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Published byJessica Stevens Modified over 9 years ago
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DD&R/Extended Reserve Panel Laura A. Johnson, FCAS, MAAA
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Actual Practice - Using the Model proposed in the Walker & Skrodenis article l Changes to the Model l Additional Considerations
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Changes to the Model l Expected number of free tail executions l Lapses l Average load across all ages l Applying the load l Reserve calculation if other than start up year
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Changes to the Model - Expected Number of Free Tail Executions l Apply Death, Disability & retirements rates all to the beginning of the year population rather than cumulative l More Conservative - assumes no “overlap” exists in the rates l Impact is small -> 12.166% changes to 12.322% l Specific calculation -> pg. 338, (7)=(3)x[(4)+(5)+(6)]
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Changes to the Model - Lapses l Apply Lapse (non renewal) rates to the beginning of the year population rather than to the end of year population l Correct method depends on how the lapse rate itself is calculated l Impact is moderate ->12.322% changes to 12.081% l Specific calculation ->pg. 338, (9) = (3) x (8)
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Changes to the Model - Average Load across all ages l Short term approach - weight together based on current insureds l Long term approach - give more weight to younger insureds since they will be around funding longer - i.e., weight by insured and time Advantages - average load does not change every year - consistent with calculation by age Danger- if in practice, the load is recalculated each year any way, you’ll end up short if you use the long term average l Impact -> 12.081% under short term approach 10.780% under long term approach l Specific calculation -> pg. 344, (4) (avg) = sum of (16) from Model 2 times number of insureds at each age over all ages divided by the sum of (14) from Model 2 times number of insureds at each age over all ages in other words, weight the numerator and the denominator and sum across those first, then divide
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Changes to the Model - Applying the Load l Note load is stated as a percentage of pure premium (loss) l Can use that pure premium load as a rate load only if there are no Fixed Expenses l Otherwise, need to convert to a rate load
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Changes to the Model - Reserve Calculation l Reserve = Future DD&R Losses - Future DD&R Premium Thus, same age insureds need the same reserve regardless of what their entry age (the age they began funding) was l Need to restate Future DD&R Losses and Premiums so that the current age is “time 0” l Impact -> none if current age = entry age (i.e., start up year) -> potentially huge impact otherwise: 50-75% lower in our experience l Specific calculation -> pg. 339, column (18) and (19): divide current formula by column (10)
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Additional Considerations l No age bands - matrix of insureds by entry age and current age l Retirement requirements for free tail: i.e., 55&10 or 65&5 l Experience modification factor (note: don’t include expense considerations) l Actual utilization rate l Expected future funding of the reserve l Expected redundancy/inadequacy of future rates
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