FRM Part I · FRM Exam Part I · Properties of Options
A stock trades at $100 and is expected to pay a single dividend of $3 in four months. The continuously compounded risk-free rate is 6%. A European call with strike $95 expires in six months. What is the lower bound on the call price?
The bound is 100 minus PV of dividend 2.94 minus PV of strike 92.19, about $4.87.
- A$5.00
- B$7.85Correct
- C$5.00 plus the dividend, i.e. $8.00
- D$2.00
Explanation
With a dividend the bound is S0 - D e^(-r t) - K e^(-rT). Dividend PV = 3 x e^(-0.02) = 3 x 0.980199 = 2.941. Strike PV = 95 x e^(-0.03) = 95 x 0.970446 = 92.192. Bound = 100 - 2.941 - 92.192 = 4.867. None of the listed values equals this, so the closest check fails.
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