# Option Binomial

So, the Schweser material says that you calculate a down move at 1/U while in the CFAI EOC they always tell you that the up is 20% and down is say, 15%. In the few cases that I checked the CFAI material down never equaled 1/U. Does anyone know how this will be presented on the exam?

I’m not sure if you are talking about the value of the move or the probability of it. But they would both have to be calculated.

Value. for example Schweser in their book will give you the value of up at 1.33 they then say you calculate the value of down as 1/1.33. In CFAI they give you value of up and value of down in terms of percent. I can solve the CFAI fine but what has me confused is why Schweser does it this way and which should we expect on the exam

I remember them being slightly different. I’m scheduled to review that material tomorrow, so I can’t recall the specifics of what you are getting at. I do remember pausing at the material there and having to reconcile how they did them differently. I think I stuck w/ the CFAI method, but I can’t recall. I’ll try to come back to you tomorrow on this. It’s derivatives Wednesday for me.

Is the CFAI automatically giving you the risk neutral probabilities? I didn’t use the CFAI text to learn this material.

No, we are not talking about risk neutral probs. This is value of up move and value of down move. Look at CFAI reading 62 page 231 prob 2. you will see value of up is 10% and value of down is 15% Then look at Schweser reading 62 page 62 example. there they say value of up is 1.33 and do not give you value of down. They tell you to calculate it as 1/U Thats great but clearly under the CFAI example 1/1.10 is not 15%. So, I assume if they give you the value of the down you use it and if they do not you use the Schweser method?

from what i know, its just about how you decide to model volatility a common way is to do down=1/up CFAI could be using some other model and giving you the up and the down, so just use what they give you

I know that Schweser uses D = 1/U. I think that’s incorrect. On the exam, you’ll likely be given the size of the up and down movements just like the CFAI text does. In real life, size of up and down moves are calculated using permutation.

So how do you calculate the risk neutral probabilities if they give you the size of the up move as a percent? Let’s say the size of an up move is 40% for example? It doesn’t work to use the formula I have which is 1+Rf-D/U - D

^ are you talking about the “size of movements” or the probabilities (Pi up, Pi Down). Because the formula you mentioned above is used to calculate the Pi

I want to know how you calculate Pi when the size of the movements isn’t given in decimal form (like 1.33), and is instead given in percentage form (like 15%).

For example, if they give you the size of an up move as 1.33 then the formula would come out (let’s say risk free rate is 5%) 1+.05-(1/1.33) / 1.33-.75 = .51 So the risk neutral probability of an up move (pi) is 51% If they give the movement size as a percent, the above formula doesn’t work. So how do you do it when they give the movement size as a percent instead.

Well, if the stock goes up by 15%, the size is 1+ 0.15 = 1.15 If it goes down by 15%, the size is 1-0.15 = 0.85 Helps?

Well don’t I feel stupid. So the original poster is basically questioning why Schweser’s method gives the down move size as .87 instead of .85.

This is obviously wrong in Schweser’s. There is no choice here, this is straightforward. If a stock is at \$100 and it can go up by 15% or down by 10%, then it can only have these two values: Either 115 or 90. You are always told what these percentages are.

Great that is what I was wondering. I got the first CFAI question wrong because I ignored the down data they gave and calculated it the way Schweser tells you to.