Term Structure Modeling with Structural Breaks: A Simple Arbitrage-Free Approach

Abstract

Economic time-series are susceptible to infrequent but severe structural breaks that stem from banking crises, changes in government policy or shifts in consumer con fidence. We present an affine, arbitrage-free, regime-switching dynamic Nelson-Siegel model of the term structure that identifies structural breaks. We develop the model in continuous time and present a class of general affine hidden Markov models of the term structure. We highlight the assumptions that are necessary to reach tractable versions in this class such as the Dai, Singleton and Yang (2007) model and the arbitrage-free regime-switching Nelson and Siegel model. We estimate an arbitrage-free hidden Markov Nelson Siegel model on historical yield curve data via a multi-regime approximate Kalman filter. We contrast the model to single-regime alternatives and conclude that our model performs better in-sample. Using likelihood ratio tests, we show that regimes are driven by long term means, mean reversions, measurement and transition covariance matrices. The regimes conform to periods of expansionary and restrictive monetary policy, but do not coincide exactly with recessions. Our regimes capture the NBER recession dates, but persist long after the recessions have ended.