Financial Derivatives Toolbox

Chapter 1
Tutorial

Introduction

The Financial Derivatives Toolbox extends the Financial Toolbox in the areas of fixed income derivatives and of securities contingent upon interest rates. The toolbox provides components for analyzing individual financial derivative instruments and portfolios. Specifically, it provides the necessary functions for calculating prices and sensitivities, for hedging, and for visualizing results.

Interest Rate Models

The Financial Derivatives Toolbox computes pricing and sensitivities of interest rate contingent claims based upon sets of zero coupon bonds or the Heath-Jarrow-Morton (HJM) evolution model of the interest rate term structure. For information, see:

• Pricing and Sensitivity from Interest Term Structure for a discussion of price and sensitivity based upon portfolios of zero coupon bonds.
• Pricing and Sensitivity from HJM for a discussion of price and sensitivity based upon the HJM model.

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 opposite of a bushy tree is a recombining tree, a tree in which branches 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 both illustrated in the next figure.

Using the Financial Derivatives Toolbox

Financial Instruments