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

An insurer values a guarantee by Monte Carlo simulation, discounting each simulated shortfall at the risk-free rate. Which description of the simulated fund returns is correct for a market-consistent valuation?

A market-consistent valuation projects the fund under risk-neutral drift equal to the risk-free rate and averages the shortfalls discounted at the risk-free rate. Mixing real-world returns with risk-free discounting gives a value inconsistent with the replicating-portfolio price.

  1. AProject the fund with drift equal to the risk-free rate (risk-neutral) and average the discounted shortfallsCorrect
  2. BProject the fund with the real-world expected return and discount at that return
  3. CProject with the real-world return and discount at the risk-free rate
  4. DProject the fund with zero drift and do not discount
  5. Project with drift equal to the risk-free rate and discount at the real-world return

Explanation

Market-consistent pricing uses risk-neutral simulation, so drift is the risk-free rate and the mean of discounted payoffs is the price. Real-world projections with risk-free discounting overstate or misstate the value, as in option 3.

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