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IAI Actuarial Core Principles · Economic Modelling · Black-Scholes derivative-pricing model

A trader delta-hedges a sold European call using the Black-Scholes delta but can only rebalance once a week, and each trade incurs costs. Which statement best describes the effect on the hedge?

The hedge is no longer riskless. Black-Scholes replication relies on continuous, costless rebalancing; weekly trading leaves residual gamma-related error and costs add to it, so the hedger faces hedging risk and extra expense.

  1. AThe hedge is no longer riskless, as the model assumes continuous costless rebalancingCorrect
  2. BThe hedge becomes exactly riskless because delta is constant
  3. CThe option price must rise to the strike price
  4. DThe hedge is unaffected because delta is independent of share price
  5. The hedge error is zero in expectation and zero in variance

Explanation

The riskless replication argument needs continuous rebalancing without costs. Discrete rebalancing leaves residual hedging error from gamma, and costs add further loss. Delta changes with the share price, so options 1 and 3 are wrong.

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