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Answer: A longevity swap where Acme periodically Pays a Fixed premium and Receives Notional Principal × (Prespecified MR - Realized MR)
**Correct answer: B** Acme is a sponsor of a **defined benefit pension plan**, so it faces **longevity risk**: if participants live longer than expected, the plan must pay benefits for a longer period. A good hedge should therefore provide a **positive payoff when actual mortality is lower than expected** (i.e., when people live longer and realized mortality rates fall below the prespecified level). ### Why B is correct A longevity swap with payoff: \[ \text{Notional Principal} \times (\text{Prespecified MR} - \text{Realized MR}) \] will pay Acme when **realized mortality is below the prespecified mortality rate**, which offsets the pension plan’s longevity losses. ### Why the others are wrong - **A** pays when realized mortality is higher than expected, which is the opposite of what Acme needs. - **C** is also the wrong sign and uses a long option payoff that benefits from higher realized mortality. - **D** is not a proper hedge description here; a short option would create additional downside exposure, not reduce longevity risk. So the best hedge is **B**.
Author: Manit Arora
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Q-21.3.3. Acme Industrial Corporate is the plan sponsor for a defined benefit pension plan. At the time of their retirements, participants are promised an annual benefit that is the product of three components: 1.5% * Number of years of service * Average three-year salary. To hedge its exposure to longevity risk, Acme seeks to employ derivatives. Let "MR" represent a mortality rate. Which of the following is the best hedge against Acme's longevity risk with respect to the defined benefit pension plan?
A
A longevity swap where Acme periodically Pays a Fixed premium and Receives Notional Principal × (Realized MR - Prespecified MR)
B
A longevity swap where Acme periodically Pays a Fixed premium and Receives Notional Principal × (Prespecified MR - Realized MR)
C
A longevity option that Acme purchases (long option) and that has a payoff equal to max(0, Realized MR - Prespecified MR)
D
A longevity option that Acme sells/write (short option) and that has a payoff equal to max(0, Prespecified MR - Realized MR)
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