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