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

An insurer uses stochastic simulation to value a maturity guarantee on a unit-linked policy. It wants a market-consistent value consistent with the price at which the guarantee could be hedged in the market. Which simulation approach is appropriate?

The guarantee should be valued with risk-neutral simulation: asset prices drift at the risk-free rate and the payoffs are discounted at the risk-free rate. This gives a price consistent with hedging in the market, unlike real-world drift combined with risk-free discounting, which is inconsistent.

  1. AProject fund values with real-world expected returns and discount at the risk-free rate
  2. BProject fund values with real-world expected returns and discount at a risk-adjusted rate reflecting the insurer's cost of capital
  3. CProject fund values with the risk-free rate as the drift and discount payoffs at the risk-free rateCorrect
  4. DProject fund values with the risk-free rate as the drift and discount payoffs at the expected equity return
  5. Project fund values with zero drift and apply no discounting

Explanation

Market-consistent valuation uses risk-neutral simulation. Under the risk-neutral measure every asset grows at the risk-free rate, and payoffs are discounted at that same rate. Mixing real-world drift with risk-free discounting overstates the value of the guarantee, because a put-like guarantee is hedged at the risk-neutral price.

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