A binomial model is a model that assumes that interest rates can take only one of two possible values in the next period. Therefore, binomial trees are used to calculate the expected interest rate and the subsequent present values of the bond.
Observe the nodes indicated with the boxes to understand this 2-period binomial tree given below. A node is a point in time when interest rates can take one of two possible paths—an upper path, U, or a lower path, L. if we consider i2, LU in the figure, this is the rate that will occur if the initial rate, i0, follows the lower path from node 0 to node 1 to become i1,L, then follows the upper of the two possible paths to node 2, where it takes on the value i2,LU.
Example of Binomial Trees: