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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 3 in 4 months. An American call has strike 55 and expires in 6 months. The continuously compounded risk-free rate is 4%. Using the standard condition for ruling out early exercise just before the ex-dividend date, which conclusion is correct? (Use exp(-0.04*(2/12)) = 0.9934.)

Early exercise cannot be ruled out. The test requires the dividend to be no more than K times one minus the discount factor over the remaining two months, which is about 0.36. The dividend of 3 exceeds this, so exercising just before the ex-dividend date may be optimal.

  1. AEarly exercise just before the dividend cannot be ruled out, because D = 3 exceeds K(1 - exp(-r*(T2-T1))) = 0.36Correct
  2. BEarly exercise is ruled out, because D = 3 is less than the strike
  3. CEarly exercise is ruled out, because the option is in the money
  4. DEarly exercise is optimal at time zero because the call is in the money

Explanation

Early exercise just before the ex-dividend date is not optimal if D <= K(1 - exp(-r(T2-T1))). Here the interval from dividend to expiry is 2 months, so K(1-0.9934) = 55*0.0066 = 0.363. Since D = 3 > 0.36, the condition does not hold and early exercise could be optimal. Being in the money alone is not a rule.

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