Put-call parity, spot the free money

Question

A non-dividend stock trades at \100. The 6-month call struck at 100 costs \6, and the 6-month put struck at 100 costs \4. Assume interest rates are negligible. Is there an arbitrage? If so, construct it. State the parity relationship it violates.

Accepted Answer

The relationship. For European options on the same strike K and expiry, put-call parity says C - P = S - K\,e^{-rT}. With r \approx 0 and K = S = 100, the right side is 100 - 100 = 0, so the call and put must trade at the same price. The market has C - P = 6 - 4 = 2 
e 0: the call is rich relative to the put. Why parity holds. A long call plus a short put (same strike) pays \max(ST - 100, 0) - \max(100 - ST, 0) = ST - 100 at expiry, no matter where ST lands. That is a forward to buy the stock at 100. Its fair cost today is S - K e^{-rT} \approx 0, so paying \2 for it is overpaying. Construct…

Put-call parity, spot the free money

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