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

Holding other inputs constant, a rise in the risk-free rate per period in a one-period binomial model most likely causes the risk-neutral probability of an up move to:

The risk-neutral up probability rises when the risk-free rate rises, because pi equals (1 + r - d) divided by (u - d). The underlying must earn the higher risk-free return in a risk-neutral world, so the up move needs more weight.

  1. Afall, because discounting becomes heavier
  2. Brise, because the underlying must grow faster in a risk-neutral worldCorrect
  3. Cstay unchanged, because it depends only on u and d

Explanation

pi = (1 + r - d)/(u - d). A higher r raises the numerator, so pi increases. In a risk-neutral world the underlying must earn the higher risk-free rate, requiring a greater up probability.

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