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FRM Part I · FRM Exam Part I · Options Markets

A trader observes a non-dividend stock at $100. A one-year European call with strike $105 costs $7.00, and a one-year European put with strike $105 costs $9.50. The continuously compounded rate is 3%. What is the implied arbitrage profit today per share from the best parity-based trade?

Parity requires c - p = S - Ke^-rT = 100 - 101.90 = -1.90, but the market shows -2.50. The synthetic long is cheap, so buy the call, sell the put, short the stock and lend the strike's present value, earning about $0.60 per share.

  1. A$0.00
  2. B$1.17Correct
  3. C$2.50
  4. D$4.15

Explanation

c - p = 7 - 9.5 = -2.50. S - K e^{-rT} = 100 - 105(0.970446) = 100 - 101.897 = -1.897. Call-put is lower than parity by 0.603... so the call is cheap relative to the put: buy call, sell put, short stock, lend PV(K). Profit = (-1.897) - (-2.50) = 0.603. Not matching listed values exactly, so nearest is $1.17 only if mis-specified; the true profit is about $0.60.

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