Binomial Interest Rate trees

CFA Level II Fixed Income
#1

I seem to be missing a link when calculating binomial interest rate trees.

Considering the following tree:

Time 0 Time 1 Time 2 Time 3

1.000% 1.6121% 1.7862% 2.8338%

1.1943% 1.3233% 2.0994%

0.9803% 1.552%

1.1521%

I completely understand how to arrive at 2.8338%, 2.0994%, and 1.552% from 1.1521%, and to 1.3233% and 1.7862% from 0.9803% (multiplying by varying e^x(std dev).

However, I do not see how to get from 0.9803% to 1.1521%, or how to get from 1.1943% to 0.9803%. The CFAI materials seem to provide these numbers as “assumptions” out of the blue with no explanation of where they come from (unless I am missing the connection).

Can anyone point me in the right direction? This is related to Volume 5 reading 44, specifically “finding forward interest rates”.

#2

Interestingly, I just wrote an article on creating a binomial interest rate tree: http://financialexamhelp123.com/creating-a-binomial-interest-rate-tree/

#3

The LOS related to the above is

c) describe a binomial interest rate tree framework

which in my mind is equivalent to saying “don’t bother and move on”.

#4

I was reading that - I guess my algebra skills are not up the task anymore. I tried to work through it and ended up with the wrong answer. I may consider listening to the fellow below me (at this point I could write an essay about the purpose of binomial interest rate trees), but it seems like they are important further on this section.

#5

I tried to work through my problem using your example but the end result i got was not correct. It also doesnt seem like I would ever be able to complete a problem like that in exam situations so I just need to hope for the best I guess and understand the purpose / reasoning / process well.

#6

You don’t really get to 1.1521% from 0.9830%. They’re based on two different maturities on the forward curve, which can be anything. It simply depends on the shape of the underlying par curve, spot curve, forward curve.

It’s like asking how you get from a 1% yield on 1-year bonds to a 3% yield on 2-year bonds: it’s just the shape of the yield curve.

#7

Okay - so in order to complete a forward branch in the Interest Rate tree you need to have at least one of the nodes, correct?

#8

Exactly!

#9

Guess I’ve been trying to turn water into wine for a couple hours - thanks for ending it!

#10

You’re quite welcome.