# CFA 2012 AM Mock: Q7 Derivatives

In the AM derivatives case they note the following:

• Up Move on Stock 15%
• Down Move on Stock 10%

I was under the impression that to calculate the down move you took the Up move 1.15 and take the reciprocal 1/1.15 = .8696

Therefore U = 1.15 & D = 0.8696

They are using U = 1.15 and D = 0.9 which is not the reciprocal. For every EOC and example in the text they used the reciprocal method…any ideas? These should be easy points for me and now I’m shakey on the easiest part…ugh!!

Schweser uses that convention, but the CFAI text doesn’t really. If you can find an example in the CFA text on pricing of options using the discrete method, please let me know bc I haven’t seen it…

No its the magnitude of the up move they’ve given you there, i.e. in an up move the stock will go up 15%

To calculate the probability you have to use 1+r-d/ (u-d). This will give you the risk neutral probability of an up move. Down move is simply 1 - u since the probabilities have to equal 100%

You’re right Cleo, but his question revolves around the size of the up move, not the probability. Ie, Schweser quotes the down move as 1 divided by the Up move, but this convention isnt really in CFA texts

the question he’s referencing does actually reference the probabiltiy of an up move. When calculating the value of the optino yo need all of the pieces.

Well, yes, but regardless of what else is in the question, he’s not asking about probability. He’s asking about the correct way to determine the down move. And the answer is that it nots always going to be 1 divided by the Up move

Ok, for the exam I’ll use the magnitde of the up and down price movements on the underlying given in the problem.

• Up move on stock 15%
• Down move on stock 10%

So U=1.15 and D = 0.9 to caluclate the risk neutral probabilities. If I don’t get the right answer I’ll try it the other way…

Thanks for the responses

another question on this item set - question 9

why dont you use 1.03^(60/365) when you are finding the up move and then ultimately discounting the option price??

i.e. 1.03^(60/365) - .90 / (1.15 - .90)

thanks!

The reciprical method is only used when you are not given the down move. If you are given a down move, then USE IT. I’m guessing they would give us both. One thing that you have to watch for is the time for the risk free rate, on this one(or maybe a different one) I couldn’t come up with an answer because I didn’t adjust the risk free rate for being less than one period.

Kzacca01…you do have to adjust the risk free rate!

Match the time period in the calculation of risk neutral probabilities as well as discounting in the binomainal tree

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I have not seen the problem but are you saying that they next option period is not assumed to be 1 year? If so that would stump me on two counts. First, would you unanualize the risk free rate to discount the option value? Second, would you use the period unanulized rate to calculate the probabiity of an up move? Say the RFR is 7% and the next node was 180 days. Would you discount at 1.035, 1.07^180/365 or something else. And when calclating the prob of up would you use 1.035 - D/U-D. I did not see any problems where it was anything but a full year. Maybe I was better off in my ignorance that such a senario was possible

You are abs right. I also found their solution wrong!

This is a clear bug/defect/error on the part of CFAI. The risk free rate compounding should match the duration of that option, ie either it should be a 1 year option or it should be discounted for 2 months only

Do others disagree with me. I could not find a similar example in CFAI text

this is why i am asking. the up/down move needs to be adjusted for time (60/365) as it says it is a 60 day option… im almost sure of it.

this is what makes me think this type of question wont even be on the real exam as its too ambiguous…