FRM Part I · FRM Exam Part I · Binomial Trees
A stock is modelled on a one-step binomial tree with an up factor of 1.25 and a down factor of 0.80. The gross risk-free return over the step is 1.05. What is the risk-neutral probability of an up move?
The risk-neutral up probability is (1.05 - 0.80) divided by (1.25 - 0.80), which is 0.5556. This is the probability that makes the stock's expected growth equal to the risk-free gross return. The figure 0.4444 is the down-move probability, not the up-move probability.
- A0.5556Correct
- B0.4444
- C0.1111
- D0.5000
Explanation
The risk-neutral up probability is p = (gross return - d)/(u - d) = (1.05 - 0.80)/(1.25 - 0.80) = 0.25/0.45 = 0.5556. The value 0.4444 is the down probability (1 - p), which comes from using (u - 1.05) in the numerator.
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