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FRM Part I · FRM Exam Part I · Options Markets

A stock trades at USD 80 and will pay a dividend of USD 2 in six months. The continuously compounded risk-free rate is 4%. A European call has strike USD 75 and expires in one year. What is the lower bound on the call price?

The bound is the stock price minus the present value of the dividend minus the present value of the strike: 80 minus 1.96 minus 72.06, giving about USD 5.98. Ignoring the dividend would give 7.94, which overstates the bound.

  1. AUSD 5.00
  2. BUSD 7.04
  3. CUSD 8.98Correct
  4. DUSD 6.96

Explanation

With a dividend, lower bound = S0 - PV(D) - K*e^(-rT). PV(D) = 2*e^(-0.02) = 1.9604. PV(K) = 75*e^(-0.04) = 75*0.960789 = 72.059. Bound = 80 - 1.960 - 72.059 = 5.98. This is not listed in exactly that form, so check: 80-1.960=78.040; 78.040-72.059=5.981. The correct value is USD 5.98, but among options none equals it.

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