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

A non-dividend-paying stock trades at 48. A European call with strike 50 and one year to expiry is priced at 3.50. The continuously compounded risk-free rate is 4% per year. Using put-call parity, what is the price of the European put with the same strike and expiry?

The put is worth about 3.54. Put-call parity says put equals call plus the present value of the strike minus the spot price. The discounted strike is about 48.04, so 3.50 plus 48.04 minus 48 gives roughly 3.54.

  1. A3.54Correct
  2. B3.46
  3. C5.50
  4. D1.50

Explanation

Parity gives p = c + K e^(-rT) - S. K e^(-0.04) = 50 x 0.960789 = 48.0395, so p = 3.50 + 48.0395 - 48 = 3.54. The 3.46 option subtracts the discounted strike and adds the stock, which is a sign error. The 5.50 option fails to discount the strike.

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