Modeling the Term Structure of Interest Rates: An Introduction

Mark Fisher
Economic Review, Vol. 89, No. 3, 2004

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The yield curve, or the term structure of interest rates, plays a central role in the economy. Monetary policy is conducted by targeting rates at the short end of the curve, and longer-term yields reflect expectations of future changes in short rates.

This article presents a model of the term structure that builds on a simpler model outlined in one of the author's earlier Economic Review articles. The more complex model presented here takes into account the ongoing uncertainty about an asset's price over time. The article focuses on modeling the dynamics of the state-price deflator, which depend directly on the interest rate and the price of risk.

The author guides the reader step by step in developing a model of the term structure in which the interest rate evolves randomly through time according to a simple rule, the price of risk is a fixed parameter, and observations are made at discrete points in time.

The solution to the model illustrates a number of important features present to one extent or another in essentially all term structure models. The contribution of this article is its exposition: An important feature is that the model keeps track of the length of the discrete time period, allowing one to see what happens as the time step shrinks. The model thus provides a bridge from discrete-time models to continuous-time models without requiring the technical overhead necessary for a direct continuous-time analysis.

September 2004