# Price of call option using one period binomial model

This about the example in CFA book 2016 under section 6.6 of reading 49. The CFA book says below

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call price of 10.0259. Can anyone help?

S+ = 71.43 and S- = 38.95

So C+ = Max(0, 71.43-50) = 21.43

and C- = MAx(0, 38.95-50) = 0

Risk Neutral probability is 0.50406 i.e. (1.0488 - 0.7385)/(1.3541-0.7385)

using all this the call price today would be [21.43 * 0.50406 + 0]/[1.0488^0.75] = 10.423

I am raising the power to 0.75 because it is 9 month option so 9/12 = 0.75.

CFA book says call price is 10.0259 but I am getting 10.423

Anyone can point where I am missing or CFA book has wrong answer?

risk

Have you checked the curriculum errata? I also get 10.42.

You can ask CFAI by emailing them. Would be nice to know who is right, the book or us.

I checked errata and it is not in their list. I was planning to write to CFAI but thought of first checking here in case anyone is getting what book is saying. I will soon drop a note to CFAI and update here when I get any response from them

Great!

Thanks

If it’s a 9-month option, then the risk-free rate should be a 9-month rate, not a 12-month rate. Isn’t 4.88% the annual rate?

He used 1.0488^(0.75) as discount factor, so that was not the error.

I was talking about the rate to use in computing the risk-neutral probability.

Good point. The risk-free rate used to calculated the risk-neutral probability is not adjusted for the tenor of the call. Not in the Schweser’s nor in the CFAI book. It uses the “r” directly. I will run a calculation for that case.

It darned-well ought to be.

Even after using 1+r as 1.03638 instead of 1.0488 the call price coming out approx 10.005 which is again different from what CFA book says.

I have dropped an email to CAFI. They have send it to Education research department. Let’s see what they say

Thanks for the calculation! Was about to do it.

Don’t forget to tell us. I could be 95% sure the book had a mistake, in the calculation or in the wording.

First CFAI replied to my emal that interest rate to be used is 0.0366 [=0.0488 * (9/12)].

I then replied back that even after using 0.0366 the answer I am getting for call price is 10.01 and not 10.0259.

Then they replied that 10.01 is also correct. The CFAI has used excel to calculate the answer and hence book is saying 10.0259

Below is what they replied second time

"The answer you get is basically the same as what we showed; the difference between the answer you arrive at and the amount shown in the exhibit is due to rounding. The exhibit was prepared using excel.

Regards,

CFA Institute"

Yuck.

Another thing is that didn’t see any example with that procedure. That was a 270-day call, what about a 2-year call? Must we use 1.098? Didn’t find that case in the books (shweser or CFAI).