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

An insurer uses Monte Carlo simulation to value a maturity guarantee on a unit-linked policy. Which statement best describes how the cost of the guarantee is estimated?

The cost is estimated by simulating many fund paths, computing the guarantee payoff on each path, discounting, and averaging. Computing the payoff from an average fund value would understate the cost, because the guarantee payoff is non-linear.

  1. ASimulate many risk-neutral or real-world fund paths, compute the guarantee payoff on each path, and take the average of the (discounted) payoffsCorrect
  2. BSimulate one fund path and multiply the payoff by the probability of death
  3. CTake the average fund value at maturity and compute the payoff from that single average
  4. DUse the highest simulated fund value to set the guarantee cost
  5. Use the median simulated fund value and ignore discounting

Explanation

The guarantee payoff is max(G - F_T, 0), a non-linear function of the fund value. It must be computed path by path and then averaged, with discounting. Applying the payoff to the average fund value understates the cost because of Jensen's inequality.

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