A NONLINEAR MODEL OF THE TERM STRUCTURE OF INTEREST-RATES

We present an economically motivated two-factor term structure model t hat generalizes existing stochastic mean term structure models. By all owing a certain parameter to acquire dynamical behavior we extend the two-factor model to obtain a nonlinear three-factor model that is show n, in a deterministic version, to be equivalent to the Lorenz system o f differential equations. With reasonable parameter values the model e xhibits chaotic behavior. It successfully emulates certain properties of interest rates including cyclical behavior on a business cycle time scale. Estimation and pricing issues are discussed. Standard PCA tech niques used to estimate HJM type models are observed to be equivalent to dimensional estimates commonly applied to 'spatial data' in nonline ar systems analysis. It is concluded that techniques commonly used in the analysis of nonlinear systems may be directly applicable to intere st rate models, offering new insights in the development of these mode ls. Tests of nonlinearity in interest rate behavior may need to focus on long cycle times.