Explanation

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

Put-Call Parity for Forwards: $C - P = \frac{F - K}{(1 + r)^T}$

Where:

• $C$ = Call premium = 0.0500 USD/EUR
• $P$ = Put premium (what we need to find)
• $F$ = Forward price = 1.2000 USD/EUR
• $K$ = Strike price = 1.2250 USD/EUR
• $r$ = Risk-free rate = 5% = 0.05
• $T$ = Time to expiration = 2 years

Step 1: Calculate the present value factor $(1 + r)^T = (1 + 0.05)^2 = (1.05)^2 = 1.1025$

Step 2: Calculate the present value of (F - K) $F - K = 1.2000 - 1.2250 = -0.0250$ $\frac{F - K}{(1 + r)^T} = \frac{-0.0250}{1.1025} = -0.022675$

Step 3: Apply put-call parity formula $C - P = \frac{F - K}{(1 + r)^T}$ $0.0500 - P = -0.022675$ $-P = -0.022675 - 0.0500$ $-P = -0.072675$ $P = 0.072675$

Step 4: Compare with answer choices $P \approx 0.0727 \text{ USD/EUR}$

This matches option B.

Why the other options are incorrect:

• A (0.0273 USD/EUR): This would result from incorrectly calculating $P = C - \frac{F - K}{(1 + r)^T}$ without considering the negative sign properly.
• C (0.0750 USD/EUR): This might result from ignoring the time value of money or using a different formula.

Key Concept: Put-call parity is a fundamental relationship in derivatives pricing that must hold for European options to prevent arbitrage opportunities. For forward contracts, the relationship accounts for the present value of the difference between forward and strike prices.