Financial Derivatives Toolbox

Trees

The Heath-Jarrow-Morton model works with a type of interest rate tree called a bushy tree. A bushy tree is a tree in which the number of branches increases exponentially relative to observation times; branches never recombine.

The Black-Derman-Toy model, on the other hand, works with a recombining tree. A recombining tree is the opposite of a bushy tree. A recombining tree has branches that recombine over time. From any given node, the node reached by taking the path up-down is the same node reached by taking the path down-up. A bushy and a recombining tree are illustrated below.

This toolbox provides the data file deriv.mat that contains two trees, HJMTree, a bushy tree, and BDTTree, a recombining tree. The toolbox also provides the treeviewer function, which graphically displays the shape and data of price, interest rate, and cash flow trees. Viewed with treeviewer, the bushy shape of an HJM tree and the recombining shape of a BDT tree are apparent.

Overview

Financial Instruments