Binomial Tree: Will It Be Tested?

CFA Level II
#1

To what extent do you think this could be tested? Conceptually or an actual calculation?

I can’t imagine having to know t = (1 + rf + d) / (u - d); d = down move on stock = 1 - % of the down move; u = up move on stock = 1 + % of up move. C = (tc+ + (1 - t)c-) / (1 + rf); c+ = S+ - Exercise Price; c- = S- - Exercise Price; S+ = Current Stock Price * u; S- = Current Stock Price * d

#2

i’ve seen interest rate trees come up multiple times during the samples. For me personally, I would very much rather they ask bionomial tree type questions which is just straight up calculation over something conceptual and theoretical.

#3

I hope so. I way prefer these quantitative questions where you either know how to do it or you don’t, than these wild qualitative questions with triple negatives and all sorts of other nonsense. “Which of the following isn’t not an incorrect sign of correct corporate governance?”.

#4

You bet your ass it’ll be tested. Be prepared to perform the calculations. They’re not tough! Don’t expect a huuuuge tree. Just a few stages. It’s easy!!

Get good at guessing if you don’t plan to perform these calculations. They’re important. Binomial trees are extremely useful. Test-makers usually check that you know the important things.

Good luck to you.

#5

Yeah I definitely think they’re important. Dr. Chance (author of the derivatives readings) always put these problems on our exams, so he at least thought they were important. One caveat that we frequently had to do was adjust the model if it was an american option. He liked to ask what was the added value from making the option american (versus just european). This is really only done with puts, but a good exercise if you don’t know how to do it. Don’t know if that would show up on a test, but at this point, it’s anyone’s guess as to what will show up on the exam.

#6

Im a bit confused on how the added value would work here? Would we just lock in a gain one node up?

#7

It can be exercised before expiry. Generally there is some rule assumed about the behavior.

#8

I’d prefer that any day to those convoluted FRA questions…

#9

+1

#10

+1

#11

I’m down with binomial tree, risk neutral probabilities, and FRA. But I agree, FRAs are much more time consuming and just tedius

#12

Yes. So it’s kind of hard to illustrate, but say you have a put option you’re valuing with the 2 period model. Strike is 120. Once you solve the p++ and p±, you find the value at p+. Say this value is $6.50. If the price of the underlying is 115, then at this node, exercising would give you a gain of 5 bucks. But the model says 6.50, so you WOULD NOT exercise.

Move down the model. Say the price of the underlying is 90 at p-. You solve the model and get $25.50. If you excercise, you have a gain of 30, which is 120 - 90. But the model only gives you 25.50. SO YOU WOULD EXERCISE.

Then to find the value today, work the model the same way you normally would, use 6.50 for the p+, but use 30 for P- instead of 25.50. Then once you get to today, say your model says it should be worth 18 bucks. But if the underlying price is 100, you can excercise for a gain of 20. So the value today would be 20.

A normal euro option would have 6.50 and 25.50 for p+ and p-, respectively. Then if you used those two numbers to get to today, say you got 17 bucks.

17 vs 20 bucks… the american aspect of this option adds 3 dollars.

I know that seems complicated, and given the text did not illustrate an example of an american option using the binomial, it miight not be worth spending too much time, especially in this, the 11th hour

#13

got it thanks great explanation!