FRM Part I · FRM Exam Part I · Binomial Trees
A stock trades at 100. Over one year it will either rise to 120 or fall to 80. The risk-free rate is 5% per year with annual compounding. What is the value today of a one-year European call option with a strike of 100?
The call is worth 11.90. The risk-neutral up probability is 0.625, the expected payoff is 0.625 × 20 = 12.50, and discounting that one year at 5% gives 11.90. Skipping the discounting step gives the incorrect figure of 12.50.
- A11.90Correct
- B12.50
- C9.52
- D7.14
Explanation
The risk-neutral probability of an up move is p = (1.05 - 0.80)/(1.20 - 0.80) = 0.625. The call pays 20 in the up state and 0 in the down state. Its value is 0.625 × 20 / 1.05 = 11.90. The 12.50 option omits discounting, and 7.14 uses the down-state probability 0.375 instead of p.
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