hello,
Can anyone explain to me please how do we perform the calculation on forward interest rates in the binomial tree for period 1, in EOC number 16 - Reading27?
we are given the middle forward rates in Exhibit2 but I can’t figure out how do they calculated the up and down rate for 1st period, from a mid value of 1.7677% and volatility=20%
Many thanks
Theoretically, you could set up a quadratic equation in the lower interest rate, then solve it using the quadratic formula.
In practice, you’ll use something like Solver in Excel.
Set the coupon on a 2-period bond to equal the par rate, calculate the price of the bond using the tree, then use Solver to adjust the lower rate (which will also adjust the upper rate) until the price equals par.
Once you’ve done that for a 2-period bond, do it for a 3-period bond. Then a 4-period bond, and so on.
This is known as calibrating the tree.
Ok thank you. It doesn’t seem to be testable this way, but very important to understand.
Thanks!
It’s not testable.
The could give you the forward rate at one node and ask you to compute the forward rate at another node at the time in the future, but that’s about it.