Generating Interest Rates for Binomial Tree

CFA Level II Fixed Income
#1

Bit of a longshot as I do not have the actual question - it is a practice question I remember being stumped by that I cannot locate. In the off-chance someone knows what I am talking about, I wanted to ask as it is bothering me I cannot find it.

There was a 2 year binomial interest rate tree, and I am quite certain we did not have any of the rates for a single time period. I believe we had the rates for year 2 filled out, but none of the other rates. Then were asked to price a bond using the tree.

Do we know how to generate rates in a binomial tree for year 1 if we have the rates for year 2 for example ? Or if we have the spot curve ?

I know the method of computing rates for different movements in the same year - multiplying the rate by e^2(sigma).

Is there any other process for filling out rates in a binomial tree that people are aware of ? Either using a spot curve or generating previous rates from later rates ?

I appreciate anyone’s response, sorry it is so vague.

#2

For the first few periods (i.e, t = 1, 2, and 3), you can solve for the rates analytically; beyond that, you have to do it numerically (e.g., using Solver in Excel).

As a practical matter, nobody ever does it analytically; in practice, all rates are computed (approximated, actually) numerically.

#3

Hmm. That makes sense. I just cant imagine how the question asked is answerable then as a mock exam question.

How could we be expected to fill out a tree with no other rates in that year provided as part of a single question to value a bond.

I must be missing something from the question. Drives me crazy I cant find it. If I see it on exam, I will be at a total loss.