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FRM Part I · FRM Exam Part I · Options Markets

A European call and put on the same non-dividend-paying stock both have strike USD 100 and expire in one year. The call trades at USD 9, the put at USD 5, the stock at USD 102, and the continuously compounded risk-free rate is 3%. Which statement is correct?

Parity requires C + PV(K) = P + S. Here the left side is 9 + 97.04 = 106.04 and the right side is 5 + 102 = 107.00, so parity fails. The call is cheap relative to the put and stock; buy the call, sell the put, and short the stock.

  1. ANo arbitrage exists because the call exceeds the put
  2. BPut-call parity is violated; the call is overpriced relative to the put, so sell the call, buy the put, and buy the stockCorrect
  3. CPut-call parity holds since C - P = 4 is close to S - K = 2
  4. DPut-call parity is violated; the call is underpriced, so buy the call and sell the put and the stock

Explanation

Parity: C + K e^{-rT} = P + S. K e^{-0.03} = 100 × 0.970446 = 97.04. Left side: 9 + 97.04 = 106.04. Right side: 5 + 102 = 107.00. The right side is larger, so the put plus stock is expensive and the call is cheap, so the call is underpriced, not overpriced. Therefore the correct arbitrage is to buy the call, sell the put, and short the stock, which is the last option.

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