This paper explores the implications of filtering and no-arbitrage for the maximum likelihood estimates of the entire conditional distribution of the risk factors and bond yields in Gaussian macro-finance term structure model (MTSM) when all yields are priced imperfectly. For typical yield curves and macro-variables studied in this literature, the estimated joint distribution within a canonical MTSM is nearly identical to the estimate from an economic-model-free factor vector-autoregression (factor-VAR), even when measurement errors are large. It follows that a canonical MTSM offers no new insights into economic questions regarding the historical distribution of the macro risk factors and yields, over and above what is learned from a factor-VAR. These results are rotation-invariant and, therefore, apply to many of the specifications in the literature.

This article develops a rich class of discrete-time, nonlinear dynamic term structure models (DTSMs). Under the risk-neutral measure, the distribution of the state vector Xt resides within a family of discrete-time affine processes that nests the exact discrete-time counterparts of the entire class of continuous-time models in Duffie and Kan (1996) and Dai and Singleton (2000). Under the historical distribution, our approach accommodates nonlinear (nonaffine) processes while leading to closed-form expressions for the conditional likelihood functions for zero-coupon bond yields. As motivation for our framework, we show that it encompasses many of the equilibrium models with habit-based preferences or recursive preferences and long-run risks. We illustrate our methods by constructing maximum likelihood estimates of a nonlinear discrete-time DTSM with habit-based preferences in which bond prices are known in closed form. We conclude that habit-based models, as typically parameterized in the literature, do not match key features of the conditional distribution of bond yields.

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.

In the setting of ‘affine’ jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed-income pricing models, with a role for intensity-based models of default, as well as a wide range of option-pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option ‘smirks’ of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both jump amplitude as well as jump timing.

ABSTRACT This paper quantifies how variation in economic activity and inflation in the United States influences the market prices of level, slope, and curvature risks in Treasury markets. We develop a novel arbitrage‐free dynamic term structure model in which bond investment decisions are influenced by output and inflation risks that are unspanned by (imperfectly correlated with) information about the shape of the yield curve. Our model reveals that, between 1985 and 2007, these risks accounted for a large portion of the variation in forward terms premiums, and there was pronounced cyclical variation in the market prices of level and slope risks.