Factor models and the correlation structure of interest rates: Some evidence for USD,GBP, DEM and JPY

The aim of this paper is to develop models for producing accurate forecasts for the correlation of spot and forward interest rates. Correlation forecasts generated from factor models, where the correlations are expressed as a function of few underlying factors, are compared to forecasts produced by less sophisticated models like the full historical and constant correlation model. Contrary to previous studies, where the selection of factors is rather arbitrary, we test two factor identification methodologies. The first is based on factor analysis and the second is based on minimising the residual cross-correlations. We show that a three-factor model, with factors identified by minimising the residual cross-correlation criterion is sufficient to describe the correlation structure of interest rates. Furthermore, we show that it might be preferable to assume that all forward rate correlations are equal rather than using a misspecified factor model and that the spot factor model developed, consistently outperformed long established models like the “Barbell” model.