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Every question in the free Exam ALTAM bank carries a full worked solution. Here is one from the pool:
Question 1
Medium
Which of the following embedded options in life insurance products is most analogous to a short position in a European call option from the insurer's perspective?
Solution
C is correct.
A guaranteed purchase rate (annuitization rate) provision gives the policyholder the right to convert the accumulated fund into an annuity at a rate fixed at policy issue. This is most analogous to a short call option from the insurer's perspective:
- Underlying: the present value of the annuity stream purchased at the prevailing market rate
- Strike: the annuity stream purchased at the guaranteed rate
When market interest rates fall, the present value of the guaranteed annuity income rises above the market-rate annuity — the policyholder exercises the annuitization option, and the insurer must provide the higher-value annuity. This is exactly how a short call functions: the insurer (option writer) must deliver value when the underlying (market annuity PV) exceeds the strike (guaranteed annuity PV).
A guaranteed purchase rate (annuitization rate) provision gives the policyholder the right to convert the accumulated fund into an annuity at a rate fixed at policy issue. This is most analogous to a short call option from the insurer's perspective:
- Underlying: the present value of the annuity stream purchased at the prevailing market rate
- Strike: the annuity stream purchased at the guaranteed rate
When market interest rates fall, the present value of the guaranteed annuity income rises above the market-rate annuity — the policyholder exercises the annuitization option, and the insurer must provide the higher-value annuity. This is exactly how a short call functions: the insurer (option writer) must deliver value when the underlying (market annuity PV) exceeds the strike (guaranteed annuity PV).
