FRM Part I · FRM Exam Part I · Properties of Options
A non-dividend-paying stock trades at 50. A European put with strike 55 expires in 1 year, and the continuously compounded risk-free rate is 4%. What is the lower bound for the put price?
The lower bound is the discounted strike minus the spot price: 55 times e to the power minus 0.04 is about 52.84, less 50 gives roughly 2.8. Using the undiscounted strike difference of 5 ignores discounting and overstates the bound.
- A5.00
- B0.00
- C2.80Correct
- D7.70
Explanation
Lower bound for a European put on a non-dividend stock is max(K e^{-rT} - S0, 0). 55 e^{-0.04} = 55 x 0.960789 = 52.84. Minus 50 gives 2.84, approximately 2.80 in the rounded option. Using undiscounted strike gives 5.00, which ignores time value of money.
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