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Illustration of Use of Trinomial Trees

To illustrate how trinomial interest rate trees are used to value derivatives, we consider the simple example shown in Figure 23.6. This is a two-step tree with each time step equal to one year in length, so that St = 1 year. We assume that the up, middle, and down probabilities are 0.25, 0.50, and 0.25, respectively, at each node. The assumed <5f-period rate is shown as the upper number at each node. 11 The tree is used to value a derivative that provides a payoff at the end of the second time step of

Figure 23.6 Example of the use of trinomial interest rate trees: upper number at each node is rate; lower number is value of instrument

We explain later how the probabilities and rates on an interest rate tree are determined.

max[100(fl-0.11), 0] where R is the St-period rate. The calculated value of this derivative is the lower number at each