FRM Part I · FRM Exam Part I · Binomial Trees
A CRR binomial tree uses quarterly steps (Δt = 0.25 years) and an up factor of u = 1.10517. What annual volatility does the tree assume?
The tree assumes an annual volatility of 20%. The log of u is 0.10, which equals σ times the square root of Δt. With Δt of 0.25 the square root is 0.5, so σ is 0.10 divided by 0.5, or 20%.
- A10.0%
- B20.0%Correct
- C40.0%
- D2.5%
Explanation
ln(1.10517) = 0.10, which equals σ√Δt. Since √0.25 = 0.5, σ = 0.10/0.5 = 20%. Dividing by Δt instead (0.10/0.25 = 40%) is the wrong scaling.
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