Explanation

This question tests the put-call parity relationship for European options on forward contracts. The put-call parity formula for forward contracts is:

C - P = (F - K) / (1 + r)^T

Where:

• C = Call premium
• P = Put premium
• F = Forward price
• K = Strike price
• r = Risk-free rate
• T = Time to expiration (in years)

Given:

• F = 1.2000 USD/EUR
• K = 1.2250 USD/EUR
• r = 5% = 0.05
• T = 2 years
• C = 0.0500 USD/EUR

First, calculate the present value factor: (1 + r)^T = (1 + 0.05)^2 = 1.1025

Now, calculate (F - K): F - K = 1.2000 - 1.2250 = -0.0250

Then, calculate (F - K) / (1 + r)^T: (-0.0250) / 1.1025 = -0.022676

Now, rearrange the put-call parity formula to solve for P: P = C - [(F - K) / (1 + r)^T] P = 0.0500 - (-0.022676) P = 0.0500 + 0.022676 P = 0.072676 ≈ 0.0727 USD/EUR

Therefore, the put premium is closest to 0.0727 USD/EUR, which corresponds to option B.

Key points:

• The put-call parity relationship is fundamental in derivatives pricing
• For forward contracts, the formula uses the forward price (F) rather than the spot price
• The present value factor accounts for the time value of money over the 2-year period
• Since F < K (1.2000 < 1.2250), the forward contract has negative intrinsic value, which explains why the put premium is higher than the call premium