Reinsurance Loss Reserving Patrik, G. S. pp

Transcription

1 Section Description Reinsurance Loss Reserving 1 Reinsurance Loss Reserving Problems 2 Components of a Reinsurer s Loss Reserve 3 Steps in Reinsurance Loss Reserving Methodology 4 Methods for Short, Medium and Long Tailed Lines of Business 5 Credibility IBNR Estimates 6 Monitoring and Testing Predictions 1 Reinsurance Loss Reserving Problems 7 Problems making Reinsurance Loss Reserving more difficult than Primary Company Loss Reserving: 1. Longer report lags to reinsurers, especially for casualty excess losses. Problems contributing to the report lag (time from date of accident until first report to the reinsurer) include: a. the cedant s perception of the claims as being reportable to the reinsurer. b. the cedant s undervaluation of serious claims, resulting in a value below the reinsurance reporting threshold (usually one half of an excess contract attachment point). c. extreme delay s in discovery/reporting of mass tort claims (e.g. asbestosis). 2. Persistent upward development of most claims reserves. This may be caused by: a. economic and social inflation. b. a tendency of claims adjusters to reserve at the modal value. c. a tendency to under reserve ALAE. 3. Differing claim reporting patterns by reinsurance line, type of contract, contract terms, cedant, and intermediary (if the latter is involved). This is a result of extremely heterogeneous exposures assumed by reinsurers and the low frequency with which claims are reported. 4. Industry statistics are not useful, due to the heterogeneity problem referenced in Problem 3. Most reinsurer s loss reserves are recorded in line 30B, excess casualty, which renders ISO loss development statistics by line non applicable without significant adjustments. ISO loss development statistics are not directly applicable because they do not apply to excess of loss coverages. The severity of loss development tends to increase with the reinsurance attachment point 5. Lack of information provided in reports to reinsurers. For proportional covers, reinsurers often receive data reported by calendar or underwriting year, which is not useful for evaluating loss liabilities by accident year. For excess covers, reinsurers often receive insufficient individual claims data. In addition, premiums and losses are often reported quarterly in arrears, which adds to the IBNR exposure for both premiums and losses. 6. Reinsurers face data coding and IT systems problems, due to heterogeneity in coverage and reporting requirements. 7. Size of an adequate loss reserve is greater for a reinsurer, due to the issues listed in problems 1 6 Exam 7, V1b Page by All 10, Inc.

2 2 Components of a Reinsurer s Loss Reserve 6 Components of a Reinsurer's Loss Reserve: 1. Case reserves (reported by the ceding company). Most pro rata contracts call for the reporting of case reserves in bulk while most excess contracts require the reporting of individual case reserve that exceed a reporting threshold amount. 2. Reinsurer additional reserves on individual claims (a.k.a. ACRs ). These vary by contract and are set by the reinsuer s claims department if deemed necessary. 3. Actuarial estimate of future development on (1) and (2) (a.k.a. Incurred but not enough reserved, IBNER). 4. Actuarial estimate of pure IBNR. Although most actuaries would prefer separate estimates for IBNER and pure IBNR, most reinsurer s combine these estimates and refer to them as IBNR. 5. Discount for future investment income. Insurance companies are allowed to take statutory credit for future investment income on assets supporting WC permanent total cases, auto PIP annuity claims and medical professional liability claims. 6. Risk load. This provision may be built in implicitly by employing conservative assumptions and loss reserving methods or may be determined explicitly. This component is extremely important for a reinsurer due to the long-tailed nature of the business assumed. 3 Steps in Reinsurance Loss Reserving Methodology 4 Steps in a Reinsurance Loss Reserving Methodology: 1. Partition the reinsurance portfolio into reasonably homogeneous exposure groups. 2. Analyze historical development patterns. Consider individual case reserve development and emergence of IBNR claims separately. 3. Estimate future development. Estimate bulk reserves for IBNER and pure IBNR separately. 4. Monitor and test the predictions, at least by calendar quarter. Note: The loss reserving categories should correspond closely to the pricing categories. Partitioning the Reinsurance Portfolio into Reasonably Homogeneous Exposure Groups o All of the following affect claim reporting lags to the reinsurer and development of case incurred. o The list is shown in approximate priority order Important variables: Examples: 1. Line of Business: Property, Casualty, Bonding, Ocean Marine 2. Type of Contract: Treaty, Facultative. Finite Risk 3. Type of Reinsurance Cover: Q.S, Surplus Share, Excess per-risk, Excess per Occ., Agg Excess, 4. Primary Line of Business for casualty 5. Attachment point for casualty 6. Contract Terms: Flat rated, Retro-rated, Sunset clause, Share of ALAE, CM or Occ, etc. 7. Type of Cedant: Small, Large, or E&S company. 8. Intermediary. If applicable. Exam 7, V1b Page by All 10, Inc.

3 4 Methods for Short, Medium and Long Tailed Lines of Business Reinsurance Categories which are Short-Tailed (with respect to claim reporting and development): The following table summarizes the reinsurance categories of business that Patrik considers to be short-tailed. Category Treaty Property Proportional Treaty Property Catastrophe Treaty Property Excess Facultative Property Fidelity Proportional Comments Beware of recent cats. Beware of recent cats. Possibly exclude high layers. Exclude Construction risks Losses are reported and settled quickly so sophisticated loss development estimation is unnecessary. Reserving Methodologies: 1. Set IBNR equal to a % of the latest year EP (consider major storms and other major cats separately). 2. Set reserves using a selected loss ratio for new lines of business or when few or no loss statistics exist. Clearly, the selected loss ratio should bear a reasonable relationship to past years experience and be larger than the reported loss ratio. Reinsurance Categories which are Medium-Tailed (with respect to claim reporting and development): Patrik considers any exposure for which claims are almost completely settled within five years and completely reported within one to two years to be medium-tailed exposures. The following table summarizes the reinsurance categories of business that Patrik considers to be medium-tailed. Category Treaty Property Excess Construction Risks Surety Fidelity Excess Ocean Marine International Property Non-casualty aggregate excess Comments If it is possible to separate these from working layers. If it is possible to separate these from other property exposure. Analyze losses gross of salvage. Consider salvage recoveries separately. Gross losses are reported quickly, but salvage recoveries have a longer tail. Lags are longer than for the underlying exposure. Exam 7, V1b Page by All 10, Inc.

4 II. Reinsurance Categories which are Medium-Tailed (continued): Reserving Methodologies: Chain ladder method applied to case incurred losses, with or without ACRs. Advantage Disadvantage Correlates reserve development with an overall lag pattern and with claims reported for each accident year. The reserve estimate is highly sensitive to the maturity level associated with reported losses to date, which is problematic for reported losses for immature accident years associated with long-tailed lines of business. An alternative to using incurred losses is to use paid losses, since paid loss development at times is more stable than reported loss development. However, the estimation error for immature accident years is likely to be greater than it is for reported loss chain ladder estimation. III. Reinsurance Categories which are Long-Tailed (with respect to claim reporting and development): Patrik considers any exposure for which the report lag is over two year and for which claims are not settled for many years to be long tailed exposures. The following table summarizes the reinsurance categories of business that Patrik considers to be long-tailed. Description Treaty Casualty Excess of Loss Treaty Casualty Proportional Facultative Casualty Casualty aggregate excess Asbestos, pollution and other health hazard and mass tort claims (APH) Comments Includes some of the longest report and development lags Some of these exposures may possibly be medium-tailed Lags are longer May be the longest of the long tails Patrik recommends that these exposures first be separated into finer, more homogeneous categories by making the following adjustments to the data: o o o Separate out claims arising from asbestos, pollution, other health hazard (collectively known as APH) and other mass tort exposures since these would distort development statistics. Further, it may be more prudent to use sophisticated models developed by large actuarial consulting firms for estimating these liabilities unless the reinsurer has a very large, long and stable claims development history. Analyze claims made coverage separately from occurrence coverages. Exclude losses from commuted reinsurance contracts since the development on these losses has been artificially cut-off. Exam 7, V1b Page by All 10, Inc.

5 Suggested Reserving Methodologies 1. Loss Development Method applied to case incurred losses 2. Bornhuetter-Ferguson method applied to case incurred losses 3. Stanard- Bühlmann Method applied to case incurred losses 4. Claim Count/Claim Severity method. This involves modeling lags from loss event to 1 st report and from report to settlement and then modeling payments on claims through settlement. 5. Chain ladder method. The problem: For very long-tailed lags, the resulting IBNR estimate for recent, green years is extremely variable, depending upon the few reported or paid claims to date. 6. BF Method: This method uses a selected loss ratio for each coverage year and an aggregate reporting pattern. Advantage to using the BF method Disadvantage to using the BF method Correlates future development with an exposure measure equal to Premium * Selected LR. 1. The IBNR estimate is heavily dependent upon an arbitrarily selected loss ratio. 2. The IBNR estimate for each AY does not reflect the reported losses for that year (unless the selected loss ratio is chosen with this in mind). Issues to consider when choosing a loss ratio. a. According to Patrik, the loss ratio for a given AY is strongly correlated with its place in the reinsurance profitability cycle. Thus, it is desirable to use this fact when selecting the ratio. b. Since the reinsurance profitability cycle is more extreme than primary insurance cycles, it is very important to select the accident year loss ratios carefully. Exam 7, V1b Page by All 10, Inc.

6 Suggested Reserving Methodologies Reinsurance Loss Reserving 7. Stanard- Bühlmann (Cape Cod) Method Here, the ultimate expected loss ratio for all years is estimated from the overall known loss experience, instead of being arbitrarily selected. The problem: the IBNR by year is highly dependent upon the rate-level adjusted premium by year. Assume yearly earned risk pure premiums (net of reinsurance commissions, brokerage fees and internal expenses) can be adjusted to remove any suspected rate-level differences by year. This implies that each adjusted year has the same expected loss ratio. Using primary insurance terminology, the risk pure premiums have been put on-level. An example of how to compute the SB IBNR estimate (in 000s) using data as of 12/31/00 is shown below: Given: Earned Adjusted Risk Pure Earned Aggregate Reported AY Premium Premium Losses Loss Lag (1) (2) (3) (4) ,000 8,000 7, ,000 7,000 5, ,000 6,000 3, ,000 7,000 2, ,000 10,000 4, Total 40,000 38,000 21,000 Calculate: Burned S-B On-Level Loss IBNR AY Premium Ratio Estimate (5) = (2)*(4) (6) = (3)/(5) , , ,062 Total 24, ,907 (7) =.866 * (2) * [1.0 - (4)] Note: For AY 1998, Patrik s computation is off by 30 (it should be 1559 and not 1589) Exam 7, V1b Page by All 10, Inc.

7 5 Credibility IBNR Estimates Reinsurance Loss Reserving When there is not complete confidence in the year-to-year rate-level premium adjustments, a credibility IBNR estimate can be computed by weighting CL and SB estimates. a. More weight is given to the SB estimate for recent, green years while the CL estimate is given more weight for the older years. b. A simple, monotonic function of the report lag can be used as the credibility weight for the CL estimate. A simple linear function that yields such a credibility estimate as follows. Cred IBNR(k) = Z(k)*CL IBNR(k)+(1 - Z(k))*SB IBNR(k), where Z(k) = CF * Rlag(k), with 0 < CF = credibility factor < 1 Rlag(k) = report lag for year k The computation of a credibility IBNR, with CF = 0.50, is shown below: Calculation of Credibility IBNR Earned Claim Risk Pure Report IBNR Estimates Credibility AY Premium Lag CL SB IBNR (1) (2) (3) (4) (5) , , , ,286 1,559 1, , ,000 3,031 2, , ,333 6,062 6,553 Total 40,000 13,869 11,907 12,043 CF Factor =.50 and is judgmentally selected (5) = CF * (2)*(3) + (1.0 - CF * (2)) * (4) Other credibility procedures: Some reinsurance actuaries compute a weighted IBNR estimate using paid and reported loss development estimates. Relative claim reporting and payment lags are used as weights. Keep in mind that the problem with reported claims data is that case reserves are set based on judgments of many claims people that perhaps vary over time. Some reinsurance actuaries want to use pricing information. Average pricing ELR s can be considered a priori ELR estimates. These a priori estimates can be used as the BF ELR estimate to compute BF IBNR. Further, this a priori IBNR estimate can be weighted with the CL IBNR to obtain a final credibility IBNR estimate. Exam 7, V1b Page by All 10, Inc.

8 6 Monitoring and Testing Predictions To validate the reserving methodology a reinsurer employs, a test of actual vs. expected claims emergence should be conducted. Monitoring and testing claims run-off against predictions may provide early warning of problems. The data shown below considers GL exposure for treaty casualty excess contracts with attachment points in RAA range 4. RAA range 4 currently has attachment points between $1,251,000 to $3,500,000. This range should be deflated via an estimated GL ground-up claims severity trend, so that appropriate contracts from earlier years are included. The table below presents one possible format. Interpreting the above table is difficult. For instance, (7) tells us there was $809,000 more claims emergence in the first half of 2001 than the $2,437,000 = $63,240,000 - $60,803,000 expected. This is about 33% more than expected. The analyst should ask him/herself the following questions: a. Is this purely random? b. Does it indicate that the beginning IBNR reserve was too small? c. Does it indicate that the lags too short? Exam 7, V1b Page by All 10, Inc.