Put-call parity, the reversal trade

Question

Stock at 50, zero interest rates, no dividends. The 1-year 50-strike European call trades at \4 and the 50-strike put at \7. Is there an arbitrage? State the parity relation, find the violation, and give the exact trade and riskless profit.

Accepted Answer

Put-call parity (zero rates, no dividends): C - P = S - K. Long call plus short put replicates a forward, paying ST - K in every state. Here the left side is 4 - 7 = -3, but the right side is 50 - 50 = 0. The synthetic forward is \3 too cheap, which means the put is expensive relative to the call. The trade (a "reversal"): buy the cheap synthetic, sell the rich leg. - Buy the call: -4 - Sell the put: +7 - Short the stock: +50 Net received today: \53. At expiry you must buy one share at \50 to cover the short, in every state: - If ST 50: exercise your call, buy at 50; the put you sold expires …

Put-call parity, the reversal trade

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