Put-call parity spot check, find the arb

Question

Stock at 100, zero interest rates, no dividends. The 1-year 100-strike European call trades at \8 and the 100-strike put at \6. 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 + short put replicates a forward: at expiry it pays (ST - K)^+ - (K - ST)^+ = ST - K in every state. Here the left side is 8 - 6 = 2, the right side is 100 - 100 = 0. The synthetic forward is trading \2 rich, calls are expensive relative to puts. The trade (a "conversion"): sell what's rich, buy the replica. - Sell the call: +8 - Buy the put: -6 - Buy the stock: -100 Net outlay today: \98. At expiry, in every state: - If ST 100: called away, deliver stock, receive 100; put dies. Total = 100. - If ST \le 100: exercise the put…

Put-call parity spot check, find the arb

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