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

A life office hedges a maturity guarantee dynamically and rebalances only once a month. Which of the following is the main reason the hedge cost in practice is likely to differ from the Black-Scholes price?

Infrequent rebalancing leaves gamma exposure between rebalance dates, so the hedge is imperfect, and transaction costs on each trade add to the cost. Black-Scholes assumes continuous, costless trading, so actual hedge costs diverge from the model price.

  1. ADiscrete rebalancing leaves gamma risk unhedged between rebalance dates, and transaction costs arise on each tradeCorrect
  2. BThe Black-Scholes model requires the fund to earn exactly the risk-free rate in real life
  3. CDelta of a put option is always zero when rebalancing is infrequent
  4. DDynamic hedging eliminates volatility risk completely if volatility is constant
  5. Transaction costs reduce the cost of hedging because trades are netted

Explanation

Black-Scholes assumes continuous costless rebalancing. With monthly rebalancing, the delta hedge is only correct instantaneously, so gamma causes hedging error between dates, and each trade incurs costs. The other options misstate the model: delta is not zero, and costs raise rather than lower hedging cost.

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