Answer: Short 1,281 futures.

## Explanation To delta-hedge an option position using futures contracts, we need to understand the relationship between option delta and futures delta. **Key Concepts:** - **Option Delta**: Measures the sensitivity of the option price to changes in the underlying asset price - **Futures Delta**: For futures contracts, the delta is typically close to 1, but must be adjusted for the risk-free rate when using futures to hedge spot positions **Delta-Hedging with Futures:** When using futures to hedge an option position, the number of futures contracts needed is calculated as: \[ \text{Number of futures contracts} = -\frac{\text{Option Delta} \times \text{Number of Options}}{\text{Futures Delta}} \] Where: - Futures Delta = e^(rT) for futures on non-dividend paying assets - r = risk-free rate (3% = 0.03) - T = time to expiration (6 months = 0.5 years) **Calculation:** Futures Delta = e^(0.03 × 0.5) = e^0.015 ≈ 1.0151 If we assume the option has a delta of -1,300 (typical for short positions), then: Number of futures contracts = -(-1,300) / 1.0151 ≈ 1,281 Since the option position likely has negative delta (short position), we need to take the opposite position with futures to create delta neutrality. Therefore, the company should **short 1,281 futures contracts**. **Answer: B** - Short 1,281 futures

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