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

An insurer values a maturity guarantee on a unit-linked policy by Monte Carlo simulation, using a stochastic model for equity returns. Which feature of the simulation is essential for the result to be a market-consistent value of the guarantee?

Scenarios must be generated under the risk-neutral measure, so that discounted asset prices are martingales and the expected discounted payoff gives a market-consistent guarantee value. Real-world drifts would embed risk premia and misprice the guarantee.

  1. AScenarios are generated under the real-world measure using the historical mean equity return
  2. BScenarios are generated under the risk-neutral measure so that discounted asset prices are martingalesCorrect
  3. CScenarios use a deterministic growth rate equal to the long-term average return
  4. DScenarios are generated with zero volatility to remove sampling error
  5. Scenarios are discounted at the insurer's cost of capital rather than the risk-free rate

Explanation

Market-consistent valuation of a guarantee needs risk-neutral scenarios, so that the discounted asset price is a martingale and the guarantee is priced like an option. Real-world scenarios discounted at the risk-free rate would give a value that includes an unrewarded risk premium and so would not be market-consistent. Zero volatility would remove the option value altogether.

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