FRM Part I · FRM Exam Part I · Binomial Trees
A stock is at 100. In each of two periods it moves up by a factor of 1.10 or down by a factor of 0.90. The per-period risk-free rate is 0%, so the risk-neutral up probability is 0.50. For a European call with strike 100 expiring after two periods, what is the delta at time 0?
The initial delta is 0.525. Roll back to the first-step nodes: the option is worth 10.5 after an up move and 0 after a down move. Dividing the 10.5 difference by the stock price difference of 20 gives 0.525.
- A0.525Correct
- B0.955
- C0.263
- D0.105
Explanation
Terminal prices are 121, 99 and 81, giving payoffs of 21, 0 and 0. The value at the up node (110) is 0.5 × 21 = 10.5, and at the down node (90) it is 0. Delta at time 0 = (10.5 - 0)/(110 - 90) = 0.525. The 0.955 option is the delta at the up node, 21/(121 - 99), which is a later-step delta.
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 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 index stands at 100 and pays a continuous dividend yield of 2%. The risk-free rate is 6% continuously compounded. In a one-year sing…
- 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…
- A stock trades at 50. Over one year it moves up by a factor of 1.2 or down by a factor of 0.8 in a single-step tree. The continuously compou…
- An American call option is written on a stock that will pay one large cash dividend during the option's life. In a binomial tree that models…
- A two-step tree has S0 = 100, u = 1.1 and d = 0.9. The risk-neutral up probability is 0.6 and the per-step discount factor is 0.96. Using ba…