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FRM Part I · FRM Exam Part I · Properties of Options

A non-dividend-paying stock trades at 30. An American put on it has a strike of 50 and is priced at 19.00. Ignoring transaction costs, which action locks in an arbitrage profit?

Buy the stock and the put for 49 in total, then exercise the put immediately and receive the 50 strike, earning 1 risk-free. An American put must be worth at least its intrinsic value of 20, so a price of 19 allows arbitrage.

  1. ASell the put and short the stock, earning 30 + 19 now
  2. BBuy the stock and the put for 49 in total, then exercise the put immediately to receive 50, a profit of 1Correct
  3. CBuy the put and short the stock, then wait until expiry
  4. DSell the put and buy the stock, then hold both to expiry

Explanation

An American put can always be exercised at once, so it must be worth at least K - S0 = 50 - 30 = 20. At 19.00 it is underpriced by 1. Buying the stock (30) and the put (19) costs 49, and immediate exercise delivers the stock for 50, a riskless profit of 1. The other strategies take on market risk or do not capture the mispricing.

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