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.

Modeling the Loss Distribution

“…This unobservable firm heterogeneity can be modeled using shared frailties models, where the hazard rate is multiplied by a latent random variable common to all firms in a given industry group (Gagliardini andGourieroux 2003, Duffie et al 2007), and which can be assumed to follow a stochastic diffusion process (Yashin and Manton 1997, Duffie et al 2009). Motivated by Dai, Singleton and Yang (2007) and Li, Li and Yu (2010) who demonstrate the importance of using regimes to model changes in the economy, we extend the shared frailty approach by developing regime frailty models at industry level. In these models, a multiplicative factor magnifies the impact of group-specific frailties during periods of economic distress, and potential distress is assessed annually at industry level thus allowing a dynamic change in the industry default risk.…”

General Formulas for Valuing Stocks and Bonds with Structural Changes

“…Di¤erent from previous reduced-form multi-regime bond pricing models (e.g., Bansal and Zhou, 2002;Dai, Singleton, and Yang, 2007), this model is consumption-based, which is the multi-regime counterpart of Barro (2005) in continuous time. By (6.10), the implied bond yield with as the time to maturity is:…”

“…In particular, the random regime switching is governed by de…ned above throughout the paper. For tractability, I assume is a constant matrix: 1 Assumption 2: Conditioned on regime s t (s t = 1; :::; n), the discount-rate (s t ) is a constant; the factors x [x 1 ; :::; x K ] 0 follow a strong Markov process in some 1 In the multi-regime literature, it is common to assume a time invariant transition matrix under the pricing measure for the purpose of tractability (e.g., Bansal and Zhou, 2002;Dai, Singleton, and Yang, 2007;Ang, Bekaert, and Wei, 2008). With priced regime-switching risk, the transition matrix could be state-dependent under the actual measure (e.g., Dai, Singleton, and Yang, 2007).…”

On the Prediction of the Inflation Crises of South Africa Using Markov-Switching Bayesian Vector Autoregressive and Logistic Regression Models

“…Hamilton (2010) has indicated that Markov-switching models (MSM) are quite amenable to the theoretical computation of how these abrupt changes in fundamentals show up, especially in financial time series. To describe the consequence of a dramatic change in the behaviour of a single series, say , Ang and Bekaert (2002) and Dai et al (2007) have discovered that the behaviour of the past can be described by the first order autoregressive denoted by Due to the failure of to account for the change in parameters, the current study establishes a larger model encompassing the change in parameters. According to Timmermann (2000) the probability law governing the parameters fully follows the Gaussian innovation , the coefficient of an autoregressive , the two intercepts and finally the twostate transition probabilities that follow homogenous Markov Chain (MC).…”