FRM Part I · FRM Exam Part I · Binomial Trees
A stock has an annual volatility of 30%. An analyst builds a Cox-Ross-Rubinstein binomial tree with time steps of 0.25 years. What is the up factor u that matches the volatility?
The up factor is 1.1618. In the CRR tree u equals e raised to σ times the square root of Δt. With σ of 30% and Δt of 0.25, the exponent is 0.15, so u is about 1.1618.
- A1.3000
- B1.0779
- C1.1618Correct
- D1.0942
Explanation
In the CRR tree u = exp(σ√Δt). Here σ√Δt = 0.30 × 0.5 = 0.15, so u = e^0.15 = 1.1618. Using 1+σ gives 1.30. Using σΔt = 0.075 gives 1.0779, because the time scaling should be the square root of Δt, not Δt itself.
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