1. Overview of the reserving process: health insurance other than disability insurance

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1 NOTES ON HEALTH INSURANCE RESERVING 1. Overview of the reserving process: health insurance other than disability insurance Health insurance reserves may be classified broadly into the following categories: - Policy reserves: amounts necessary for contract obligations created by future claims. - Claim reserves: amounts needed to pay claims already incurred but not yet paid. - Expense liabilities: amounts needed to pay loss adjustment expenses, taxes and other expenses related to liabilities incurred by the insurer from operations prior to the statement date. Reserving practices for health insurance in general are governed by the NAIC Model Minimum Reserve Standards for Individual and Group Health Insurance. Policy reserves for long-term health insurance policies There are some health insurance policies that require policy reserves: policies that are long-term and are priced using level periodic premiums. Long-term care policies, individual disability policies, and permanent hospital benefit policies are examples of that type of policies. Reserves for this type of policies are calculated in a manner similar to life insurance reserves, as the actuarial present value of future benefits minus the actuarial present value of future valuation net (i.e., only providing for benefits) premiums. Statutory reserves valuation basis is given by designated morbidity tables, persistency rate tables, and a maximum interest rate. The minimum reserve requirements (i.e., maximum interest rate, maximum morbidity table, and appropriately conservative lapse table) are based on the date of issue, just as for the life insurance policies. For long-term health products two-year full preliminary term methodology is allowed, although one-year full-preliminary term is recommended. Reserves for the purposes of the Generally Accepted Accounting Principles (GAAP) valuation are calculated using the insurer s realistic expectations for morbidity, mortality, persistency, and investment return, and on a net level premium basis. Expense reserves The need for these reserves arises when there are significant expenses of settling claims. They are generally based on experience studies. Other than

2 claim expenses, the reserve for expenses may be accounted for in the unearned gross-premium reserve (i.e., reserve accounting for the fact that the unearned portion of the gross premium will be due the insured if the policy is cancelled). One special case is the situation when the first year unpaid commissions and expenses turn out to be higher than the expense loading in that year s premium. Claim reserves In this work, we are interested first and foremost in the claim reserves. They represent the amounts that the insurer expects to pay in the future on claims that have been incurred prior to the date of the financial statement being produced and have not yet been paid in full. Claim reserves are the amount yet to be paid. Three major types of these liabilities are: items due, unpaid claims, and claims in course of settlement. The first of the three is usually small, and known with reasonable precision. Unpaid claims whose amount is known again can be valued with reasonable precision. Only the claims that are still in the process of development, either because the ultimate value has not been established, or because the insurance firm has no knowledge of the claim yet, produce a significant level of uncertainty requiring actuarial analysis. The basic methodology of claim reserving for health insurance liabilities is very similar to the methodology used in property/casualty insurance loss reserving. There are, however, significant differences. Let us summarize them here: A health insurer encounters a significantly greater variety of types of claims, as there is a plethora of medical procedures for which payments can be made. Property/casualty insurers have significantly greater access to the structure of the data underlying the claim, such as individual characteristics of the claimant. Health actuaries commonly price and value their products using per-member, per-month (PMPM) rates, and, for example, federally qualified Health Maintenance Organizations (HMO) must use of the approved community rating approaches, effectively expressing all rates on PMPM basis, with possibly some classification and adjustment (but adjusted rating requires notification of the federal authorities).

3 2. Loss reserving methodologies in property/casualty insurance The amount ultimately paid on a claim submitted to an insurer is determined in the process of development. This process can be described by showing the ratios of amounts paid in consecutive years (development factors) or percentages of ultimate cost paid up to a given date (completion factors). The approach is also termed the chain-ladder method. Let us describe it with the help of some examples. Suppose that Mr. Bean Actuary had a car accident on July 1, 2005, and the cumulative amounts paid on the claim for this accident are: August 1, 2005 September 1, 2005 October 1, 2005 $ $ $ and the claim is determined to be paid in full on October 1, Then the development factors for this claim are: September 1, 2005 October 1, Each factor is the ratio of the amount paid up-to-date to the amount paid upto-date in the previous period. The completion factors are: August 1, 2005 September 1, 2005 October 1, % 80.00% % Here, the percentages represent the ratios of the amount paid up-to-date to the amount ultimately paid. If the valuation date is September 1, 2005, then the insurance company will have paid $1200, and it will ultimately pay $1500. The difference of these two amounts, $300, is the claim reserve. But in practice, the company does not know the ultimate amount, and instead estimates it based on the amount paid up-to-date at the valuation date, as either = 1500 based on the development factor, or = 1500 based on the completion factor. But the development factors/completion factors are not known, either. They are estimated from the historical data. For that reason, development of claims from previous periods is studied and presented in a development triangle. The triangle shows full development in an early period, and partial development, less and less developed, in subsequent periods. Suppose that Mr. Bean Actuary, Mr. Casimir Piast (a.k.a., Casimir The Great), Ms. Alexandrina Sachsen-Coburg (since she prefers her middle name, Victoria, we will refer to her simply as Vicky Coburg, and she is also known as Her Royal Majesty Queen Victoria), Mr. Chief Lapu-Lapu, and Mr. Darth

4 Warner have had the basements of their homes flooded due to sump-pump backup in their homes (luckily they purchased the sump-pump riders on their homeowners insurance policies) on July 1, August 1, September 1, October 1, and November 1, 2005, respectively, and supposed that full loss development lasts five months. Assume it is now December 1, 2005, and the cumulative amounts of claims have been as follows (recall that we assume all claims are fully developed after five months): 8/1/5 9/1/5 10/1/5 11/1/5 12/1/5 B. Actuary C. Piast V. Coburg C. Lapu-Lapu D. Warner 5000 Then the development factors (on the previous period), organized by time lag since claim occurred (instead of the calendar order presented above) are: 2 months 3 months 4 months 5 months B. Actuary C. Piast V. Coburg C. Lapu-Lapu 1.50 D. Warner The completion factors for Mr. Bean Actuary are: 1mo. 2 mos. 3 mos. 4 mos. 5 mos. B. Actuary 36.36% 54.55% 72.73% 80.00% % We do not know the exact completion factors for Mr. Casimir Piast, Ms. Vicky Coburg, Mr. Chief Lapu-Lapu, and Mr. Darth Warner, because their claims are not fully developed. This problem is set up so that the development factors, and, as a consequence, the completion factors, are the same for all insured. Consequently, the development triangle for completion factors as of December 1, 2005 is:

5 1mo. 2 mos. 3 mos. 4 mos. 5 mos. B. Actuary 36.36% 54.55% 72.73% 80.00% % C. Piast 36.36% 54.55% 72.73% 80.00% V. Coburg 36.36% 54.55% 72.73% C. Lapu-Lapu 36.36% 54.55% D. Warner 36.36% Given that the payments made up-to-date for the five insured were: B. Actuary 5500 C. Piast 6600 V. Coburg 8000 C. Lapu-Lapu 1500 D. Warner 5000 These amounts represent the following percentages of the ultimate value of the claims: B. Actuary % C. Piast 80.00% V. Coburg 72.73% C. Lapu-Lapu 54.55% D. Warner 36.36% Therefore, the projected ultimate amounts of these claims are: B. Actuary 5500 C. Piast = 8250 V. Coburg = C. Lapu-Lapu = D. Warner = The claim reserves for these claims as of December 1, 2005 are: B. Actuary = 0 C. Piast = 1650 V. Coburg = 3000 C. Lapu-Lapu = D. Warner =

6 In practice, development factors of completion factors are estimated based on the historical data concerning developments of other claims. The estimate may be the mean of factors in the same stage of development in the triangle, or a longer-term average from data collected by the insurance company (such as a multi-year average), or a weighted average (e.g., assigning higher weight to data closer to the present time), or some other statistic derived from the data. Expected Loss Ratio Method The expected loss ratio method is a very simple alternative to the chain ladder approach. In this method, Estimated Ultimate Loss = Expected Loss Ratio Earned Premium. Therefore, Loss Reserve = Estimated Ultimate Loss Losses Paid Up-to-Date. The Bornhuetter-Ferguson Method The chain-ladder method gives the following estimate for the ultimate losses: Estimated Ultimate Loss = Losses Paid Up-to-Date f j, where f j is the development factor between time j 1 loss reserve is estimated as: Estimated Loss Reserve = = Estimated Ultimate Loss Losses Paid Up-to-Date = = Losses Paid Up-to-Date f j 1 j. It is convenient to write f ULT = f j, this is termed the ultimate factor. Then Estimated Loss Reserve = = Losses Paid Up-to-Date ( f ULT 1) = j j ( ) and time j. The = Estimated Ultimate Loss 1 1 f ULT. The Bornhuetter-Fergusson method combines the expected loss ratio and chain-ladder methods. For each accident month row of the loss-development triangle, we start by estimating the ultimate loss ratio expected for the period, considering all available information. Using this estimated loss ratio

7 and the earned premium for the period, we then calculate the estimated ultimate loss for the period. Then we use the paid period-to-period development factors from the chain ladder method to calculate the ultimate factors f ULT = f j. Here are the steps in the method: j Estimated Ultimate Loss = Expected Loss Ratio Earned Premium. Calculate the factors f ULT = f j. Estimated Loss Reserve = = Estimated Ultimate Loss 1 1 j f ULT.

8 Health insurance IBNR reserve calculation Suppose that the ABC Insurance Company has paid the following amounts for claims incurred in July 2005, with all claims paid by October 2005: Month Number Month Amount Paid In Month Cumulative Paid 0 July 2005 $ 0 $ 0 1 August 2005 $1,000 $1,000 2 September 2005 $ 200 $1,200 3 October 2005 $ 300 $1,500 Then the development factors for this claim are: September 2005 October Each factor is the ratio of the amount paid up-to-date to the amount paid upto-date in the previous period. The completion factors are: August 2005 September 2005 October % 80.00% % Here, the percentages represent the ratios of the amount paid up-to-date to the amount ultimately paid. If the valuation date is September 2005, then the insurance company will have paid $1200, and it will ultimately pay $1500. The difference of these two amounts, $300, is the claim reserve. But in practice, the company does not know the ultimate amount, and instead estimates it based on the amount paid up-to-date at the valuation date, as either = 1500 based on the development factor, or = 1500 based on the completion factor. But the development factors/completion factors are not known, either. They are estimated from the historical data. For that reason, development of claims from previous periods is studied and presented in a development triangle. The triangle shows full development in an early period, and partial development, less and less developed, in subsequent periods. Suppose we have the following claim patterns by incurred and paid month. Assume it is now December 2005, and the claims paid have been as follows (note that we are now assuming, for simplicity of this presentation that all claims are fully developed after five months in practice the actuary will have to estimate this number of month after which full development occurs as well):

9 Paid Month in 2005 Aug Sep Oct Nov Dec Incurred Month In 2005 August September October November December 5000 Then the development factors (on the previous period), organized by time lag since claim occurred (instead of the calendar order presented above) are: Month August September October November 1.50 December The completion factors for August are: % 54.55% 72.73% 80.00% % We do not know the exact completion factors for September through December, 2005 because their claims are not fully developed. This problem is set up so that the development factors, and, as a consequence, the completion factors, are the same for all insured. Consequently, the development triangle for completion factors as of December 2005 is: Month August 36.36% 54.55% 72.73% 80.00% % September 36.36% 54.55% 72.73% 80.00% October 36.36% 54.55% 72.73% November 36.36% 54.55% December 36.36%

10 We are given that the payments made up-to-date for the five insured were: August 5500 September 6600 October 8000 November 1500 December 5000 These amounts represent the following percentages of the ultimate value of the claims: August % September 80.00% October 72.73% November 54.55% December 36.36% Therefore, the projected ultimate amounts of these claims are: August 5500 September October November December = = = = The claim reserves for these months as of December 2005 are: August = 0 September = 1650 October = 3000 November = December =

11 In practice, development factors of completion factors are estimated based on the historical data concerning developments of other claims. The estimate may be the mean of factors in the same stage of development in the triangle, or a longer-term average from data collected by the insurance company (such as a multi-year average), or a weighted average (e.g., assigning higher weight to data closer to the present time), or some other statistic derived from the data. References Black, Kenneth Jr., and Harold D. Skipper, Jr., Life and Health Insurance, Thirteenth Edition, Prentice Hall, Upper Saddle River, New Jersey, Bornhuetter, and Ferguson "The Actuary and IBNR" Proceedings of the Casualty Actuarial Society, vol. 59, No. 112, Brown, R. L., Introduction to Ratemaking and Loss Reserving for Property and Casualty Insurance, (Second Edition), Actex Publications, Winsted, Connecticut, 2001.

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