Answer: EUR 5.93

## Explanation The Black-Scholes-Merton model for pricing options on futures contracts uses the following formula: \[ c = F_0e^{-rT}N(d_1) - Ke^{-rT}N(d_2) \] Where: - \( F_0 \) = current futures price = EUR 63 - \( K \) = strike price = EUR 68 - \( T \) = time to expiration of option = 0.5 years (6 months) - \( r \) = risk-free interest rate = 3% = 0.03 - \( N(d_1) \) = 0.4678 - \( N(d_2) \) = 0.3449 **Step-by-step calculation:** 1. Calculate the discount factor: \( e^{-rT} = e^{-0.03 \times 0.5} = e^{-0.015} \approx 0.9851 \) 2. Calculate the first term: \( F_0e^{-rT}N(d_1) = 63 \times 0.9851 \times 0.4678 \approx 29.04 \) 3. Calculate the second term: \( Ke^{-rT}N(d_2) = 68 \times 0.9851 \times 0.3449 \approx 23.11 \) 4. Calculate the call option price: \( c = 29.04 - 23.11 = EUR 5.93 \) **Key points:** - The time to maturity of the underlying futures contract (18 months) is not used in the BSM formula for options on futures - The formula uses the current futures price rather than the spot price - Both terms are discounted using the same discount factor \( e^{-rT} \) - The result matches option B: EUR 5.93

Author: LeetQuiz .