FRM Part I · FRM Exam Part I · Binomial Trees
A stock has annual volatility of 20%. A one-year binomial step is built with the Cox-Ross-Rubinstein (CRR) approach, which sets u = e^(σ√Δt) and d = 1/u. What is the down factor d, to four decimals?
The down factor is 0.8187. Under CRR, d is the reciprocal of u, so d equals e raised to minus σ times the square root of Δt. With σ of 20% and a one-year step, d = e^-0.20, which is 0.8187, not 1 minus 20%.
- A0.8187Correct
- B0.8000
- C0.8333
- D0.7788
Explanation
With Δt = 1, σ√Δt = 0.20, so u = e^0.20 = 1.2214 and d = e^-0.20 = 0.8187. The value 0.8000 is the common mistake of using 1 − σ, which is not the CRR formula. The value 0.8333 comes from 1/1.2.
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 modelled on a one-step binomial tree with an up factor of 1.25 and a down factor of 0.80. The gross risk-free return over the ste…
- A stock trades at 50 and in one period will move to 60 or 40. A European put with strike 48 expires at the end of the period. What is the pu…
- A stock starts at 100 and in each of two periods moves up by a factor of 1.2 or down by a factor of 0.8. The risk-free rate is 5% per period…
- A stock is at 100 and will move to either 110 or 90 in one period. The risk-free rate is 2% per period (simple). Investors believe the real-…
- In a one-period binomial tree, a stock priced at 100 can move up to 120 or down to 80. A European call option with strike 100 expires at the…
- An analyst values an American call option on a stock that pays no dividends during the option's life, using a multi-step binomial tree with …