A Non-Linear Model of the Term Structure of Interest Rates

Abstract

In financial models of the term structure of interest rates, variation in the levels of rates, as well as day to day fluctuations in the value of rates, is explained by changes in the values of underlying stochastic state variables. This is unsatisfactory as the underlying state variables are often not associated with economic fundamentals. In this paper we present an economically motivated non-linear model of interest rates in which most of the large scale variation in rates is attributable to the chaotic evolution of explicitly modeled deterministic processes. A stochastic term with small variance is included in the model to represent 'noise' in the system. The model generalises existing stochastic mean models of interest rates. It successfully emulates certain properties of interest rates including a cyclical behaviour reminiscent of business cycles, and it casts light on the role of 'measurement error' in introducing risk into interest rate models.

JEL Classification: E43, E32