Explanation

In the Black model for European put options on futures:

Put price formula: P = X × e^(-rT) × N(-d₂) - F × e^(-rT) × N(-d₁)

This can be rewritten as: P = [X × N(-d₂) × e^(-rT)] - [F × N(-d₁) × e^(-rT)]

Where:

• Bond component = X × N(-d₂) × e^(-rT)
• Futures component = F × N(-d₁) × e^(-rT)

Therefore: Put value = Bond component - Futures component

This means to replicate a long put position, an investor would:

• Go long the bond component
• Go short the futures component

This combination creates the same payoff profile as holding a long put option on the futures contract.

Therefore, option B is correct.