Modelling the Yield Curve with Orthonomalised Laguerre Polynomials: An Intertemporally Consistent Approach with an Economic Interpretation

This article provides theoretical foundations for the popular orthonormalised Laguerre polynomial (OLP) model of the yield curve, as originally introduced by Nelson and Siegel (1987). Intertemporal consistency is provided by deriving the volatility-adjusted OLP (VAO) model of the yield curve using the risk-neutral Heath, Jarrow and Morton (1992) framework, and including an allowance for term premia as noted in Duffee (2002). An economic interpretation is provided by deriving the relationship between the VAO model and the Berardi and Esposito (1999) yield curve model that is based on a generic general equilibrium model of the economy. In empirical applications using almost 50 years of United States data, the VAO model outperforms the random walk when used to forecast the yield curve out of sample, and the level of the yield curve as measured by the VAO model is shown to be cointegrated with CPI inflation, as predicted.