FRM Part I · FRM Exam Part I · Binomial Trees
A stock trades at 80 and has volatility of 30% per year. A CRR tree uses time steps of three months (Δt = 0.25). What is the stock price at the up node after the first step?
The up-node price is 92.95. The CRR up factor is e raised to σ times the square root of Δt, which is e^0.15 = 1.16183 for 30% volatility and a quarter-year step. Multiplying the starting price of 80 by 1.16183 gives 92.95.
- A92.95Correct
- B86.23
- C92.00
- D107.99
Explanation
σ√Δt = 0.30 × 0.5 = 0.15, so u = e^0.15 = 1.16183. The up node is 80 × 1.16183 = 92.95. The value 86.23 uses σΔt = 0.075 instead of σ√Δt. The value 107.99 ignores Δt and uses e^0.30.
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