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IAI Actuarial Core Principles · Economic Modelling · Valuing benefit guarantees using simulation

A life insurer sells a unit-linked contract with a guaranteed minimum maturity benefit (GMMB) equal to the premium paid, with the fund invested in equities. From the insurer's viewpoint, which option payoff does the guarantee most closely resemble?

The guarantee is equivalent to the insurer being short a European put on the unit fund with strike equal to the guaranteed amount, because the insurer must pay the shortfall max(G minus fund value, 0) at maturity.

  1. AA long European call option on the unit fund, struck at the guaranteed amount
  2. BA short European put option on the unit fund, struck at the guaranteed amountCorrect
  3. CA short European call option on the unit fund, struck at the guaranteed amount
  4. DA long European put option on the unit fund, struck at the guaranteed amount
  5. A long forward contract on the unit fund

Explanation

At maturity the insurer pays max(G - F, 0) on top of the fund value F, which is the payoff of a put on the fund with strike G. The insurer bears this liability, so it is short the put. A call would pay off when the fund rises, which is not the shortfall the guarantee covers.

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