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CFA Level I · CFA Level I Exam · Valuing a Derivative Using a One-Period Binomial Model

A stock trades at 50. Over one period it can rise to 60 (u = 1.20) or fall to 40 (d = 0.80). The risk-free rate is 5% per period. The risk-neutral probability of an up move is closest to:

The risk-neutral up probability is (1.05 - 0.80) divided by (1.20 - 0.80), which equals 0.625. The numerator uses the risk-free growth factor less the down factor, and the denominator is the spread between up and down factors.

  1. A0.50
  2. B0.625Correct
  3. C0.75

Explanation

pi = (1 + r - d)/(u - d) = (1.05 - 0.80)/(1.20 - 0.80) = 0.25/0.40 = 0.625. Using 0.50 ignores the risk-free rate; 0.75 is wrongly (u - 1.05)/... style miscalculation, e.g. 0.30/0.40.

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