FRM Part I · FRM Exam Part I · Properties of Options
A European put has strike 60, expires in 6 months, and the stock is at 52. The continuously compounded risk-free rate is 5% and the stock pays no dividends. What is the lower bound p >= K*exp(-rT) - S0 (nearest cent)?
The lower bound is 6.52. For a European put on a non-dividend stock, the minimum value is the discounted strike minus the stock price. Discounting 60 at 5% for six months gives 58.52, and subtracting 52 leaves 6.52, which is below the 8.00 undiscounted intrinsic value.
- A8.00
- B6.52
- C7.26Correct
- D9.48
Explanation
PV of strike = 60*exp(-0.025) = 60*0.975310 = 58.519. Lower bound = 58.519 - 52 = 6.52. Check: option listed as 7.26 would be wrong; recompute: 58.52 - 52 = 6.52, so the correct value is 6.52.
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