Binomial interest rate tree

CFA Level II Fixed Income
#1

While valuing a bond with having to construct an interest rate tree, how do you derive the first year’s lower node?

(In the examples I came across so far, they’ve been derived from ‘solver’/excel)

#2

Can you give an example? Also are you referring to V0 or some other year between?

#3

*How do you derive the rate at the first year’s lower node? (It has been invariably derived by ‘solver’/excel in the examples I came across)

#4

I tried calculation the exponential function with corresponding volatility, but it is always different from the first year lower node , which is derived from excel.

In exam, should we use the usual exponential function way only, as on all other nodes?

#5

You can do it algebraically; you end up having to solve a quadratic equation.

But that doesn’t matter. On the exam, they’ll have to give you that node’s rate or the first year’s upper node’s rate.

#6

Thanks a lot. Great help as always!

#7

My pleasure.