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

A unit-linked maturity guarantee promises the policyholder the greater of the unit fund value and a guaranteed sum at maturity. From the insurer's viewpoint, which option position does the guarantee most closely represent?

The guarantee is a short European put on the unit fund with strike equal to the guaranteed sum. The insurer pays the shortfall whenever the fund is below the guarantee at maturity, which is exactly the liability of a put writer, so the insurer is short the put.

  1. AA short European put option on the unit fund, with strike equal to the guaranteed sumCorrect
  2. BA long European call option on the unit fund, with strike equal to the guaranteed sum
  3. CA short European call option on the unit fund, with strike equal to the guaranteed sum
  4. DA long European put option on the unit fund, with strike equal to the guaranteed sum
  5. A short forward contract on the unit fund at the guaranteed sum

Explanation

The payout is max(F, G) = F + max(G - F, 0). The insurer must pay the shortfall G - F when the fund falls below G, which is the payoff of a put the insurer has sold. A long put would benefit the insurer, so it is wrong.

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