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

TLDR

This article develops and empirically implements an arbitrage‑free, dynamic term‑structure model that incorporates priced factor and regime‑shift risks. The model assumes risk factors follow a discrete‑time Gaussian process while regime shifts are governed by a discrete‑time Markov process with state‑dependent transition probabilities. It yields closed‑form zero‑coupon bond prices, an analytic likelihood for bond yields, and demonstrates that priced, state‑dependent regime‑shift risks are essential for explaining excess return dynamics, with distinct factor‑risk behavior and volatility‑term‑structure shapes across high‑ and low‑volatility regimes.

Abstract

This article 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, an analytic representation of the likelihood function for bond yields, and a natural decomposition of expected excess returns to components corresponding to regime-shift and factor risks. Using monthly data on U.S. Treasury zero-coupon bond yields, we show a critical role of priced, state-dependent regime-shift risks in capturing the time variations in expected excess returns, and document notable differences in the behaviors of the factor risk component of the expected returns 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 behavior of interest rates. The shapes of the term structure of volatility of bond yield changes are also very different across regimes, with the well-known hump being largely a low-volatility regime phenomenon.