Hi Tutor, In chapter 22 Under proportionate paid up section, am not able to understand this paragraph on page 9 Early premiums buy a larger proportion of the sum assured than later premiums, because of the time to maturity and the effect of compound interest. At most durations this means that a proportionate value understates the true value of the policy, although it will tend to the maturity value as the duration of making the policy paid-up approaches the maturity date. However, early on it is the initial expenses that dominate, causing the ‘true’ paid-up sum assured to be negative (ie a paid-up value should not be offered). Kindly help please
Hi Kamal A numerical example may help. Consider an endowment assurance with sum assured of 120, annual premium of 10 and term of 10 years. The proportionate paid up method implicitly assumes that all the premiums are worth the same, ie each premium buys 120/10 = 12 of the sum assured. But this is not true. The last premium will accumulate with only one year of interest, while the sixth premium will accumulate with five years of interest (and so is more valuable). Also the first premium will largely be spent on the initial expenses and so will not have bought much of the sum assured. Best wishes Mark
Hi Tutor--- Doubts from Chapter 23: Cost of Guarantees and Options 1. Ques is --> Suppose that an insurance company offers guaranteed annuity payments on its without-profits deferred annuity contract, but invests to meet the open market cash option. Explain whether the company is at risk from low or high interest rates at retirement. Solution given is -->The company is at risk from low interest rates since the annuity may cost more to buy than the cash available. The reverse is true if it invests to be able to pay the annuity. In this case, the risk is that interest rates are high and that the annuity the company has invested to be able to pay is worth less than the cash alternative Am not able to understand this question + What is this Open market cash Option And please correct my understanding of Guaranteed annuity payments --> Suppose Policyholder is currently aged 40, Insurer said to Policyholder ," We will pay you annuity from age 65 of $1 every year in return of $16 lumpsum at Age 65. Now the risk for an insurer is suppose interest rate falls, so it means Cost of annuity of 1$ level payments for an individual aged 65 would be $25 (say). Am i correct???
Doubt from Chapter 23: Cost of guarantee > Topic: Investment guarantee > Use of option price Hi Tutor. please help in understanding of what is guaranteed annuity rate, can you give any example. [Like what is annuity rate ? is it a percentage %] ++ A guaranteed annuity rate corresponds to a call option on the bonds that would be necessary to ensure the guarantee was met, ie at an exercise price which generates the required fixed rate of return. Alternatively, it can be mirrored by an option to swap floating rate returns at the option date for fixed rate returns sufficient to meet the guaranteed annuity option (a ‘swaption’). --> Am not able to understand this paragraph and there is one question also based on same. Kindly explain --: Ques: An insurance company offers guaranteed annuity payments on its without-profits deferred annuity contract, but invests to match the open market cash option. Explain how the insurance company could protect itself from the annuity rate guarantee by: (i) purchasing call options on bonds (ii) purchasing interest rate swap options. Ans: (i) Buying call options At the maturity (retirement) date of the policy, the insurance company will have cash available equal to the open market cash option. If interest rates are now lower than used in the guaranteed annuity rates, then the bonds that the company needs to buy to match the annuity payments will cost the company more money than the cash available from the policy maturity. A call option essentially fixes a maximum purchase price for the bonds at the exercise date. So holding the option means that the company will not need to pay more money (than it can afford) for the bonds if interest rates do fall below the guaranteed level. (This means that the current market price of the call option represents the expected cost of the annuity rate guarantee provided by the company.) (II) Buying interest rate swap options For this the company would buy options that would permit it to undertake ‘receive fixed / pay floating’ swaps as from the retirement date, where the fixed rate in the swap agreement was equal to the interest rate in the guaranteed annuity basis. The option would only lead to the swap being undertaken if bond yields had fallen below the guaranteed rate at the retirement date. Thereafter (assuming the option is exercised) the insurance company would have to keep its assets as cash, so that it could cover its obligation to ‘pay floating’ under the swap agreement. Meanwhile the swap agreement will pay the insurer the income shortfall on its (cash) returns, making this up to the level of income required to cover the guaranteed annuity payments. (So this time it is the current market price of the necessary swap options that represents the market valuation of the annuity rate guarantee.)
Hi Kamal Yes, your example is correct. So the policyholder in this contract has a choice between taking $16 at age 65 as a lump sum (this is the open market cash option, which the policyholder could then use to buy an annuity from any company) or the policyholder could opt to receive the guaranteed annuity of $1. The risk is that if the insurer invests to get $16 at age 65, then interest rates may have fallen making the annuity payments cost $25. If instead the insurer invests to get $1 per annum, the risk is then that interest rates rise, the value of the insurer's assets fall, but the policyholders then opts to take the cash of $16. Best wishes Mark
Hi Kamal A guaranteed annuity rate would normally be expressed as an amount of money required to buy a given annuity. Using your earlier example, the guarantee could be that $1 of annuity can be bought at the rate of $16. I'll return to the rest of this query later. Best wishes Mark
Hi Kamal Again we'll use your earlier example. We were guaranteeing that an annuity of $1 per annum could be bought for 16 (this is fine if the matching bonds cost 16). We were worried that interest rates could rise rise and the annuity costs 25 (ie the matching bonds actually end up costing 25). So a call option to buy the bond for exercise price of 16 would remove the risk. The bond price of 16 may correspond to 4% interest, while a bond price of 25 may correspond to 3% interest. So instead we could have a swaption that gives us the right to swap the current interest rate (which turns out to be 3%) for the required rate of 4% to pay the annuity. Best wishes Mark
Now question says that insurer is matching the open market cash option i.e. $16 at age 65 (say). So the risk is that interest rate may go down which will cost $25. So insurer can buy a call option so that it can exercise that at age 65 with strike price of 16$. Whatever the premium is for that call option, that premium is the cost of option provided to my policyholder right ?
