FRM Part I · FRM Exam Part I · Binomial Trees
A stock index stands at 100 and pays a continuous dividend yield of 2%. The risk-free rate is 6% continuously compounded. In a one-year single-step tree, u = 1.15 and d = 0.90. What is the value of a one-year European put on the index with strike 100?
The put is worth about 4.11. With the 2% dividend yield, the up probability is (e^0.04 - 0.90)/0.25 = 0.563. Only the down node pays 10, with probability 0.437. Discounting 4.368 at 6% for one year gives 4.11.
- A4.11Correct
- B3.32
- C4.20
- D5.30
Explanation
p = (e^(0.06-0.02) - 0.90)/0.25 = (1.040811 - 0.90)/0.25 = 0.5632. The put pays 0 at 115 and 10 at 90. Value = e^-0.06 x (1 - 0.5632) x 10 = 0.94176 x 4.3676 = 4.11. Ignoring the dividend yield gives 3.32.
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