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FRM Part I · FRM Exam Part I · Options Markets

For European options on a non-dividend-paying stock with the same strike and maturity, the stock price is $40, the strike is $42, and the call is worth $3.00 while the put is worth $4.50. If the put is actually quoted at $4.00 and nothing else changes, which statement is correct about the implied strike present value PV(K) from parity, and the mispricing?

Rearranging parity gives present value of the strike as stock price plus put minus call, which is 40 + 4.50 - 3.00 = 41.50. The fair put is $4.50, so a quoted put of $4.00 is cheap by $0.50.

  1. APV(K) implied is $41.50; the market put at $4.00 is cheap relative to parity by $0.50Correct
  2. BPV(K) implied is $41.50; the put at $4.00 is rich by $0.50
  3. CPV(K) implied is $40.00; there is no mispricing
  4. DPV(K) implied is $43.50; the put at $4.00 is cheap by $0.50

Explanation

Parity: PV(K) = S0 + p - c = 40 + 4.50 - 3.00 = 41.50, which is consistent with the parity-implied put of 4.50. Parity-consistent put is 4.50, so a market put at 4.00 is $0.50 cheap. Rich would be the reverse; using S0 + c - p gives 38.50 mistakes.

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