FRM Part I · FRM Exam Part I · Properties of Options
A non-dividend-paying stock trades at 50. A European call on the stock has strike 45 and expires in one year. The continuously compounded risk-free rate is 4% per year. What is the no-arbitrage lower bound for the call price?
The lower bound is the stock price minus the present value of the strike: 50 - 45e^(-0.04) = about 6.76. The strike is discounted because it is paid in one year. Using the undiscounted intrinsic value of 5.00 understates the bound.
- A6.76Correct
- B5.00
- C3.16
- D0.00
Explanation
For a European call on a non-dividend stock, the lower bound is max(S - K e^(-rT), 0). 45 x e^(-0.04) = 43.24, so the bound is 50 - 43.24 = 6.76. Using S - K (5.00) ignores discounting of the strike. Using K e^(+rT) compounds the strike forward and gives 3.16, which is wrong.
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