FRM Part I · FRM Exam Part I · Binomial Trees
A stock is priced at 100 and can move to 120 or 80 in one year. The risk-free rate is 5% per year with annual compounding. What is the value of a one-year European put option with a strike of 110?
The put is worth 10.71. Only the down state pays, with a payoff of 30, and its risk-neutral probability is 0.375. The discounted expected payoff is 0.375 × 30 / 1.05 = 10.71. Using the up probability or skipping discounting gives incorrect values.
- A10.71Correct
- B17.86
- C11.25
- D14.29
Explanation
The risk-neutral up probability is 0.625, so the down probability is 0.375. The put pays 0 if the stock is at 120 and 110 - 80 = 30 if it is at 80. Its value is 0.375 × 30 / 1.05 = 10.71. The 17.86 option uses 0.625 for the down state, and 11.25 omits discounting.
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