FRM Part I · FRM Exam Part I · Binomial Trees
A stock is priced at 50. A two-step tree has u = 1.20, d = 0.80 and a risk-free rate of 5% per step. What is the value of an American put with strike 52, which may be exercised at any node?
The American put is worth about 5.14. At the down node (stock 40), exercising gives 12, which beats the continuation value of 9.52. Using 12 there and 1.43 at the up node, the discounted risk-neutral expectation at the root is 5.14.
- A4.25
- B5.14Correct
- C6.35
- D4.69
Explanation
With p = 0.625, at the down node (S = 40) the continuation value is (0.625×4 + 0.375×20)/1.05 = 9.52. Immediate exercise is worth 12, which is higher, so the node value is 12. At the up node (S = 60) the value is 0.375×4/1.05 = 1.43. At the root, (0.625×1.4286 + 0.375×12)/1.05 = 5.14. This exceeds the immediate exercise value of 2. The European value of 4.25 ignores early exercise.
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
- 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 stock is at 50 and will be either 60 or 40 after one year. The risk-free rate is 5% per year with annual compounding. A trader replicates …
- A stock trades at 100 with annual volatility of 20%. A two-step CRR tree uses Δt = 0.5 years with d = 1/u. What is the difference between th…
- A stock trades at 50. Over one year it can rise by a factor of 1.20 or fall by a factor of 0.80. The continuously compounded risk-free rate …
- A risk analyst values an American call option on a stock that pays no dividends, using a binomial tree. Which statement about early exercise…
- For an American put on a non-dividend-paying stock, holding the other inputs fixed, which statement about the incentive to exercise early at…