Explanation

Put-call-forward parity establishes the relationship between European put and call options, risk-free bonds, and forward contracts. The parity relationship states that:

Long Put = Long Call + Long Risk-Free Bond + Short Forward

This can be derived from the basic put-call parity formula:

P + S = C + PV(K)

Where:

• P = Put option price
• S = Spot price of underlying asset
• C = Call option price
• PV(K) = Present value of strike price (risk-free bond)

Rearranging: P = C + PV(K) - S

In forward contract terms, a short forward position is equivalent to -S (since forward price F = S × (1+r)^T). Therefore:

P = C + PV(K) + Short Forward

This corresponds to option C: long call + long risk-free bond + short forward.

Why the other options are incorrect:

• Option A (short call + short risk-free bond + long forward): This would create a synthetic short put position, not a long put.
• Option B (short call + long risk-free bond + short forward): This combination doesn't create a synthetic long put position according to put-call-forward parity.

Key Concept:

Put-call-forward parity is an extension of put-call parity that replaces the spot position with a forward contract. It's particularly useful when dealing with forward contracts rather than spot positions.