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

A stock trades at 60 and will pay a dividend of 2 in exactly six months. A European call on the stock has strike 55 and expires in one year. The continuously compounded risk-free rate is 5% per year. What is the lower bound for the call price?

The lower bound is the stock price minus the present value of the dividend minus the present value of the strike: 60 - 2e^(-0.025) - 55e^(-0.05), which is about 5.73. The dividend must be discounted. Ignoring it gives 7.68, which is too high.

  1. A5.73Correct
  2. B7.68
  3. C5.68
  4. D9.63

Explanation

With a known dividend, the lower bound is S - PV(D) - K e^(-rT). PV(D) = 2 x e^(-0.025) = 1.95. PV(K) = 55 x e^(-0.05) = 52.32. The bound is 60 - 1.95 - 52.32 = 5.73. Ignoring the dividend gives 7.68. Subtracting the dividend undiscounted gives 5.68. Adding the dividend gives 9.63, which is the wrong sign.

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