Answer: The bond component minus the futures component

## 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.

Author: LeetQuiz Editorial Team