A Tale of Two Yield Curves : Modeling the Joint Term Structure of Dollar and Euro Interest Rates

Modeling the joint term structure of interest rates in the United States and the European Union, the two largest economies in the world, is extremely important in international finance. In this paper, we provide both theoretical and empirical analysis of multi-factor joint affine term structure models for dollar and euro interest rates. In particular, we provide a systematic classification of multi-factor joint affine term structure models similar to that of Dai and Singleton (2000). A principal component analysis of daily dollar and euro interest rates reveals four factors in the data. We estimate four-factor joint affine term structure models using the approximate maximum likelihood method of Ait-Sahalia (2002, 2007) and compare the in-sample and out-of-sample performances of these models using some of the latest nonparametric methods. We find that a new four-factor model with two common and two local factors captures the joint term structure dynamics in the U.S. and the E.U. reasonably well