Modelling the Yield Curve: A Two Components Approach

Using parametric return autocorrelation tests and non parametric variance ratio statistics show that the UK and US short-term interest rates are unit root processes with significant mean reverting components. Congruent with this empirical evidence, we develop a new continuous time term structure model which assumes that the dynamics of the instantaneous interest rate are given by the joint effect of a (stationary) mean reverting component and a (nonstationary) martingale component. We provide a closed-form solution for the equilibrium yield curve when the temporary component is modelled as an Ornstein-Uhlenbeck process and the permanent component is modelled as an Arithmetic Brownian motion process.