CFA Level I · CFA Level I Exam · Valuing a Derivative Using a One-Period Binomial Model
A stock trades at 50. In a one-period binomial model the up factor is 1.20, the down factor is 0.90, and the risk-free rate for the period is 5%. The risk-neutral probability of an up move is closest to:
The risk-neutral up probability equals (1 + r − d) divided by (u − d). With r of 5%, u of 1.20 and d of 0.90, this is 0.15 divided by 0.30, which is 0.50.
- A0.33
- B0.50Correct
- C0.67
Explanation
π = (1 + r − d)/(u − d) = (1.05 − 0.90)/(1.20 − 0.90) = 0.15/0.30 = 0.50. Using 1.05 − 0.90 over 1.20 gives a wrong denominator. Option C results from (1.20 − 1.05)/(1.20 − 0.90)... which is 0.50 too, so the 0.67 value comes from dividing by 0.225.
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