Regime Shifts in a Dynamic Term Structure Model of U.S. Treasury Bond Yields

Abstract

This paper develops and empirically implements an arbitrage-free, dynamic term structure model with "priced" factor and regime-shift risks. The risk factors are assumed to follow a discrete-time Gaussian process, and regime shifts are governed by a discrete-time Markov process with state-dependent transition probabilities. This model gives closed-form solutions for zero-coupon bond prices and an analytic representation of the likelihood function for bond yields. Using monthly data on U.S. Treasury zero-coupon bond yields, we document notable differences in the behaviours of the market prices of factor risk across high and low volatility regimes. Additionally, the state-dependence of the regime-switching probabilities is shown to capture an interesting asymmetry in the cyclical behaviour of interest rates. The shapes of the term structures of bond yield volatilities are also very different across regimes, with the well-known hump in volatility being largely a low-volatility regime phenomenon.