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

When valuing a guarantee on a unit-linked policy by stochastic simulation under the risk-neutral approach, which feature is correct for the simulated asset paths?

In risk-neutral simulation the fund is projected with drift equal to the risk-free rate, after allowing for charges, and the average payoff is discounted at the risk-free rate. Mixing real-world drift with risk-free discounting is inconsistent.

  1. AThe fund grows at the expected real-world return, and payoffs are discounted at the risk-free rate
  2. BThe fund grows at the risk-free rate (adjusted for charges), and payoffs are discounted at the risk-free rateCorrect
  3. CThe fund grows at the risk-free rate, and payoffs are discounted at the real-world expected return
  4. DThe fund grows at the expected real-world return, and payoffs are discounted at that same return
  5. The fund has zero volatility, and payoffs are discounted at the risk-free rate

Explanation

Risk-neutral valuation sets the drift of the asset to the risk-free rate (net of any charges or dividends) and discounts the average payoff at the risk-free rate. Using real-world drift with risk-free discounting mixes the two measures and misprices the guarantee.

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