FRM Part I · FRM Exam Part I · Binomial Trees
A analyst builds a multi-step tree with Cox-Ross-Rubinstein parameters for a stock with annual volatility of 30%. Each step is 0.5 years (Δt = 0.5), so u = e^(σ√Δt) and d = 1/u. What is the up factor u per step?
The up factor is about 1.2363. Under the CRR calibration, u equals e raised to volatility times the square root of the step length, which is 0.30 × 0.7071 = 0.2121, and e^0.2121 ≈ 1.2363.
- A1.1618
- B1.2363Correct
- C1.3000
- D1.3499
Explanation
σ√Δt = 0.30 × √0.5 = 0.2121. u = e^0.2121 ≈ 1.2363, and d = 1/u ≈ 0.8089. The 1.3499 option forgets the square root of time. The 1.1618 option uses σΔt = 0.15 instead of σ√Δt.
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