FRM Part I · FRM Exam Part I · Binomial Trees
A analyst builds a Cox-Ross-Rubinstein tree for a non-dividend-paying stock with annual volatility of 20%, using time steps of 0.25 years (u = e^(σ√Δt), d = 1/u). Which pair gives the correct up and down factors?
The up factor is 1.1052 and the down factor is 0.9048. With volatility 20% and Δt of 0.25, σ√Δt equals 0.10, so u = e^0.10 and d = e^-0.10. This choice makes the tree's volatility match the lognormal model.
- Au = 1.1052, d = 0.9048Correct
- Bu = 1.2214, d = 0.8187
- Cu = 1.0513, d = 0.9512
- Du = 1.1052, d = 0.8948
Explanation
σ√Δt = 0.20 × 0.5 = 0.10. So u = e^0.10 = 1.1052 and d = e^-0.10 = 0.9048. Using e^0.20 forgets to scale by the square root of Δt; using 1 - 0.1052 for d breaks the u·d = 1 condition.
Did you get it right without looking?
One question tells you little. A timed set on Binomial Trees shows your real accuracy, how long you take and where you lose marks.
More Binomial Trees questions
- A stock is priced at 40. After one period it will be either 50 or 32. The risk-free rate is 5% per period (simple, one-period compounding). …
- A stock trades at 100. Over one year it will either rise to 120 or fall to 80. The risk-free rate is 5% per year with annual compounding. Wh…
- 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?
- A risk manager prices a European call on a non-dividend-paying stock with a CRR binomial tree and steadily increases the number of steps. As…
- A stock trades at USD 50. Over the next year it will either rise to USD 60 or fall to USD 40. A one-year European call has a strike of USD 5…
- A stock is at 100 and in one period will move to either 110 or 90. A European put option with a strike price of 105 expires at the end of th…