in the part dealing with approximate methods.
2
28.A distinction must be drawn between the best estimate for premiums and the best estimate for claims. In the absence of available data, the company may use a proxy (see part 2 of this paper).
General principles relating to premiums
29.The problems relating to premiums are described in the Appendix 2.9.2 of this paper.
30.The “Code des assurances” (see Article R 331-6) sets forth a methodology to assess unearned premiums. Depending on the contents of the Directive’s implementation measures (for example the Liability Adequacy Test), other methods, based on a projection of claims experience, will have also to be implemented.
31.It should be noted that all projections made will depend on the method of assigning claims, either by year of occurrence or underwriting year.
32.The portion ceded to reinsurers should also be taken into account, along with any retroactive3 premium adjustments, depending on the claims experience.
General principles relating to claims
33.The claims best estimate should be determined by distinguishing between the gross reinsurance elements, the effects of inflation, recoveries, the reserve for claims management expenses (calculated gross of reinsurance and borne exclusively by the insurer) and the reinsurance impacts.
34.It therefore seems reasonable to calculate, initially, a best estimate gross of reinsurance, then one net of reinsurance. The best estimate calculation should include the following phases (see Appendix 2.9.1.):
‐ Projection of charge and payment triangles gross of recoveries received, by category and factoring in inflation;
‐ Projection of recoveries-received triangles, by category;
‐ Estimated impact of reinsurance, depending on the nature of treaties (various special clauses) and changes in the treaties;
‐ Discounted future cash flows at the risk-free rate (mid-year) - Section 1.3.
35.In parallel, other factors must be taken into account according to the nature of policies (contractual profit-sharing clauses, etc.).
3
1.2.2.Break elements
36.As a rule, the methods used to determine the development factors and definitive projections presuppose that the data observed follow fairly regular developments. In many situations however, we register accidental variations which show no regular features.
37.Several accidental elements are developed in Appendix 2.6. We can group them into several categories:
‐ Missing data, with truncated or insufficient histories;
‐ Breaks in information caused by new market rules (legal, the market organisation, etc.) or within the company (new management rules, a new price list, etc.);
‐ Changes in trends and development factors by year (in the portfolio structure, in the organisation, etc.).
38.Among the new standards, cite two factors of particular interest can also be quoted, namely inflation and reinsurance.
Inflation
39.We generally assume that past histories integrate inflation elements into the ordinary data and that future developments continue to show this type of development. We therefore consider that future inflation corresponds to past inflation.
40.Nevertheless, in certain conditions these assumptions must be questioned. This is regularly the case for claims with long developments, whose management can span relatively different time periods. The difficulty then arises in determining past inflation and anticipating future inflation over a period of several decades (see Appendix 2.6.2).
Reinsurance
41.To achieve a best estimate of the reinsurance impact, it is important to factor in the nature of the line of business, the weight of cessions and changes in treaties over time:
‐ Quota-share treaties: analyse gross reinsurance, then apply cession rates to deduct automatically all volumes ceded from gross projections;
‐ Excess of loss reinsurance: estimates are rendered difficult by several factors (changes in cession rules over time with variable limits and special clauses, etc.) - Appendix 2.9.1.
1.3.
Discounting reserves
42.Discounting technical provisions is one of the key points raised in the draft Solvency II directive, which states that the best estimate must be calculated while “using the relevant risk free yield curve”.
43.In the case of property and casualty insurance, it seems advisable to consider the following approximations:
‐ To the extent that the services show little correlation to changes in the yield curve, we can use a deterministic yield curve (doing without projecting probable interest rates);
‐ We can also do without projecting probable claims-payment maturities and merely use deterministic maturities.
44.These approximations allow us to calculate the best estimate using today’s risk-free yield curve as the basis for discounting all future maturities. They enable us to process separately our calculation of the insurer’s mathematically anticipated services (and thus to use the “standard” principles in calculating technical provisions) and the discounted reserve.
Methodology:
45.In terms of methodology, we propose to use the non discounted data, then to adjust them at the end in order to take the discount into account.
46.Since the yield curve is variable, we recommend using the data on non discounted payments and charges in order to be able to reuse and compare these data from one year to the next and set up a number of homogeneous time series.
47.If we have the projected timetable for claims payments (most frequently the case when we use a payment-by-instalment method; if not, see the “proxy” part of this paper), it is enough to discount each future flow thus shown at the corresponding rate.
48.If the data are sufficiently precise, we can use infra-annual payment maturities.
49.However, if the payments are known only by year, one solution is to use the following approximation: assume that the annual charge is paid in mid-year.
2.
Approximate methods (Proxies)
50.When an insurer lacks the necessary information to calculate estimated definitive charges, we may use approximate methods or proxies. These proxies must make it possible to anticipate changes in results, at least roughly. They are less precise in principle and must be used on a provisional basis only. They are a temporary substitute for standard statistical methods, until more relevant data is available.
51.Several situations can be distinguished depending on whether market references are available or not.
2.1.
No market references available
52.Under these circumstances, we can propose few methods. In the absence of market data or an internal history, it is possible to neutralise underwriting profit.
53.The uncertainty generally has to do with claims showing reduced volumes due to late information (late reporting, assessment difficulties). In this case, we neutralise underwriting profit and set aside a reserve equal to the profit.
54.This method has the merit of not showing an unwarranted profit, but it includes such major flaws as the following:
‐ It does not take into account observed claims experience;
‐ It does not take into account the gain or loss margins factored into pricing.
55.Note that before we can measure gain or loss margins on an a priori basis, it is necessary to possess a minimum amount of information with which to analyse developments and other factors.
2.2.
Market references available
56.In advising the use of proxies, the use of market data strikes us as viable. These data may be published by a local actuarial association, an association of insurers, the regulator or any other organisation able to collect reliable data on a sufficiently large scale.
57.These data may validly be published for only a few lines of business showing a measure of homogeneity and stability. They must allow for uncertainty arising from the use of data not specific to the entity. In addition, they must be representative of all market players and not merely reflect the features of a single dominant player.
58.However, methods that rely on market data have the following drawbacks:
‐ They do not take account of the insurer’s own underwriting terms;
‐ They provide general results based on structures which do not necessarily correspond to the one under study;
‐ The market data may arrive late, particularly for the latest financial year.
59.We consider using different references, according to the need.
2.2.1.Based on average market costs
60.One useful proxy could be based on average market cost references per relevant year, as released by the line of business’s regulator.
61.Using a spacing-out method for a given number of reported claims, insurers could then assess the number of late claims and deduce the corresponding amount of Incurred But Not Reported (IBNR) claims to add to case-by-case provisions.
62.To avoid discrepancies due to late information from the market, the average cost used by the insurer could be that of the past year, corrected for observed inflation.
2.2.2.Based on market frequencies
63.One useful proxy could be based on “market” frequencies per relevant year, as released by the line of business’s regulator.
64.Insurers could then assess the corresponding IBNR amount to add to case-by-case provisions, first assessing their average costs or using average market costs.
2.2.3.Based on development factors by type of cover
65.If the market knows the development patterns adapted to each line of business, we can use these as reference bases to assess the run-off of the insurer’s charges (charges, payments and recoveries, and all of these must be assessed gross of reinsurance).
66.Companies with little experience could use all these patterns, and companies with insufficiently long histories could use them partially, for extended liquidation reporting periods.
67.Merits:
‐ They allow average developments to be applied using a substantial base of information;
‐ They allow developments to be applied according to discriminating factors related to the nature of occurred claims.
2.2.4.Based on loss ratio by occurrence or underwriting year
68.If the market possesses information about the ultimate loss ratio, this information can serve as a reference in the insurer’s approaches, particularly for the most recent years.
69.As in exposure methods, we could use a result combined of market data and the insurer’s own data, according to a credibility factor built on the market data’s development rate.
70.Merits:
‐ This avoids assessing the result on a fragile base by taking account of the market situation.
2.2.5.Based on exceptional market claims
71.This method sets aside a reserve for the claims charge of an event, in view of the company’s exposure, according to the assessment made at the market’s overall level (a major claim affecting several insurers).
72.Merits:
‐ This method is easy to use on the basis of only two pieces of information: ‐ the insurer’s own exposure/overall market exposure;
‐ the overall claims charge, estimated at market level;
‐ Provided the above two pieces of information are available, it can be implemented rapidly;
‐ It is possible to use sophisticated market estimates based on advanced simulation tools, whose cost is born by the market (e.g. the provisional cost of flooding based on satellite data matched up with geo-referencing of the properties involved).
3.Drawbacks: 7
‐ Erroneous assessment due to the insurer’s poor knowledge of its own exposure; ‐ Possible repercussions from errors in the market’s estimate of claims;
Lack of reliable inform
‐ ation about the market’s claims experience and the
‐ s claim level for the charge related to intangible
losses such as operating losses. insurer’s own exposure;
‐ Difficulties in taking account of distinctive policy features in the insured portfolio; Poor assessment of the market’
2.2.6.Based on the development of claims management costs by type of cover
The so-called "New-York" method
74.Calculation of average paid management costs for €1 in paid claims: the ratio of management costs paid / (paid claims gross of recoveries received + recoveries received). The calculations must be carried out gross of reinsurance.
75.Assuming that this ratio holds steady in the coming years, application: ‐ at 50%4of file reserves;
‐ at 100% on IBNR.
76.One variant is to distinguish the ratios observed in the current and previous years (the opening and examination of files generates most internal management costs and is generally carried out during the current year; hence the higher rates during the first year).
77.This proxy is fairly simple to implement but has the drawback of making the reserve for future management costs directly proportional to loss reserves.
78.Due to this proportionality, the proxy takes into account a discount factor, provided it is applied to discounted loss reserves.
2.3.
Factoring in the discount
79.If we do not know the entity’s specific payment intervals, we can use market payment intervals, if available. These intervals or instalments allow us to estimate future payment flows and apply the risk-free rate to obtain the discount.
80.If all we have is the data about the overall service charge, then the payment timetable is unknown. In this case, our approximation using an average duration by type of cover appears acceptable. This would be a non discounted duration published by a central organisation able to supply this information.
2.4.
Factoring in reinsurance
81.A simple method that allows us to assess the impact of reinsurance is to determine the ratio (ceded payable loss provisions) / (booked payable loss provisions), with or without late claims.
4
3.
Applicable methods by risk category
82.It is necessary to adapt the methods to the specific features of risk categories in order to understand as well as possible the expected development of each of the various elements.
83.We have therefore attempted to describe in a table form the problems involved in the data and methods used in setting up reserves, including the best adapted techniques and possible approximate methods for each of the following risk categories:
‐ Motor Third Party Liability; ‐ Third Party Bodily Injury Auto; ‐ Transport; ‐ Fire / Property; Liability; ‐ Third Party ‐ Assistance; on; ‐ Legal Protecti ‐ Construction; ‐ Natural Events; ‐ Credit / Surety; ‐ Reinsurance Acceptances.
84. vailable on the market, but it
attempts to deal with a maximum number of categories.
85.
applied solutions. These approaches should be adapted to the information available.
This paper cannot claim to deal with all types of cover a
Given the host of impacts due to the different management modes of various insurers and other parameters, the information provided in our tables does not correspond to absolute rules, but rather to generally
3.1.
Motor Third Party Liability
Market / Product MOTOR
Risk segments Comprehensive motor and Third Party Collision Specific features Fleets of cars
Insurance Mandatory for the Third Party Collision part System IRSA mechanism (Recoveries) Distribution network Agents, Salaried and Broker networks
Characteristics Description Cover
Description Property and Casualty: Theft, Fire, Glass Breakage, etc.
Third Party Collision.
Special features Management of car fleet franchises.
Time base Occurrence mode only.
__________________________________________________________________________________________________________________________ Market Private individuals.
Companies,car fleets. Data Time unit Annual - Required.
Duration of liquidation Short development.
History 5 years.
Nature Number of claims / Frequency of reports / Average Costs – Desirable. Gross payments / Recoveries Received – Required.
Gross Case-by-case charges / C/C charges net of recoveries – Required. Inflation – Reference system Indexed repair costs or inflation.
Methods of C/C assessment
Real management cost Possible if volume is low (manual management based on adjustors’ report). Average or flat fee mgt cost Recommended if significant volume (automatic management per made-claim
covered).
Methods Segmentation Analysis by cover or by risk family (Comprehensive and 3rd Party). Restatements Restated impacts of major claims (Third Party Collision) and Natural
Catastrophes (Comprehensive).
Problems Stepped-up payment development mainly due to improved management process.
Method of recording Fleet excesses (negative claims, recoveries received, etc.) Problem of allocating Recoveries.
Processing inflation Risk segments insensitive to inflation given liability duration. Flat fees used for C/C claims assessment generally integrate inflation. Best Estimate Methods Development methods, restated for exceptional claims, applied to payments,
recoveries, C/C
claims numbers and charges.
Number of methods A minimum of 2 methods to analyse recoveries separately.
Indicators to follow Analysis of claims/premium ratios (first and last years) per year, factoring in changes in underwriting policy - Required.
Analysis of changes in frequency of reports and average costs – required. Analysis of estimated recovery rates over the observation period –Required. Analysis of disparities in estimated results via different approaches - Required.
Possibility of using approximate method
Use of Proxy Yes, barring development in specific niches.
Possible methods Report Frequency Approach / Average cost on the basis of available market information, taking serious claims into account.
Neutralisation of result, taking serious claims into account for year Y and taking the C/C charge into account for year Y-1 (1)
Comments The above methods must be compared with C/C charges to measure the weight and consistency of reserves for late claims.
The recommended method should take into account the portfolio’s size and the reinsurance programme.
(1) Neutralisation of the result:
3.2.
Third Party Bodily Injury Auto
Market / Product MOTOR
Risk segments Third Party Bodily Injury
Specific features Unlimited cover / IRCA claims management / Annuities (reserves and currently being paid) Insurance Mandatory
System IRCA mechanism (Recoveries) Distribution network Agents, Salaried and Broker networks
Characteristics Description Cover
Description Third Party Bodily Injury. Special features Management of IRCA claims
Annuities: reserves and currently being paid
Time base Occurrence mode only.
__________________________________________________________________________________________________________________________ Market Private individuals
Companies,car fleets Data Time unit Annual - Required.
Duration of liquidation Long development. History 10 - 15 years.
Nature Number of claims / Average costs with Attritional/Large distinction (threshold to be defined €500,000, €1m etc.) - Required.
Gross payments / Recoveries Received with Attritional/Large distinction (threshold to be defined €500,000, €1m etc.– Required.
Gross Case-by-case charges / C/C charges net of recoveries with Non-Serious/Serious distinction (threshold to be defined €500,000, €1m etc.– Required.
Inflation – Reference system Methods of C/C assessment
Real management cost Manual management based on various adjusters’ reports and the writer’s experience (required for claims above a given PPI – partial permanent incapacity - level). Average or flat fee mgt cost.
Possible for claims with a low PPI level (automatic assessment by loss entry). Methods Segmentation Analysis by risk family (Third Party Bodily Injury, IRCA claims) and by tranche of
claims cost (Non-Serious and Serious separation).
Restatements Restatement of exceptional claims and impact of discount rate in terms of potential annuities (or other parameters) (1).
Problems Changes in methods of assessing C/C claims files (hourly rate, mortality table, discount rate or other parameters).
Data used must exclude back interest and mathematical reserves on annuities currently being paid.
A sufficient data history and a separating (Attritional/Large) approach is necessary to understand fully the liquidation of this long-development risk. Processing inflation The segment is highly sensitive to inflation. Due to steep changes in legal precedent
and economic factors, the inflation observed in recent years is much higher than economic inflation.
Best Estimate Methods Development methods applied to payments, recoveries and C/C claims charges. Exposure methods applied to payments, recoveries and C/C claims charges. An approach based on ultimate loss ratios according to the claims already occurred
and to pricing policy.
Number of methods A minimum 3 methods to analyse recoveries separately.
Indicators to follow Analysis of premium ratios (first and last years) per year, factoring in changes in underwriting policy - Required.
Analysis of changes in numbers of claims and average costs –Required. Analysis of recovery rates- Desirable.
Analysis of disparities in estimated results via different approaches - Required.
Possibility of using approximate method
Use of Proxy Delicate given the changes in legal precedent and economic conditions noted in the French market.
Possible methods Premiums approach on the basis of available market information and the pricing used, taking account of serious claims.
Neutralisation of result, taking serious claims into account for year Y-1 and Y (2). Comments The methods below must be compared with C/C charges to measure the weight and
consistency of reserves for late claims.
The recommended method should take into account the portfolio’s size and the reinsurance programme.
(1) Problems caused by the discount rate as a parameter to assess annuities currently being paid (or other parameters).
In the absence of restatement in terms of incurred loss triangles for serious claims (reserves for annuities), analyses carried out using these developments are implicitly distorted by variations in discount rates over time (or other assessment parameters). In general, methods to assess C/C
claims have considerably advanced in recent years. It is therefore desirable to reconstitute the run off statistics for these claims on the basis of the discount rates (and other parameters) used in the latest inventory (a similar problem to the foreign-exchange one – see Transport line of business).
For information, the mortality table used by the market is TD88/90. In the event of any recent change, a similar restatement must be made. Another approach is to keep the discount rate uniform in assessing C/C claims over the observation period and at the same time estimate the impacts from rate differentials (the difference between the rate used in claims management and the one used at closure).
(2) Neutralisation of the result:
3.3.
Transport
Market / Product TRANSPORT
Risk segments Bodily Injury, Cargo and Third Party Collision Specific features International markets – Foreign-exchange problem Insurance
System Coinsurance system Distribution network Underwriting agents and Brokers
Characteristics Description Cover
Description Maritime, Land and Aviation: Bodily Injury, Cargo and Third Party Collision Space: launches (rockets and satellites), smooth running of orbiting satellite and
possibly life in satellite’s orbit.
International markets – Foreign-exchange problem (multi-currency deals). Coinsurance.
Special features Pools are not ruled out of the study’s scope.
Time base Underwriting year.
________________________________________________________________________________________________________________________ Market Maritime Transport, Land Transport Aviation and Space Transport.
Maritime: Rivers, Fishing, Yachts. Private Aviation, Commercial Aviation. Data Time unit Annual - Required.
Duration of liquidation Average development (Bodily Injury and Cargo), development (Third Party risks). History 5 years (Bodily Injury and Cargo risks), 10-15 years (Third Party risks).
Nature Gross payments / Recoveries-Rescues received with Attritional/Large distinction (threshold to be defined €500,000, €1m etc.) - Required.
Gross Case-by-case charges / C/C charges net of recoveries with Attritional/Large distinction (threshold to be defined €500,000, €1m etc.– Required.
Inflation – Reference system Methods of C/C assessment
Real management cost Manual management based on adjusters’ reports and the writer’s experience. Average or flat fee mgt cost Not recommended.
Methods Segmentation Analysis by type of transport (see market), by nature (Bodily Injury, Cargo and Third Party Collisions and by distribution channel (exchange-rate problem).
Restatements Restatement of major claims and impact of changes in exchange rates (1). Problems Risk segments with multi-currency transactions generate follow-up in the original
currency in time.
A highly competitive market with numerous insurance cycles, making for high volatility from one year to the next.
Numerous late reported claims, partly due to the distribution mode and mode of assigning the year.
Processing inflation Segments which are highly sensitive to inflation.
Best Estimate Methods Development methods, restated for exceptional claims, applied to payments, recoveries and C/C claims charges.
Exposure methods, restated for exceptional claims, applied to payments, recoveries -rescues and C/C claims charges.
An approach based on ultimate loss ratios according to the claims already occurred and to pricing policy.
Number of methods A minimum 3 methods to analyse recoveries/rescues separately by nature of risk. Indicators to follow Analysis of premium ratios (first and last years) per year, factoring in changes in
underwriting policy - Required.
Analysis of recovery rates- Required depending on nature of risks.
Analysis of disparities in estimated results via different approaches - Required.
Possibility of using approximate method
Use of Proxy Delicate given the special features of this market.
Possible methods Premiums approach on the basis of available market information and the pricing used, taking account of serious claims.
Neutralisation of result, taking serious claims into account for the two or three latest years (counting from underwriting year) (2).
Comments The methods below must be compared with C/C charges to measure the weight and consistency of reserves for late claims.
The recommended method should take into account the portfolio’s size and the reinsurance programme.
(1) Problems arising from changes in exchange rates over time:
In the absence of restatement in terms of incurred loss triangles for segments which mainly use foreign currencies, analyses carried out using these developments are implicitly distorted by variations in exchange rates over time.
As a result, it is advisable to:
o Convert the resulting data histories at the latest inventory’s exchange rate.
This approach allows us to frame the data used with the accounting data and eliminate exchange rate effects at the level of liquidation coefficients. (2) Neutralisation of the result:
3.4.
Fire / Property
Market / Product FIRE/PROPERTY
Risk segments Individual property, professional property, farmowners’ insurance Specific features
Insurance Mandatory
System
Distribution network Agents, Salaried and Broker networks
Characteristics Description Cover
Description Third Party Liability, Fire, Weather, Water damage, Theft, Property, Glass breaking
Special features
Time base Occurrence mode only.
________________________________________________________________________________________________________________________ Market Private individuals and professionals.
Data Time unit Annual - Required.
Duration of liquidation Long development (short without serious claims). History 10 years (5 years without serious claims).
Nature Number of claims / Frequency of reports / Average Costs – Desirable. Gross payments / Recoveries Received - Required.
Gross Case-by-case charges / C/C charges net of recoveries - Required. Inflation – Reference system Construction cost or inflation index.
Methods of C/C assessment
Real management cost Possible if volume is low (manual management on the basis of adjustors’ report). Average or flat fee mgt cost Recommended if significant volume (automatic management per made-claim
for claims below a given threshold).
Methods Segmentation Analysis by cover or by risk family (Comprehensive, Fire, Weather and other).
Restatements Restatement of the impact of major claims (Comprehensive, Fire) and Natural Catastrophes.
Problems Stepped-up payment development mainly due to improved management process. Processing inflation A transversal problem.
Best Estimate Methods Development methods, restated for exceptional claims, applied to payments, recoveries and numbers of C/C claims charges.
Number of methods A minimum of 2 methods to analyse recoveries separately. Indicators to follow Analysis of premium ratios (first and last years) per year, - Required.
Analysis of changes in claims-report frequency and average costs- Required. Analysis of recovery rates estimated over the observation period - Required. Analysis of disparities in estimated results via different approaches - Required.
Possibility of using approximate method
Use of Proxy Yes.
Possible methods Claims-frequency / Average cost approach on the basis of available market information.
Development methods, restated for exceptional claims, applied to payments, recoveries, C/C
claims numbers and charges, on the basis of market developments.
Comments The methods below must be compared with C/C charges to measure the weight and consistency of reserves for late claims.
3.5.
Third Party Liability
Market / Product THIRD PARTY LIABILITY
Risk segments Comprehensive Product, Comprehensive Operations, Comprehensive Professional, Comprehensive Environment, Comprehensive Individual (property and casualty), Comprehensive Personal
Specific features Business sectors (industry, medical, directors, etc.) Insurance
System
Distribution network Agents, Salaried and Broker networks
Characteristics Description Cover
Description Comprehensive Product, Comprehensive Operations, Comprehensive Professional, Comprehensive Environment, Comprehensive Individual (property and casualty), for private individuals and professionals / companies.
Special features (*) Business sectors (industry, medical, directors, etc.).
Time base Yearly period: by occurrence, claim, event giving rise to claim. Special issue: case of extended reporting period.
________________________________________________________________________________________________________________________ Market Private individuals.
Businesses.
Data Time unit Annual - Required. Duration of liquidation Very long development.
History 10 to more than 30 years.
Nature Number of claims / Frequency of reports / Average Costs – Required. Gross payments / Recoveries Received – Required.
Gross Case-by-case charges / C/C charges net of recoveries – Required. Inflation – Reference system Cost of damages index or inflation.
Methods of C/C assessment
Real management cost Mainly manual management based on adjustors’ report. Methods Restatement Restatement of impacts of major claims / exceptional events.
Problems Slicing of all major claims – Required. .
Processing inflation Assessment of the impact of sector inflation – Required (past and future). Possibly no restatement of past inflation if a spiralling inflation rate is used.
Best Estimate Methods Development methods, restated for exceptional claims, applied to payments, recoveries, C/C claims numbers and charges. Exposure methods.
Number of methods A minimum of 2 methods to analyse recoveries separately. Indicators to follow Non indemnified claims should preferably be isolated.
Analysis of changes in report frequencies and average costs - Required. Analysis of development of closures. - Required.
Analysis of disparities in estimated results via different approaches - Required.
Possibility of using approximate method
Use of Proxy Yes, barring development in specific niches. Possible methods Tail factor, if history is lacking.
Exposure methods (for long triangles) based on a study of the development of market payments.
Laundering of the result taking account of serious claims in year Y and taking the C/C charge into account for year Y-1 (1).
Comments The methods below must be compared with C/C charges to measure the weight and consistency of reserves for late claims.
The recommended method should take into account the portfolio’s size and the reinsurance programme.
(*) Some risks require specific studies. These are mainly emerging market risks, asbestos risk, pollution, etc. These risks affect a significant portion of the market and sometimes all the players find themselves sharing the same positions. Moreover, regulatory or precedent issues may play a part and considerably influence assessment of the risk.
3.6.
Assistance
Market / Product ASSISTANCE Risk segments See Covers and Markets Specific features
Insurance System Insurer
Distribution network Large accounts (banks, etc.)
Characteristics Description Cover Description a. Automobile b. Travel c. Health d. Home assistance. Special features
Time base Occurrence.
________________________________________________________________________________________________________________________
Market 1. Large accounts
2.Private individuals.
Data Time unit Annual – Required (not applicable for a.) Half yearly
Quarterly: recommended
Monthly: desirable.
Duration of liquidation a. 1 year or less b. 2 years or less c. 2 years or less d. 1 year or less.
History 1 - 2 years. Duration 0.5 of a year.
Nature Number of claims, payments, C/C assessments, recoveries – Required.
Inflation – Reference system Not applicable except for c. (economic inflation). Methods of C/C assessment
Real management cost b., c., d. Average or flat fee mgt cost a. (use of price grids).
Methods Segmentation By cover (required) and by large account (desirable). Restatement b. and c. Large claims (e.g. tsunami) and serial claims. Problems
.
Processing inflation c. Desirable (if possible distinguishing by geographic area). Best Estimate Methods Case-by-case required.
Average cost: required (for c., average cost per claim or family of claims).
c. Developments: - by number: desirable - by payment: recommended - by charge: desirable - by recovery: desirable - by closing: desirable.
(but for cover whose liquidation is less than 1 year, development methods are not applicable unless we take a quarterly or monthly view).
Number of methods A minimum of 2 methods (C/C and average cost). Indicators to follow.
Possibility of using approximate method
Use of Proxy No.
Possible methods Not applicable.
Comments It is not necessary to use an approximate method. Since claims are liquidated very quickly, risks and claims charges are usually known by the end of the year.
3.7.
Legal Protection
Market / Product LEGAL PROTECTION Risk segments See Covers and Markets Specific features Subsequent cover Insurance
System
Distribution network - the insurer
- brokers
}
Direct business - partnerships (e.g. banks)- acceptances
Characteristics Description Cover
Description - Out of court. - Legal.
Special features
Time base Occurrence.
________________________________________________________________________________________________________________________ Market a. Private individuals
b.Professionals. Data Time unit Annual – Required.
Duration of liquidation a. 5 years minimum
b.10 years minimum
History 5-10 years minimum
Nature Number of claims, payments, C/C assessments, recoveries – Required.
Claims management costs A reserve for claims management costs is calculated separately from the reserve for claims payable (assessment C/C + IBNER + IBNYR). The calculation is based on general costs attributable to unclosed claims management (suspended + late claims). It requires setting up a cost accounting system.
Inflation – Reference system Difficult. Future inflation from legal developments is possible (reform of French legal protection insurance (1), class actions in France,etc.).
Methods of C/C assessment
Real management cost a. and b.
Average or flat fee mgt cost a. and b. (legal advisory services).
Methods Segmentation By market (required) and by cover (desirable). Restatement Follow-up of large claims, but no specific restatement. Problems
Processing inflation Recommended. Best Estimate Methods Case-by-case – Required.
by average cost: desirable (IBNER + IBNYR) by development of number of claims: recommended by development of payment: desirable by development of charges: desirable.
Number of methods A minimum of 1 (C/C). Indicators to follow
Possibility of using approximate method
Use of Proxy No (a specialised business requiring considerable legal expertise, difficult for an insurer to acquire if it wishes to enter legal protection).
Possible methods
Comments
Remarks:
(1) Reform of legal protection (French law dated 19 February 2007). 3 key provisions: - insurers may not negotiate fees with lawyers;
- requirement to hire a lawyer in out-of-court settlements if the opposing party is assisted by a lawyer; - Insured party free to choose lawyer.
3.8.
Construction
Market / Product CONSTRUCTION
Risk segments Owner’s liability, 10-year general risk Specific features 10-year general cover
Insurance Mandatory and Facultative System CRAC payment agreement Distribution network Agents, Salaried and Broker networks
Characteristics Description Cover
Description Owner’s liability, 10-year general risk, mandatory and facultative coverage. Processing of other non 10-year types of Construction coverage is stated in their respective categories.
Special features Reserves are set up for claims made (occurring on the calculation date, reported or late): outstanding reserves, or not yet made (claims which may occur from the calculation date to the end of the 10-year period): PSNEM (specific construction provision).
Time base Official opening of construction site (DROC) and occurrence (claim report).
________________________________________________________________________________________________________________________ Market For mandatory 10-year general risk: craftsmen (lump-sum premium policies),
companies, designers. For owner’s liability, specific policies (Combined builders’ policy), a distinction by CMI, breakdown by size of worksite. The appropriate segmentation must be defined by company. An overly fine segmentation could in some cases lead to non significant or highly volatile results.
Data Time unit Annual - Required. Duration of liquidation Long development.
History 15 years (by occurrence) to 30 years (by DROC).
Nature Payments gross and net of recoveries, charges gross and net of recoveries, recoveries, numbers, premiums, changes in prices.
Claims management costs Care must be taken to factor in management costs in calculating PSNEM.
Inflation – Reference system A composite index, made up for instance of the Cost of Construction (CCI) and BT01
(all trades)..
Methods of C/C assessment
Real management cost Manual management based on various elements in the file – Frequent revisions (at least once every six months) are required.
Average or flat fee mgt cost Recommended at opening if no information is available. To change once new elements are received.
Methods Segmentation By cover (owners liability, 10-year general risk) and analysed separately from mandatory and facultative covers.
Separate analysis of serious claims if appropriate. Restatement
Problems Systematic separate analysis of outstanding reserves and PSNEM.
Owner’s liability: prior analysis of recovery rate required (substantial recoveries in this cover: take account of changes in CRAC agreement, patients’ contributions to social security, etc.).
PSNEM: need a substantial history to calculate “BE” scale in PSNEM. Processing inflation Required.
Best Estimate Methods Development methods (for liquidation, making of claims) and exposure methods (particularly for recent DROCs and processing of serious claims).
- 10-year general risk: calculations can be net of recoveries;
- Owner’s liability: calculation of gross recoveries, factoring in a study of the recoveries rate;
- PSNEM: the regulation approach is not BE scale. Recalculating the regulation scale using the specific data does not always provide stable results from one year to the
next.
In a BE approach, work by DROC regardless of occurrence, or using a breakdown of the data by occurrence for each DROC.
Number of methods Compare several methods.
Indicators to follow Changes in rates: IBNR compared with C/C reserves by year of occurrence (for outstanding reserves).
Analysis of 10-year general risk recovery rate.
Analysis of disparities in estimated results using various approaches (including for PSNEM using a regulatory approach as well as a “recalculated regulation” approach).
Possibility of using approximate method
Use of Proxy Distinction between a outstanding reserves proxy and a PSNEM proxy. Possible methods For the outstanding reserves proxy: methods similar to those used for other
comprehensive cover.
For the PSNEM proxy,: methods similar to the regulation approach with a market- premiums scale and a market-claims scale (calculated using a market made-claims schedule).
Comments WARNING: for the PSNEM proxy, the current regulation scale factors in only a partial discount between the DROC year and the year the claim is made, but not between the year the claim is made and the payment year.
We recommend a discounted PSNEM proxy:
- in addition, use a market payments schedule to take account of a total discount; - if possible, use distinct developments for 10-year general risk and owner’s liability.
3.9.
Natural Events
Market / Product NATURAL EVENTS
Risk segments (Exceptional) Weather events, Natural Catastrophes Specific features
Insurance Mandatory
System
Distribution network Agents, Salaried and Broker networks
Characteristics Description Cover
Description (Exceptional) Weather events, Natural Catastrophes.
Special features
Time base Date of occurrence.
________________________________________________________________________________________________________________________ Market Private individuals and professionals.
Data Time unit Annual - Required. Duration of liquidation.
History 10 years minimum.
Nature Number of claims / Average Costs – Required, taking account of the insurer’s risk exposure.
Inflation – Reference system Cost of construction index or inflation. Methods of C/C assessment
Real management cost Manual management based on adjusters’ reports.
Average or flat fee mgt cost Recommended if volume is significant (automatic management per made-claim up to a stated threshold).
Methods Segmentation Analysis by type of event (frost, drought, flooding, etc.). Restatement
Problems Given the rareness of these events, it may be difficult to work using developments. Sorting of events by occurrence date is recommended. This makes it possible to work from average costs and number of reported claims per event.
.
Processing inflation A transversal problem .
Best Estimate Methods Frequency / Average cost method. Number of methods
Indicators to follow Exposure to risk (using maps).
Possibility of using approximate method
Use of Proxy Yes.
Possible methods Number of risks / Average cost approach.
An approach based on a market scenario and application of the company’s exposure. Comments The methods below must be compared with C/C charges to measure the weight and
3.10.
Credit / Surety
Market / Product Credit / Suretyship
Risk segments Credit suretyship, Credit insurance, Market suretyship, Financial Guarantees Specific features See below
Insurance Compulsory for regulatory suretyships (1990 law for Private Properties Builders, Hoguet Law for real estate administrators, Excise taxes…)
System Joint suretyship vs. simple suretyship (*) Distribution network Insurers, partners (e.g credit institutions)
Characteristics Description Cover
Description Credit suretyship: Protection offered to lenders against clients' insolvency (retail, corporate clients)
Credit insurance: Protection against financial losses resulting from insolvency of one or more debtors on the domestic or export market
Market and tax suretyship: Technical or financial Cover: holdback bond, performance bond (coverage of the satisfactory completion of the contrat according to its terms and conditions), bid bond, return of advance payment bond, sub-contractors' bond, customs and excises…
Financial Guarantees: Financial guarantees to house builders, real estate developers, real-estate agents, real estate administrators…
Special features Niche insurance
Surety bonds can be issued by insurance companies or banks Surety bonds are ruled both by civil and insurance codes
Cover durations can be quite heterogeneous across the various segments (from several weeks for excises to several years for credit suretyship)
Exchange rate risk for international credit insurance (export ...)
Time base Analysis by occurrence periods for the BE of outstanding claims reserves Analysis by underwriting periods for the BE of technical reserves
Market Credit suretyship: retail market, enterprises (sme), trade associations, social economy, social housing Credit insurance: small, medium & large enterprises
Market and tax suretyship : enterprises
Financial Guarantees: enterprises (Industialists, manufacturers, real estate developers…)
Data Time unit Yearly : essential (for claims development on an occurrence and underwriting basis) Monthly: recommended on short-tailed business (ex: joint suretyship) when reserves are on an occurrence basis
Duration of liquidation. From a few months to several years according to the type of Cover
History Claims development by occurrence periods : 15 years for the longest segments (eg simple credit suretyship)
Claims development by underwriting periods : 15 years for credit suretyship. Nature Payments and incurred (gross and net of paid and reserved recoveries), evolution of
initial exposure, premiums, duration of the cover: essential Number of claims, notification delays: recommended Premium rates changes : preferable.
Claims management costs Claims handling expenses reserves are calculated distinctly from the outstanding claims reserves (and must take into account the allocated expenses when those are not included in the C/C reserves)
The overhead costs that are imputable with claims management are derived from a cost accounting system
Inflation – Reference system Real-estate price index, market interest rates evolution.
Methods of C/C assessment
Real management cost On the basis of experts' reports and any piece of information provided by the lenders,…
Regular update is required taking into account other sureties' involvement, … Average or flat fee mgt cost Recommended at claims opening for some markets ( simple suretyship, financial
Methods Segmentation By types of cover, suretyship (simple or joint) and customer (private individuals, companies): essential
By business sectors for financial guarantees : recommended
The level of segmentation must take into account both market specificities and volumes of the various segments in order to increase the robustness of the estimation
Restatement Restatement of major claims, exchange rates
Problems Small numbers of claims (intensity risk rather than frequency risk) on some segments. Difficulty in evaluating claims occurrence date (particularly for simple suretyship)
A sufficient claims history should be constituted.
Changes in C/C reserves estimation methods (especially changes in the flat opening amounts)
Adequacy of unearned premium reserves to future claims (UPR can be a significant item for pluriannual covers)
UPR calculation : the prorata temporis method may not be the best (e.g decreasing risk over time for credit suretyship)
Processing inflation Low sensitiveness to inflation, the estimated maximum loss is generally known at the declaration of the claim (even at the underwriting date for some segments)
Best Estimate Methods
BE of the reserves for claims Development method, restated of major claims, applied to incurred (gross of
(by year of occurrence) recoveries) and to the recoveries (payments + reserves)
Exposure methods : payment probability and loss percentage applied to exposures at default
Duration models for long tailed business (claims handling expenses reserves, probability of default over time in credit suretyship)
BE of technical provisions Projection of claims (net of recoveries) and expenses by underwriting years (PD LGD methods for credit suretyship)
Number of methods At least 2 for the best estimate of the outstanding claims reserve (including 1 C/C) 1 when projecting the technical reserves as a whole
Indicators to follow Exposure at default (EAD), probability of default (PD), loss given default (LGD) (credit suretyship)
Analysis of loss ratios, claims frequencies and average costs
Possibility of using approximate method
Use of Proxy Yes
Possible methods Risk estimation based on the coefficients used in the RWA calculation under Basel II standard approach (for credit suretyship).
(*) For joint surety bonds, the cover is activated at beneficiary's first request. For simple surety bonds, the indemnification only occurs once all other sureties / recoveries have been activated.
3.11.
Reinsurance / Acceptance
Market / Product REINSURANCE - Acceptance
Risk segments Facultative / proportional / non proportional treaties
Specific features International markets – exchange rate problems – late receipt of cedent company’s data Insurance
System
Distribution network Direct / Broker / retrocessions
Characteristics Description Cover
Description Proportional / non proportional / facultative treaties.
All underlying businesses (e.g. Fire, Motor, Aviation, Allied Perils, etc.). Special features International markets – exchange rate problems – late receipt of ceding company’s
data.
Time base Occurrence, underwriting or statement of claim, depending on cover. Development: cedent booking year or reinsurer’s accounting year. Full / incomplete account projections.
________________________________________________________________________________________________________________________
Market All businesses.
Data Time unit Annual - Required.
Duration of liquidation Variable, depending mainly on underlying businesses (generally medium to long or even very long, up to 40 years maximum – e.g. asbestos, pollution, silicone). History Depends on the underlying business.
Nature Premiums (estimated by the underwriter and accountants), payments, charges. Possible exceptional events and underlying comprehensive claims.
Inflation – Reference system Depends on the market and business involved. Methods of C/C assessment
Real management cost Ceding company’s data except for exceptional events (asbestos, pollution, etc.). Average or flat fee mgt cost
Methods Segmentation By type, cover, market, underlying business.
Restatement Projection of the two latest diagonals (proportional treaties), translation of entries into a single currency, possible restatement of incomplete accounts.
Prospective adjustments related to stabilisation introduction clauses, changes in the market, etc.
Problems Multi-currency transactions – a single rate for all the years or application of a rate per year of origin.
Late receipt of data / a chronic lack of detailed information (e.g. breakdown of claims per type of loss often not available in XL).
Complete / incomplete accounts.
Accounting processes (occurrence, clean cut, etc.). Processing inflation Depends on the market and the business involved.
Best Estimate Methods Projection of the latest diagonal is necessary. Development methods for payments and charges. Exposure methods for premiums. Possibly, average costs of exceptional events.
Number of methods 2 recommended: an exposure and a development method. Indicators to follow Analysis of premiums / burning costs.
Measure of the impact of exchange rates.
Possibility of using approximate method
Use of Proxy Delicate, given the specific features of each treaty / each market.
Possible methods The laundering method, i.e. establish a 100% underwriting ratio. Comments Used when statement of claims takes too long.
APPENDIX I: Supplementary material
1. Statement of the problem ... 31 2. Determining definitive charges ... 32 2.1. The basic techniques ... 33 2.2. A more academic technique ... 33 2.3. Integrating trend elements ... 34 2.4. Integrating dispersion elements... 35 2.5. Integrating volatility elements... 37 2.6. Integrating break elements ... 38 2.6.1. Changes in organisation or management mode... 38 2.6.2. Effects of inflation... 39 2.7. Integrating additional elements ... 40 2.7.1. Incomplete information ... 40 2.7.2. Serious claims ... 41 2.7.3. Construction claims... 42 2.8. Summary ... 44 2.9. Projections of the various items ... 45 2.9.1. Claim projections ... 45 2.9.2. Premium projections ... 48 2.9.3. Cost projections... 49
1.
Statement of the problem
1. Certain data regarding property and casualty insurance are known only on a provisional basis.
2. This is generally the case for claims, which may be declared more or less rapidly and subsequently take more or less time to be settled definitively. These time periods vary sharply depending on the nature of the claim. They are generally shorter for small property claims and may stretch out over several decades for serious personal injuries. Although these claims are constantly being assessed, their assessment may undergo substantial changes until they are definitively settled.
3. However, the same phenomena can also be observed in premiums. Although premiums are generally written at the start of the policy, cases may be observed in which premiums undergo adjustments or are split, which no longer comply with the basic principle.
4. Whether for claims or premiums, we find that an observation made at any given time does not correspond to the definitive situation. Instead, we find that in such situations we possess only a fraction of the definitive data at any given time.
5. If these phenomena show regular, systematic behaviour, we are led to anticipate these developments to factor them into the calculation from the outset.
6. Highlighting this type of behaviour is usually made easier by observing data development over time. We therefore observe changes in charges for various years at their respective anniversary dates. Depending on the nature of the data, a year may either be that of the claim event or of the underwriting, with anniversary dates usually corresponding to financial year-end; but shorter frequencies may also be used.
7. This provides us with the following type of data:
8. Anniversary date 1 2 3 4 5 6 7 8 9 10 Clain eve tn n-10 n-9 245,315 210,219 344,593 281,589 344,142 281,136 345,771 346,506 348,261 348,965 351,257 286,462 352,216 283,764 352,194 n-8 169,734 234,325 235,619 233,461 284,525 284,104 285,103 286,371 237,458 237,714 236,439 233,120 n-7 159,262 208,067 210,093 212,902 213,678 212,195 212,132 n-6 n-5 159,180 138,039 194,269 183,745 190,079 185,689 191,166 191,053 191,505 n-4 165,660 222,570 222,973 184,663 184,062 222,004 n-3 171,371 225,600 229,742 n-2 178,981 265,658 n-1 176,723
Changes in cumulative charges 0 50 000 100 000 150 000 200 000 250 000 300 000 350 000 400 000 1 2 3 4 5 6 7 8 9 10 age Am o u n t
Changes in cumulative charges
0 50 000 100 000 150 000 200 000 250 000 300 000 350 000 400 000 1 2 3 4 5 6 7 8 9 10 age Am o u n t n-10 n-9 n-8 n-7 n-6 n-5 n-4 n-3 n-2 n-1
The chart opposite shows changes in cumulative charges for various years, underscoring the regular and systematic aspect of this phenomenon.
We observe here a steep rise between age “1” and age “2”. Thereafter, the charges show only weak changes.
9. A presentation by flows recorded each year highlights this observation.
Changes in annual flows
-50 000 0 50 000 100 000 150 000 200 000 250 000 300 000 1 2 3 4 5 6 7 8 9 10 age Am o u n t n-10 Changes in annual flows
-50 000 0 50 000 100 000 150 000 200 000 250 000 300 000 1 2 3 4 5 6 7 8 9 10 age Am o u n t n-10 n-9 n-8 n-7 n-6 n-5 n-4 n-3 n-2 n-1 Charges recognised In first year Charges recognised In second year
The chart opposite shows the charges recognised each year.
We observe here that the charge is relatively high in the first year but remains relatively material in the second year.
Thereafter, charges show only marginal changes.
10.These presentations provide the definitive charges for all years but the last. To obtain the latter, it is necessary to estimate the charge that will be recorded during the second year to get a better idea of that year’s definitive charge.
2.
Determining definitive charges
11.To solve this problem, several techniques are available, all of which analyse the base triangle. They show the cumulative charges for each year at each age. The years are more or less developed depending on the anniversary date.
Anniversary date Claim event 1 2 a n-1 n 1 2 3 e Ce,a n-1 n
12.Most of these methods involve identifying development factors that measure the rate of growth between two successive ages. Thus the first development factor measures the difference in charges between age 1 and age 2.
F
inancial year
f0 f1 f2 f3 fy-1
2.1.
The basic techniques
13.The basic techniques determine the factors by examining the transformation over all the years.
14.The best known and most frequently used method is the Chain Ladder Standard. It establishes the factors by relating the total charges for all the years observed at these two ages.
15.The least squares method determines these factors by assuming:
Ce,a+1= fa . Ce,a + ue,a
16.In which “u” is an error variable.
2.2.
A more academic technique
17.The method proposed by Florent De Vylder seeks to set up a theoretical table of changes on the basis of:
‐ the percentage of charges recognised each year (
