FRM Part I · FRM Exam Part I · Binomial Trees
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 a positive risk-free rate. Which statement about the tree is correct?
With no dividends and a positive interest rate, an American call is never exercised early because its continuation value always exceeds its intrinsic value. Early exercise would give up interest on the strike and the option's insurance value. So the binomial tree values the American call the same as the European call.
- AAt every node the call's continuation value is at least its intrinsic value, so early exercise is never optimal and the American call equals the European callCorrect
- BEarly exercise is optimal at nodes where the call is deep in the money, because holding it exposes the holder to downside risk
- CEarly exercise becomes optimal at the final-but-one step whenever the up factor exceeds 1.2
- DThe American call must be worth strictly more than the European call because it can be exercised at any time
Explanation
For a non-dividend-paying stock, the call's value before expiry is at least S minus the present value of K, which exceeds S minus K when rates are positive. Exercising early would forfeit the time value of money on the strike and the option's insurance value. So the tree gives continuation value above intrinsic value at every node, and the American and European values coincide. The other options wrongly assume an early-exercise premium.
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 100. In a two-step binomial tree each step is one year, with u = 1.10 and d = 0.90. The risk-free rate is 5% per year, com…
- 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 …
- 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…
- For an American put on a non-dividend-paying stock, holding the other inputs fixed, which statement about the incentive to exercise early at…