Scenario ( ) = = Answer E.

Transcription

1 Exercise. You are the valuation actuary for Glorious Life Insurance Company. You are implementing a new principle-based reserving methodology for your company. You have created a set of 10 economic scenarios that represent an appropriate range of possible outcomes for your company s future, so that you can treat them as a complete probability space with equal probability assigned to each scenario. Your company has just received a $1000 single premium for a deferred annuity policy. Your analysis has shown that the present value at time 0 of the accumulated deficiency (i.e., the excess of future interest credited to customer s account over the amount earned on investments, after all expenses) at the end of each year is as given in the table below. The regulation requires the reserve to be calculated as the current account balance plus the 70-th percentile Conditional Tail Expectation (CTE) of greatest present value of accumulated deficiency. Calculate that reserve Scenario Present value of accumulated deficiency at time t = A. Less than 1000 B. At least 1000 but less than 1005 C. At least 1005 but less than 1010 D. At least 1010 but less than 1015 E. At least 1015 The greatest present values (GPV) of accumulated deficiencies for scenarios 1 through 10 are: 11, 10, 0, 7, 8, 2, 4, 6, 14, 0. CTE70 calculation requires us to average the largest 0 percent of Scenario GPVs of initial account balance plus GPV of accumulated deficiency. That means we need to add the starting asset amount 1000 to each GPV for scenarios with greatest GPV calculate their average: Answer E ( ) = = 1016.

2 Exercise. We have an example of scenarios runs for years, with 10 scenarios each year shown below. The starting value of assets, equal to the single premium paid, is Calculate the CTE70 reserve. Scenario Value of accumulated deficiency at each year Annual effective interest i (%) for each year V 0 V 1 V 2 V i 1 i 2 i A. Less than 1000 B. At least 1000, less than 1050 C. At least 1050, less than 1100 D. At least 1100, less than 1150 E. At least 1150 PV at time 0 of accumulated Scenario deficiency at time t = GPV (greatest present value) for scenarios 1 through 10: 10.7, 80, 0, 0, 68.6, 181.4, 9.2, 8.5, 89.8, 0. CTE70 requires us to average the largest 0 percent of current account value plus Scenario GPVs of accumulated deficiency. That means we need to add the starting

3 asset amount 1000 to each GPV for those scenarios calculate their average: Answer D. = 1125.

4 Exercise You are the valuation actuary for the Hard Knocks Life Insurance Company offering life annuities life insurance to guinea pigs. The valuation interest rate is 2%, mortality of guinea pigs follows De Moivre s Law with l x = 4 x, 0 x 4. You can assume that times after age 4 are ignored. Your company issues fixed deferred annuities to guinea pigs. The interest rate is guaranteed at % for the first two years, 1% thereafter. The surrender charge is 10% the first year, 5% the second year, 0% thereafter. Calculate the reserve for a $1000 single premium deferred annuity at issue sold to a newborn. There are no front-end loads. Assume that you use Commissioners Annuity Reserve Valuation Method you are not doing this in the state of New York. Regulations require that surplus must be % of assets at the policy issue date. Find the additional surplus investment requirement for this policy under this stard reserving policy. Then consider a new principles-based reserving requirement that the valuation rate must be replaced by three possible yield curves of forward rates: = 1.85%, f 2, = 1.95%, f,4 = 2.15%; = 1.95%, f 2, = 2.15%, f,4 = 1.75%; = 1.75%, f 2, = 1.65%, f,4 = 1.55%. Calculate the CARVM reserve defined as the maximum under all three scenarios the new capital requirement. Find the difference between the two capital requirements. A. Less than 5 B. At least 5 but less than 7 C. At least 7 but less than 9 D. At least 9 but less than 11 E. 11 or more Because you are not doing business in the state of New York, you only need to do the calculations at the end of each policy year. Under constant valuation rate, the values are: The CARVM reserve is given by the present value of the guaranteed cash value at the end of the second policy year, when the surrender charge wears off, it equals Without a surplus contribution, the company only has 1000 worth of assets,

5 would not be allowed to issue the policy. If the minimum surplus investment is x, then we must have x = 0.0, x x = = Under the first possible yield curve, we have = 1.85%, f 2, = 1.95%, f,4 = 2.15%, Under the second possible yield curve = 1.95%, f 2, = 2.15%, f,4 = 1.75%, Under the third possible yield curve = 1.75%, f 2, = 1.65%, f,4 = 1.55%, Thus the new CARVM reserve is To find the capital requirement, we set x = 0.0, x resulting in x = The difference in capital requirements is = Answer C.