Explanation

Put-call parity is a fundamental relationship between the prices of European call and put options with the same strike price and expiration date. The correct put-call parity formula is:

$C_0 + X/(1 + r)^T = P_0 + S_0$

Rearranging this equation to solve for the put price gives:

$P_0 = C_0 - S_0 + X/(1 + r)^T$

This matches option A.

Why the other options are incorrect:

Option B: $C_0 = P_0 - S_0 + X/(1 + r)^T$

• This would rearrange to $C_0 + S_0 = P_0 + X/(1 + r)^T$, which is not the correct put-call parity relationship.

Option C: $S_0 = C_0 - P_0 - X/(1 + r)^T$

• This would rearrange to $C_0 = P_0 + S_0 + X/(1 + r)^T$, which is also incorrect.

Key Concepts:

1. Put-call parity shows that a portfolio consisting of a long call and a short put with the same strike and expiration is equivalent to a forward contract.
2. The relationship must hold to prevent arbitrage opportunities.
3. The formula incorporates:
   • $C_0$ = Call option price
   • $P_0$ = Put option price
   • $S_0$ = Current stock price
   • $X$ = Strike price
   • $r$ = Risk-free rate
   • $T$ = Time to expiration

This relationship is essential for understanding option pricing and identifying arbitrage opportunities in derivatives markets.