Skip to content

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

A trader delta-hedges a short call using Black-Scholes, rebalancing only once a day, while the true share price occasionally jumps sharply overnight. Which statement best describes the consequence?

The hedge leaves residual risk. Black-Scholes replication needs continuous rebalancing and continuous price paths, so daily rebalancing and overnight jumps produce hedging errors that can be gains or losses, not a riskless position.

  1. AThe hedge remains perfect because delta is recalculated daily
  2. BThe hedge is exact only if the volatility is zero
  3. CThe hedge leaves residual risk, because replication requires continuous rebalancing and continuous price pathsCorrect
  4. DThe hedge fails only if the risk-free rate is stochastic
  5. The hedge error is always positive for the trader

Explanation

Black-Scholes perfect replication relies on continuous trading and continuous sample paths. Discrete rebalancing and jumps mean the portfolio is not riskless over the interval, leaving hedging error that can be of either sign. Recalculating delta daily does not remove the jump risk.

Did you get it right without looking?

One question tells you little. A timed set on Black-Scholes derivative-pricing model shows your real accuracy, how long you take and where you lose marks.

Practise Black-Scholes derivative-pricing modelFree diagnostic mock

More Black-Scholes derivative-pricing model questions