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

## 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.

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