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Chapter 7 Development Technique - PDF
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Hester Quinn
1 Sec Description Pages 1 Introduction 84 2 Key Assumptions 84 3 Common Uses of the Development Technique Mechanics of the Development Technique Unpaid Claim Estimate Based on the Development Technique Reporting and Payment Patterns Observations and Common Relationships 95 8 When the Development Technique Works and When It Does Not XYZ Insurer Influence of a Changing Environment on the Claim Development Technique Introduction 84 In this chapter, estimates of ultimate claims and unpaid claims based on the reported and paid claim development methods (a.k.a. the chain ladder technique) are developed. 2 Key Assumptions 84 The underlying assumption in the development technique is that: o claims recorded to date will continue to develop in a similar manner in the future (i.e. the past is indicative of the future). o the relative change in a given year's claims from one evaluation point to the next is similar to the relative change in prior years' claims at similar evaluation points. Other key assumptions of the development method include: consistent claim processing, a stable mix of types of claims, stable policy limits, and stable reinsurance (or excess insurance) retention limits throughout the experience period. 3 Common Uses of the Development Technique The development technique can be applied to: paid and reported claims as well as number of claims. all lines of insurance including short-tail lines and long-tail lines. To use the development method, data is organized into different time intervals, including: * Accident year; * Policy year; * Underwriting year; * Report year; * Fiscal year (e.g. for a self-insured public entity with a fiscal year ending March 31, the actuary will likely organize the claim development data by April 1 to March 31 fiscal year). This technique can be applied to monthly, quarterly, and semiannual and annual data. Exam 5, V2 Page by All 10, Inc.
2 4 Mechanics of the Development Technique The development method consists of seven steps: Step 1 Compile claims data in a development triangle Step 2 Calculate age-to-age factors Step 3 Calculate averages of the age-to-age factors Step 4 Select claim development factors Step 5 Select tail factor Step 6 Calculate cumulative claim development factors Step 7 Project ultimate claims To demonstrate the seven steps, industry-aggregated accident year claim development data for U.S. private passenger automobile insurance (labeled "U.S. Industry Auto") is used. Step 1 Compile Claims Data in a Development Triangle Exhibit I, Sheets 1 and 2: consists of: cumulative reported and paid claim development triangles, respectively. Part 1 of each exhibit is the data triangle for AYs The 10 diagonals in each triangle have annual valuation dates of 12/31/ /31/2007 data net of reinsurance and includes the defense cost portion of claim adjustment expenses (a.k.a. DCC for U.S. statutory accounting). U.S. Industry Auto Exhibit I Reported Claims($000) Sheet 1 PART 1 - Data Triangle Accident Reported Claims as of (months) Year ,017,487 43,169,009 45,568,919 46,784,558 47,337,318 47,533,264 47,634,419 47,689,655 47,724,678 47,742, ,954,484 46,045,718 48,882,924 50,219,672 50,729,292 50,926,779 51,069,285 51,163,540 51,185, ,155,776 49,371,478 52,358,476 53,780,322 54,303,086 54,582,950 54,742,188 54,837, ,394,069 50,584,112 53,704,296 55,150,118 55,895,583 56,156,727 56,299, ,755,243 52,971,643 56,102,312 57,703,851 58,363,564 58,592, ,163,102 52,497,731 55,468,551 57,015,411 57,565, ,417,309 52,640,322 55,553,673 56,976, ,360,869 53,790,061 56,786, ,582,684 54,641, ,853,563 PART 2 - Age-to-Age Factors Accident Age-to-Age Factors Year To Ult Exam 5, V2 Page by All 10, Inc.
3 Step 2 Calculate Age-to-Age Factors (a.k.a. report-to-report factors or link ratios) To calculate the age-to-age factors for the 12-month-to-24-month period, divide the claims as of 24 months by the claims as of 12 months. Using the reported claims presented in Exhibit I, Sheet 1, calculate the following: factor for accident year 1998: reported claims at 24 months for accident year 1998 $43,169, reported claims at 12 months for accident year 1998 $37,017, factor for accident year 2002 reported claims at 48 months for accident year 2002 $57,703, reported claims at 36 months for accident year 2002 $56,102,312 Continue in the same manner down the columns and across the rows of the triangles. Step 3 Calculate Averages of the Age-to-Age Factors The most common averages include: * Simple (or arithmetic) average * Medial average (average excluding high and low values) * Volume-weighted average * Geometric average (the nth root of the product of n historical age-to-age factors) Shown In Part 3 of Exhibit I, Sheets 1 and 2, are: * Simple averages for the latest five years and the latest three years * Medial average for the latest five years excluding one high and one low value (medial latest 5x1) * Volume-weighted averages for the latest five years and the latest three years * Geometric average for the latest four years PART 3 - Average Age-to-Age Factors Averages To Ult Simple Average Latest Latest Medial Average. Latest 5x Volume-weighted Average Latest Latest Geometric Average Latest Examples (simple average and medial average): For reported claims, the month simple average of the latest five factors is based on the average of the month factors for AYs = = ( ) / 5. To calculate the month medial average development factor of the latest 5x1, consider the month factors for AYs ; we exclude the highest value (1.062 for accident year 2001) and the lowest value (1.055 for accident year 2004) and take an average of the remaining three values. The month medial average of the latest 5x1 = = ( ) / 3). Exam 5, V2 Page by All 10, Inc.
4 Examples (volume weighted and geometric): The formula for this type of average uses the sum of the claims for the specific number of years divided by the sum of the claims for the same years at the previous age. The month volume-weighted average of the latest three years = the sum of the reported claims for AYs at 48 months ($57,703,851 + $57,015,411 + $56,976,657 = $171,695,919) divided by the sum of the reported claims for AYs as of 36 months ($56,102,312 + $55,468,551 + $55,553,673 = $167,124,536), or The geometric average (a.k.a. geometric mean) for the latest four years is equal to the fourth root of the product of the last four age-to-age factors. The geometric average for the latest four years at months = (1.162 x x x 1.173).25 = The geometric average for the latest four years at months = (1.010 x x x 1.010).25 = Actuaries often rely on the most recent experience as this data reflects the effect of the latest changes in the insurer's internal and external environments. There is often a trade-off between stability (the number of experience periods included in the average values) and responsiveness (where only the most recent experience periods are considered). Step 4 Select Claim Development Factors The selected age-to-age factor (a.k.a. claim development factor or loss development factor) represents the growth anticipated in the subsequent development interval. Selections are based on a review of the historical claim development data, the age-to-age factors, the various averages of the age-to-age factors, and a review of the prior year's claim development factor selections. Benchmarks: When the credibility of the insurer's historical experience is limited, there may be a need to supplement the experience with benchmark data. Possible benchmark includes: experience from similar lines with similar claims handling practices within the insurer. claim development patterns from the insurance industry when comparable. When using benchmarks, there may be significant differences between the line of business being analyzed and the benchmark with regard to claims practices, policy coverages, underwriting, geographic mix, claim coding, policyholder deductibles and/or limits, legal precedents, etc. When selecting claim development factors, consider the following characteristics: 1. Smooth progression of individual age-to-age factors and average factors across development periods. A steadily decreasing incremental development from valuation to valuation 2. Stability of age-to-age factors for the same development period. A relatively small range of factors (small variance) within each development interval (i.e. down the columns). 3. Credibility of the experience. Credibility is based on the volume and the homogeneity of the experience for a given AY and age. Benchmark development factors from the insurance industry may be needed when credibility is lacking. 4. Changes in patterns. May suggest changes in the internal operations or external environment. 5. Applicability of the historical experience. Has the insurer s book of business and insurer operations changed over time? Have the effects of changes in external factors manifested themselves in the reported claims experience? Exam 5, V2 Page by All 10, Inc.
5 In Part 4 of Exhibit I, Sheets 1 and 2: Actuarial judgment is used to choose selected factors after reviewing all of the age-to-age factors, the various averages, and the prior year's selected factors. The term "To Ult" (i.e. To Ultimate) is used to designate the tail factor (e.g. 120 months-to-ultimate). Selections of development factors are subjective, differ from one actuary to another, and there is more than one reasonable selection of age-to-age and tail factors. Table 1 - Selected Age-to-Age Factors ultimate Reported Paid Step 5 Select Tail Factor If data is available, analyze development out to the point at which the development ceases (i.e. until the selected development factors are equal to 1.000). When development factors for the most mature development periods are still greater than 1.000, a tail factor is needed to bring the claims from the latest observable development period to an ultimate value. The tail factor is crucial as it: influences the unpaid claim estimate for all accident years (in the experience period) and can create a disproportionate leverage on the total estimated unpaid claims. Approaches to select the tail factor: 1. Use industry benchmark development factors 2. Fit a curve to the selected or observed development factors to extrapolate the tail factors (exponential decay is a common for curve fitting). 3. For paid development, when reported development is at ultimate, use reported-to-paid ratios at the latest observed paid development period. Step 6 Calculate Cumulative Claim Development Factors (CDF) Cumulative claim development factors (a.k.a. age-to-ultimate factors and claim development factors to ultimate): are calculated by successive multiplications beginning with the tail factor and the oldest age-to-age factor. projects the total growth over the remaining valuations. Using the selected age-to-age factors from Step 4 and the tail factor in Step 5, calculate the following: Reported CDF at 120 months = selected tail (120-ultimate) factor = Reported CDF at 108 months = (selected tail factor) x (selected development factor months) = x = Reported CDF at 96 months = (selected tail factor) x (selected development factor months) x (selected development factor months) = (CDF at 108 months) x (selected development factor months) = x = Continue in this manner until computing the Reported CDF at 12 months = (CDF at 24 months) x (selected development factor months) = x = Table 2 summarizes the cumulative claim development factors based on the selected age-to-age factors, from Exhibit I, Sheets 1 and 2. Table 2 Cumulative Claim Development Factors Reported Paid Exam 5, V2 Page by All 10, Inc.
6 Step 7 Project Ultimate Claims Ultimate claims equal the product of the latest valuation of claims (the amounts on the last diagonal of the claim triangles) and the cumulative claim development factors. Calculations are shown in Exhibit I, Sheet 3, an excerpt of which is shown below: Column (3) is the last diagonal of the reported claim development triangle in Exhibit I, Sheet 1, and Column (4) is the last diagonal of the paid claim development triangle in Exhibit I, Sheet 2. Columns (5) and (6) are the cumulative claim development factors that are calculated in Step 5. Each cumulative claim development factor refers to a specific age. Chapter 7 - Development Technique Exhibit I U.S. Industry Auto Sheet 3 Projection of Ultimate Claims Using Reported and Paid Claims($000) Age of Projected Ultimate Claims Accident Year Claims at 12/31/07 CDF to Ultimate Using Dev. Method with Year Reported Paid Reported Paid Reported Paid (1) (2) (3) (4) (5) (6) (7)= [(3) x (5)] (8)= [(4) x (6)] ,742,304 47,644, ,742,304 47,739, ,853,563 27,229, ,118,803 65,079,626 Projected ultimate claims for accident year 1998 = (reported claims for 1998 as of 12/31/07) x (reported CDF at 120 months) = $47,742,304 x = $47,742,304 Projected ultimate claims for accident year 2007 = (reported claims for 2007 as of 12/31/07) x (reported CDF at 12 months) = $48,853,563 x = $63,118,803 Perform similar calculations for the projection of ultimate claims using the paid claim development technique. Projected ultimate claims for accident year 2007 = (paid claims for 2007 as of 12/31/07) x (paid CDF at 12 months) = $27,229,969 x = $65,079,626 Exam 5, V2 Page by All 10, Inc.
7 5 Unpaid Claim Estimate Based on the Development Technique Using the development technique, unpaid claim estimates = projected ultimate claims - actual paid claims. Because AY data is used, the unpaid claim estimate includes both case outstanding and the broad definition of IBNR. To compute estimated IBNR based on the development technique: i. IBNR = projected ultimate claims - reported claims ii. IBNR = estimated total unpaid claims - case O/S Exhibit I, Sheet 4, summarizes the calculations for the unpaid claim estimate based for U.S. Industry Auto. Columns (2) and (3) contain reported and paid claims data as of 12/31/2007 (the latest diagonals in our claim development triangles). Columns (4) and (5) are the projected ultimate claims (developed in Exhibit I, Sheet 3). The equations to compute Columns (6) (10) are shown below in the excerpt from Exhibit I, Sheet 4. Chapter 7 - Development Technique Exhibit I U.S. Industry Auto Sheet 4 Projection of Ultimate Claims Using Reported and Paid Claims($000) Unpaid Claim Estimate at 12/31/07 Projected Ultimate Claims Case IBNR - Based on Total - Based on Accident Claims at 12/31/07 Using Dev. Method with Outstanding Dev. Method with Dev. Method with Year Reported Paid Reported Paid at 12/31/07 Reported Paid Reported Paid (1) (2) (3) (4) (5) (6) =[(2) - (3)] (7)=[(4) - (2)] (8)=[(5) - (2)] (9)=[(6) + (7)] (10)=[(6) + (8)] ,742,304 47,644,187 47,742,304 47,739,475 98, ,829 98,117 95, ,185,767 51,000,534 51,185,767 51,204, , , , ,002 6 Reporting and Payment Patterns A reporting pattern of claims is the % of ultimate claims that are reported in each year. Reporting patterns are derived from cumulative reported claim development factors (CDFs). The following table shows the reporting pattern from the cumulative reported CDFs for U.S. Industry Table 3 Reporting Pattern Cumulative Age Reported Claim Cumulative% Incremental % (Months) Development Reported Reported % 77.4% % 12.7% % 5.0% % 2.7% % 1.1% % 0.5% % 0.3% % 0.2% % 0.1% % 0.0% The % reported = 1/CDF Exam 5, V2 Page by All 10, Inc.
8 At 12 months, the percentage reported = 1.000/1.292 = 77.4% (i.e. 77.4% of ultimate claims are reported through 12 months). The incremental percentage reported for the month period = 90.1% %, or 12.7%. An implied payment pattern based on the cumulative paid claim development factors can also be determined. Table 4 Payment Pattern Age Cumulative Cumulative Incremental % (Months) Paid Claim Paid Paid Development % 41.8% % 29.4% % 13.3% % 7.7% % 4.0% % 1.8% % 0.9% % 0.5% % 0.2% % 0.2% Note: The incremental %s reported and paid in each successive interval are less than or equal to that of the previous age interval. These patterns are consistent with reasonable expectations for the underlying process of settling a portfolio of claims. When underlying development patterns are erratic, actuarial judgment is needed in the selection process to achieve claim development patterns that exhibit such a steady, decreasing pattern. The reporting and payment patterns can be used in other techniques for estimating unpaid claims and in monitoring the development of claims during the year. The payment pattern is also often used for present value (i.e. discounting) calculations. 7 Observations and Common Relationships 95 Cumulative CDFs are often greatest for the most recent AYs and the smallest for the oldest accident years. Actuaries refer to the most recent, less-developed AYs as immature and the oldest, most-developed AYs as mature. Therefore, the highest values of estimated IBNR are for the most recent accident years (the less mature years). As AYs mature and more claims are reported and settled, the estimate of total unpaid claims will go to zero. Exam 5, V2 Page by All 10, Inc.
9 Also, development factors tend to increase as the retention increases. In E. Pinto and D.F. Gogol s paper titled "An Analysis of Excess Loss Development" they observed that: excess business exhibits much slower reporting than primary business, there is a relationship between the layer for which business is written and the resulting development pattern. development is not only caused by late reported claims and increases in the average reported loss per claim but also by changes at successive maturities in the proportion of claims with losses which are large multiples of the average. Thus, the shape of the size of loss distribution changes at successive valuations. Pinto and Gogol developed a model which illustrates the two influences underlying claim development: 1. the reporting pattern of claims over time and 2. the changing characteristics of the size of claims distribution at successive maturities. Pinto and Gogol conclusions: Loss and ALAE development varies significantly by retention. Pricing and reserving estimates using development factors may produce large errors if this is not taken into account. As this applies to paid as well as reported loss development, recognizing the retention is a major factor in estimating discounted losses using paid development factors. 8 When the Development Technique Works and When It Does Not The primary assumption of the development technique is that the reporting and payment of future claims will be similar to the patterns observed in the past. When using reported claims, it is assumed that there have been no significant changes in the adequacy of case outstanding during the experience period; When using paid claims, it is assumed that there have been no significant changes during the experience period in the speed of claims closure and payment. The development method is appropriate for insurers in a stable environment. If there are changes to the insurer's operations (e.g. new claims processing systems; revisions to tabular formulae for case outstanding; or changes in claims philosophy, policyholder deductibles, or the insurer's reinsurance limits), the past may not be predictive of the future. Environmental changes, such as a major tort reform occurring (e.g. a cap on claim settlements or a restriction in the statute of limitations), may cause historical claim development experience to be less predictive of future claims experience. The development technique requires a large volume of historical claims experience. It works best when the presence or absence of large claims does not greatly distort the data. If the volume of data is not sufficient, large claims could greatly distort the age-to-age factors, the projection of ultimate claims, and finally the estimate of unpaid claims using a development method. The development technique may not be suitable when there is not a sufficient volume of credible data, as in the following situations: When entering a new line of business or new territory For smaller insurers with limited portfolios. While the development technique may be used in such situations, relying on benchmark patterns (e.g. from comparable lines of business or available industry data) to select claim development factors, may be warranted. Exam 5, V2 Page by All 10, Inc.
10 The development technique is used for high-frequency, low-severity lines with stable and timely reporting of claims (evenly spread throughout the AY, PY, RY, etc.) For long-tail lines of insurance (e.g. WC or GL), cumulative CDFs can become very large for the most recent AYs when using the paid claim development technique. These highly leveraged factors can result in unreasonable projections of ultimate claims for the most recent accident years. In these situations, alternative techniques for estimating unpaid claims are often used. 9 XYZ Insurer Chapter 6 Recap: After discussions with XYZ insurer claims department management, we know that: both a speed up in the rate of claims settlement and a strengthening in case reserves have been implemented. during the experience period, a major tort reform modifying the liability covered by the insurance product resulted in a change in the insurance product and in the insurer's market presence. Q: Given the above, is the development technique appropriate for XYZ Insurer to use? A primary assumption of the reported claim development method is that there have been no significant changes in the adequacy of case outstanding over the experience period. A primary assumption of the paid claim development method is that there have been no significant changes in the rate of settlement over the experience period. A: The underlying assumptions do not hold true, and we conclude that an adjustment for these changes is necessary for the development technique to be appropriate for XYZ Insurer. However, for demonstration and comparison purposes to other methods presented in later chapters, the development technique is shown in Exhibit II, Sheets 1-4, for XYZ Insurer. Exhibit II, Sheets 1 and 2 contain the reported and paid claim development triangles. There is significant variability in the age-to-age factors down each column of the triangle, which we expect given our knowledge of the changing environment. Selected age-to-age factors are based on the volume-weighted average of the latest two years (although in reality a higher degree of judgment would be needed in selecting the age-to-age factors). Exam 5, V2 Page by All 10, Inc.
11 XYZ Insurer - Auto BI Exhibit II Reported Claims($000) Sheet 1 PART 1 - Data Triangle Accident Reported Claims as of (months) Year ,171 12,380 13,216 14,067 14,688 16,366 16,163 15,835 15, ,255 16,405 19,639 22,473 23,764 25,094 24,795 25,071 25,107 ::: ::: ::: ::: ::: ::: ::: ::: ::: ,477 31, ,632 PART 2 - Age-to-Age Factors Accident Age-to-Age Factors Year To Ult ::: ::: ::: ::: ::: ::: ::: ::: ::: PART 3 - Average Age-to-Age Factors Averages To Ult Simple Average Latest Latest Latest Medial Average. Latest 5x Volume-weighted Average Latest Latest Latest Geometric Average Latest PART 4 - Selected Age-to-Age Factors Development Factor Selection To Ult Selected CDF to Ultima Percent Repo 39.2% 66.1% 83.6% 92.2% 94.0% 98.7% 99.7% 100.8% 100.8% 100.1% 100.0% Exam 5, V2 Page by All 10, Inc.
12 Projected ultimate claims based on the development technique applied to reported and paid claims are shown in Exhibit II, Sheet 3. XYZ Insurer - Auto BI Exhibit II Projection of Ultimate Claims Using Reported and Paid Claims($000) Sheet 3 Age of Projected Ultimate Claims Accident Year Claims at 12/31/08 CDF to Ultimate Using Dev. Method with Year Reported Paid Reported Paid Reported Paid (1) (2) (3) (4) (5) (6) (7) (8) ,822 15, ,822 15, ,107 24, ,082 25,164 ::: ::: ::: ::: ::: ::: ::: ::: ,732 11, ,979 77, ,632 3, ,530 74,995 Total 449, , , ,028 Column Notes: (2) Age of accident year in (1) at December 31, (3) and (4) Based on data from XYX insurer. (5) and (6) Based on CDF from Exhibit 2, Sheets 1 and 2. (7) = [(3) x (5)]. (8) = [(4) x (6)]. Estimated IBNR and the total unpaid claim estimate for the two development projections are shown in Exhibit II, Sheet 4. XYZ Insurer - Auto BI Exhibit II Projection of Ultimate Claims Using Reported and Paid Claims($000) Sheet 4 Unpaid Claim Estimate at 12/31/08 Projected Ultimate Claims Case IBNR - Based on Total - Based on Accident Claims at 12/31/08 Using Dev. Method with Outstanding Dev. Method with Dev. Method with Year Reported Paid Reported Paid at 12/31/08 Reported Paid Reported Paid (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) ,822 15,822 15,822 15, ,107 24,817 25,082 25, ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ,732 11,865 47,979 77,941 19,867 16,247 46,209 36,114 66, ,632 3,409 47,530 74,995 15,223 28,898 56,363 44,121 71,586 Total 449, , , , ,999 65, , , ,401 Column Notes: (2) and (3) Based on data from XYZ Insurer. (3) and (4) Developed in Exhibit 2, Sheet 3 (6) =[(2) - (3)]. (7) =[(4) - (2)]. (8) =[(5) - (2)]. (9) =[(6) + (7)]. (10) =[(6) + (8)]. Comparison of the estimated IBNR for the U.S. Industry Auto and for XYZ Insurer: For U.S. Industry Auto, the estimated IBNR generated by the reported and paid claim development methods differs by approximately 10% and the estimate of total unpaid claims differs by only 4%. For XYZ Insurer, the estimated IBNR using the paid claim development technique differs by 138% from the reported claims indication; the total unpaid claim estimate differs by almost 50%. Thus, alternative projection methods should be reviewed. Exam 5, V2 Page by All 10, Inc.
13 10 Influence of a Changing Environment on the Claim Development Technique Changes in Claim Ratios (i.e. loss ratios) and Case Outstanding Adequacy To examine the effect of a changing environment on the estimates produced by the development technique, the U.S. private passenger automobile is used as an example. Similar reporting and payment patterns as well as a similar ultimate claim ratio are used. Compare estimated IBNR from the development technique to the "actual IBNR" under the following 4 scenarios: * Scenario 1 is a steady-state environment: Claim ratios are stable; there are no changes from historical levels of case outstanding strength (U.S. PP Auto Steady-State) * Scenario 2 environment: Increasing claim ratios; no change in case outstanding strength (U.S. PP Auto Increasing Claim Ratios) * Scenario 3 environment: Sable claim ratios; an increase in case outstanding strength (U.S. PP Auto Increasing Case Outstanding Strength) * Scenario 4 environment: Increasing claim ratios and increasing case outstanding strength (U.S. PP Auto Increasing Claim Ratios and Case Outstanding Strength) This example with its four scenarios are used in Chapters 8, 9, and 10. Key Assumptions Computation of Actual IBNR (not known in real life) For the purpose of demonstrating the affect of a changing environment, we calculate the "actual" or "true" IBNR requirement. In this example: A ten-year experience period is used (AYs ). Assume EP is $1M for the first year (i.e. 1999), and increases 5% annually. Actual IBNR is calculated in Exhibit III, Sheet 1, equals ultimate claims projection (based on the given ultimate claim ratio for each AY) minus the reported claims as of 12/31/2008. Exam 5, V2 Page by All 10, Inc.
14 Impact of Changing Conditions Exhibit III Summary of Earned Premium and Claim Ratio Assumptions and Actual IBNR Sheet 1 Reported Reported Accident Earned Ultimate Ultimate Claims at Actual Ultimate Ultimate Claim at Actual Year Premium Claim Ratio Claims 12/31/08 IBNR Claim Ratio Claim 12/31/08 IBNR (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Steady-State Increasing Claim Ratios ,000, % 700, , % 700, ,000 0 :: :: :: :: :: :: :: :: :: :: ,276, % 893, ,463 8, % 1,021,026 1,010,815 10, ,340, % 938, ,306 18, % 1,139,082 1,116,300 22, ,407, % 984, ,722 49, % 1,266,390 1,203,071 63, ,477, % 1,034, , , % 1,403,582 1,263, , ,551, % 1,085, , , % 1,551,328 1,194, ,805 Total 12,577,892 8,804,524 8,365, ,636 10,249,349 9,647, ,982 Increasing Case Outstanding Strength Increasing Claim Ratios and Case Outstanding Strength ,000, % 700, , % 700, ,000 0 :: :: :: :: :: :: :: :: :: :: ,276, % 893, ,463 8, % 1,021,026 1,010,815 10, ,340, % 938, ,377 4, % 1,139,082 1,133,386 5, ,407, % 984, ,808 22, % 1,266,390 1,237,897 28, ,477, % 1,034, ,922 54, % 1,403,582 1,329,895 73, ,551, % 1,085, , , % 1,551,328 1,330, ,064 Total 12,577,892 8,804,524 8,551, ,335 10,249,349 9,901, ,658 Column Notes: (2) Assume 51,000,000 for first year in experience period (1999) and 5% annual increased thereafter. (3) and (7) Ultimate claim ratios assumed to be known for purpose of example. (4) =[(2) * (3)]. (5) Latest diagonal of reported claim triangles in Exhibit III, Sheet 2 and 6 (6) =[(4) - (5)]. (8) =[(2) + (7)]. (9) Latest diagonal of reported claim triangles in Exhibit III, Sheet 4 and 8 (10) =[(8) - (9)]. In the steady-state environment, assume an ultimate claim ratio of 70% for all ten accident years Table 5 Key Assumptions Steady-State Environment Reporting and Payment Patterns 0/0 % As of Month Reported Paid 12 77% 42% 24 90% 71% 36 95% 84% 48 98% 92% 60 99% 96% 72 99% 98% % 99% % 99% % 100% % 100% Exam 5, V2 Page by All 10, Inc.
15 In the increasing claim ratio scenarios, assume the following claim ratios by accident year: Table 6 - Key Assumptions Increasing Claim Ratio Scenarios Accident Year Ultimate Claim Ratio % % % % % % EP, ultimate claim ratios, and the above reporting and payment patterns are used to create reported and paid claim development triangles for each of the 4 scenarios (shown in Exhibit III, Sheets 2 9). To simplify, select reported and paid age-to-age factors based on a five-year volume-weighted average. By not incorporating judgmental adjustments to the examples showing changes in the environment, we demonstrate how the development technique reacts to a changing situation. Scenario 1 U.S. PP Auto Steady-State As expected, the projected ultimate claims are the same for both the reported and paid claim development methods. Both methods produce estimated IBNR equal to actual IBNR (see the top section of Exhibit III, Sheet 10). Impact of Changing Conditions Exhibit III U.S. PP Auto - Development of Unpaid Claim Estimate Sheet 10 Age of Projected Ultimate Claims Estimate IBNR Difference from Actual Accident Accident Claims at 12/31/08 Case CDF to Ultimate Using Dev. Method with Using Dev. Method with Actual IBNR Year at 12/31/08 Reported Paid Outstanding Reported Paid Reported Paid Reported Paid IBNR Reported Paid (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) Steady-State , , , , :: :: :: :: :: :: :: :: :: :: :: :: :: :: , , , ,034,219 1,034, , , , , , , ,085,930 1,085, , , , Total 8,365,888 7,573, ,341 8,804,527 8,804, , , ,636 Scenario 2 U.S. PP Auto Increasing Claim Ratios (and no case reserve strengthening) See the bottom section of Exhibit III, Sheet 10. Increasing Claim Ratios , , , , :: :: :: :: :: :: :: :: :: :: :: :: :: :: ,263, , , ,403,582 1,403, , , , ,194, , , ,551,328 1,551, , , , Total 9,647,367 8,575,113 1,072,254 10,249,351 10,249, , , ,982 Observations: When comparing the top and bottom sections of Sheet 10, there are differences between reported and paid claims in Columns (3) and (4), as well as differences in the claim development triangles. The claim development triangles in Sheets 4 and 5 (increasing claim ratio scenario) are the same as the triangles in Sheets 2 and 3 (steady-state) for AYs However, beginning in AY 2004, the reported and paid claims for all remaining years are higher for the increasing claim ratio scenario than the steady-state scenario (consistent with our assumption of increasing claim ratios for AYs ). Exam 5, V2 Page by All 10, Inc.
16 Key: Since we assume no change in the adequacy of case outstanding, there are no changes in the age-to-age factors, and thus no changes in the cumulative claim development factors between the increasing claim ratio scenario and the steady-state environment. The higher value of projected ultimate claims is solely due to higher values of claims reported and paid as of 12/31/2008. The estimated IBNR is the same for both the reported and paid claim development methods, and is equal to the actual IBNR. Thus, conclude that the development technique is responsive to changes in the underlying claim ratios assuming no changes in the underlying claims reporting or payment pattern. Scenario 3 U.S. PP Auto Increasing Case Outstanding Strength (and stable claim ratios) Exhibit III, Sheets 6 and 7 contain the claim development triangles for this scenario. Sheet 11 shows the calculations for projected ultimate claims and estimated IBNR in the top section. Assume that case outstanding adequacy increased by 6% in 2007 and 25% in 2008 over the steady-state case outstanding (for the latest 4 AYs only) in the reported triangle. This means that the next to last diagonal is 6% greater in this scenario than the steady-state scenario, and that the last diagonal is 25% greater in this scenario than the steady-state scenario. What is expected to be seen? The true ultimate claims have not changed from the steady-state environment (since ultimate claims equal 70% of EP for each year in the experience period). We expect higher reported claims since case outstanding strength has increased. Given the same value of ultimate claims with higher values of reported claims at December 31, 2008, the IBNR should decrease. However, actual IBNR for this scenario of stable claim ratios and increases in case outstanding strength are $253,336, which is lower than the actual IBNR of the steady-state, which are $438,638. See the top section of Exhibit III, Sheet 11. Impact of Changing Conditions Exhibit III U.S. PP Auto - Development of Unpaid Claim Estimate Sheet 11 Age of Projected Ultimate Claims Estimate IBNR Difference from Actual Accident Accident Claims at 12/31/08 Case CDF to Ultimate Using Dev. Method with Using Dev. Method with Actual IBNR Year at 12/31/08 Reported Paid Outstanding Reported Paid Reported Paid Reported Paid IBNR Reported Paid (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) Increasing Case Outstanding Strength , , , , ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: , , , ,096,235 1,034, ,313 54,296 54,296-62, , , , ,227,589 1,085, , , , ,659 2 Total 8,551,189 7,573, ,642 9,052,121 8,804, , , , ,597 2 Comparing the projections of Scenario 3 with those of the steady-state environment, we notice: For AYs , reported claims in Column (3) are greater than those in the steady-state. Reported CDFs (Column (6)) are higher for the latest three AYs as well. Projected ultimate claims based on the reported claim development technique are greater in Scenario 3 than the steady-state projection due to higher reported claims and higher CDFs. Conclusion: Without adjustment, the reported claim development method overstates the projected ultimate claims and thus the IBNR in times of increasing case outstanding strength. An increase in case outstanding adequacy leads to higher CDFs. Multiplying a higher value of reported claims by a higher CDFs leads to an overstated the estimate of total unpaid claims. Exam 5, V2 Page by All 10, Inc.
17 Paid claim development triangles: There are no differences between the paid claim development triangles of Scenario 3 and the steadystate environment (because only the case outstanding are affected). Thus, the age-to-age factors, CDFs, and projected ultimate claims remain the same as the steady-state. Since there has been no change in the settlement of claims, the primary assumption of the development technique still holds true for paid claims. In times of changing case outstanding adequacy, the paid claim development method is an alternative to the reported claim development method. One problem with the paid claim development method: The highly leveraged nature of the CDF for the most recent years in the experience period (especially for long-tail lines of insurance). Scenario 4 U.S. PP Auto Increasing Claim Ratios and Case Outstanding Strength See the bottom section of Exhibit III, Sheet 11. The claim ratios are the same as those of the second scenario Assume changes in case outstanding strength that is similar to the third scenario. Impact of Changing Conditions Exhibit III U.S. PP Auto - Development of Unpaid Claim Estimate Sheet 11 Age of Projected Ultimate Claims Estimate IBNR Difference from Actual Accident Accident Claims at 12/31/08 Case CDF to Ultimate Using Dev. Method with Using Dev. Method with Actual IBNR Year at 12/31/08 Reported Paid Outstanding Reported Paid Reported Paid Reported Paid IBNR Reported Paid (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) Increasing Claim Ratios and Case Outstanding Strength , , , , ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ,329, , , ,488,875 1,403, ,980 73,688 73,687-85, ,330, , , ,756,504 1,551, , , , ,176 0 Total 9,901,691 8,575,113 1,326,578 10,595,469 10,249, , , , ,119-1 Column Notes: (2) Age of accident year at December 31, 2008 (3) and (4) From last diagonal of reported and paid claim triangles in Exhibit III, Sheets 6 through 9. (5) =[(3) - (4)]. (6) and (7) CDF based on 5-year volume-weighted average age-to-age factors presented in Exhibit III, Sheets 6 throught 9. (8) =[(3) * (6)]. (9) =[(4) * (7)]. (10) =[(8) - (3)]. (11) =[(9) - (3)]. (12) Developed in Exhibit III, Sheet 1. (13) =[(12) - (10)]. (14) =[(12) - (11)]. Again, the paid claim development method produces the actual value for IBNR. The reported claim development method, while responsive to the increasing claim ratios, overstates the estimate of unpaid claims due to the changing case outstanding adequacy. Effects of Changes in Product Mix on the Development Technique A portfolio of contains both private passenger and commercial automobile insurance for the purpose of estimating unpaid claims. While these types of business have different underlying claim development patterns and ultimate claim ratios, the development technique is an acceptable method for determining estimates of unpaid claims for the combined portfolio as long as there are no changes in the mix of business (i.e., one line of business is not significantly increasing or decreasing in volume relative to the other line of business). Exam 5, V2 Page by All 10, Inc.
18 Key Assumptions We compare a steady-state environment that has no change in product mix (called U.S. Auto Steady-State) with a changing product mix (called U.S. Auto Changing Product Mix). Assume: For U.S. Auto Changing Product Mix, the portfolio includes the same private passenger premiums as the steady-state, but commercial automobile insurance premiums increase at 30% instead of 5% per year starting in The ultimate claim ratio is 70% for private passenger automobile and 80% for commercial automobile. The following table shows the reporting and payment patterns for the two categories of business. Table 7 Key Assumptions Product Mix Scenarios Reporting and Payment Patterns Private Passenger Commercial Automobile As of % % % % Month Reported Paid Reported Paid 12 77% 42% 59% 22% 24 90% 71% 78% 46% 36 95% 84% 89% 67% 48 98% 92% 96% 82% 60 99% 96% 98% 91% 72 99% 98% 100% 95% % 99% 100% 97% % 99% 100% 98% % 100% 100% 99% % 100% 100% 100% The claim development triangles are created using the EP and ultimate claim ratios by AY as well as the given reporting and payment patterns. Exhibit IV, Sheets 2 and 3 show reported and paid development triangles assuming no change in product mix; Exhibit IV, Sheets 4 and 5 show the claim development triangles based on a changing product mix Exhibit IV, Sheet 6 shows the calculation of actual IBNR. U.S. Auto Steady-State (No Change in Product Mix) See the top section of Exhibit IV, Sheet 6 Both the reported and paid development techniques produce estimated IBNR equal to the actual IBNR. As long as the distribution between the different categories of business remains consistent (and there are no other operational or environmental changes), the claim development method should produce an accurate estimate of unpaid claims. Impact of Change in Product Mix Example Exhibit IV U.S. Auto - Development of Unpaid Claim Estimate Sheet 6 Age of Projected Ultimate Claims Estimate IBNR Difference from Actual Accident Accident Claims at 12/31/08 Case CDF to Ultimate Using Dev. Method with Using Dev. Method with Actual IBNR Year at 12/31/08 Reported Paid Outstanding Reported Paid Reported Paid Reported Paid IBNR Reported Paid (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) Steady-State ( No Change in Product Mix) ,500,000 1,500, ,500,000 1,500, ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ,852,729 1,277, , ,216,183 2,216, , , , ,568, , , ,326,992 2,326, , , , Total 17,472,205 15,270,788 2,201,417 18,866,839 18,866,837 1,394,634 1,394,632 1,394, Exam 5, V2 Page by All 10, Inc.
19 U.S. Auto Changing Product Mix See the bottom section of Exhibit IV, Sheet 6 There are no differences between the two examples until AY 2005, in which commercial auto began to increase at a 30% annual rate. We expect higher reported and paid claims for 2005 through We expect higher CDFs for both paid and reported claims for AYs 2006, 2007 and However, even with larger claims and CDFs, the development technique falls short of the actual IBNR. Impact of Change in Product Mix Example Exhibit IV U.S. Auto - Development of Unpaid Claim Estimate Sheet 6 Age of Projected Ultimate Claims Estimate IBNR Difference from Actual Accident Accident Claims at 12/31/08 Case CDF to Ultimate Using Dev. Method with Using Dev. Method with Actual IBNR Year at 12/31/08 Reported Paid Outstanding Reported Paid Reported Paid Reported Paid IBNR Reported Paid (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) Changing Product Mix ,500,000 1,500, ,500,000 1,500, ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ::: ,680,487 1,766, , ,217,775 3,091, , , ,924 59, , ,556,695 1,097,644 1,459, ,842,646 3,592,941 1,285,951 1,036,246 1,445, , ,139 Total 20,067,180 16,738,685 3,328,495 22,219,968 21,789,881 2,152,788 1,722,701 2,391, , ,382 Column Notes: (2) Age of accident year at December 31, 2008 (3) and (4) From last diagonal of reported and paid claim triangles in Exhibit IV, Sheets 2 through 5. (5) =[(3) - (4)]. (6) and (7) CDF based on 5-year volume-weighted average age-to-age factors presented in Exhibit IV, Sheets 2 throught 5. (8) =[(3) * (6)]. (9) =[(4) * (7)]. (10) =[(8) - (3)]. (11) =[(9) - (3)]. (12) Developed in Exhibit IV, Sheet 1. (13) =[(12) - (10)]. (14) =[(12) - (11)]. What is the correct age-to-age factor when a portfolio is changing its composition (see Exhibit IV, Sheet 1)? We know that commercial auto has a longer reporting pattern than private passenger automobile (and thus requires higher selected age-to-age factors). Since commercial auto claims are increasing in the portfolio, increasing age-to-age factors appear. Changing from a 5-year to 3-year volume-weighted average for selecting age-to-age factors helps move the estimated IBNR closer to the actual IBNR, but its still falls short by a significant amount. Conclusions the reported development method is more responsive than the paid claim development method due to the shorter time frame in which claims are reported versus paid. both methods result in estimated IBNR that are significantly lower than the actual IBNR. Exam 5, V2 Page by All 10, Inc.
20 Sample Questions: 1. When analyzing data triangles of claims by accident year (AY), using Development Techniques: a. Explain how a cumulative reported CDF is calculated. b. Explain how a cumulative reported CDF is applied to calculate ultimate claim estimates, for one AY. c. What is the term used in Friedland to describe the ultimate claims minus the reported claims? d. Explain how a cumulative paid CDF is calculated. e. Explain how a cumulative paid CDF is applied to calculate ultimate claim estimates, for one AY. f. What is the term used in Friedland to describe the ultimate claims minus the paid claims? ( CDF = claim development factor) 2. Describe a typical relationship between reporting patterns and payment patterns for many lines of P&C insurance. 3. What name does Brosius give to the method described in Friedland as the Development technique? What name does Patrik use for this method? 4. Summarize Friedland s key points re: When the Development Technique Works and When it Does Not. List the two limitations mentioned. 5. List 5 characteristics Friedland suggests that actuaries may reference when reviewing claim development experience. 6. Based on the following data as of 12/31/08: Reported Claims including ALAE ($000's omitted) Earned Accident 1st 2nd 3rd 4th 5th 6th Premium Year Report Report Report Report Report Report 2, ,620 1,700 1,750 1,750 1,750 2, ,200 1,690 1,710 1,800 1,800 2, ,250 1,725 1,800 1,950 2, ,400 1,550 1,900 3, ,500 1,900 3, ,250 a. Estimate the IBNR as of 12/31/08 using the following method: Development Technique To select claim development factors, use the volume-weighted averages for the latest three years. See also Friedland Chapter 8 and 9 for other methods. b. Using the data above and based on the discussion by Friedland, what is the month age-to-age factor using: (i) Simple (arithmetic) average of the last three years (ii) Geometric average of the last four years (iii) Medial average for the latest five years excluding one high and low value, Medial latest 5x1 Exam 5, V2 Page by All 10, Inc.
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