anonymous referees and seminar participants at Stanford University and the 1999 Econometric Society

Changes in nominal interest rates must be due to either movements in real interest rates, expected inflation, or the inflation risk premium. We develop a term structure model with regime switches, time-varying prices of risk, and inflation to identify these components of the nominal yield curve. We find that the unconditional real rate curve is fairly flat at 1.44%, but slightly humped. In one regime, the real term structure is steeply downward sloping. Real rates (nominal rates) are pro-cyclical (counter-cyclical) and inflation is negatively correlated with real rates. An inflation risk premium that increases with the horizon fully accounts for the generally upward sloping nominal term structure. We find that expected inflation drives about 80 % of the variation of nominal yields at both short and long maturities, but during normal times, all of the

Using a new Bayesian method for the analysis of diffusion processes, this article finds that the nonlinear drift in interest rates found in a number of previous studies can be confirmed only under prior distributions that are best described as informative. The assumption of stationarity, which is common in the literature, represents a nontrivial prior belief about the shape of the drift function. This belief and the use of ``flat'' priors contribute strongly to the finding of nonlinear mean reversion. Implementation of an approximate Jeffreys prior results in virtually no evidence for mean reversion in interest rates unless stationarity is assumed. Finally, the article documents that nonlinear drift is primarily a feature of daily rather than monthly data, and that these data contain a transitory element that is not reflected in the volatility of longermaturity yields.

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 behaviors 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 behavior of interest rates. The shapes of the term structures of bond yield volatilities are also very different across regimes, This paper develops and empirically implements an arbitrage-free, dynamic term structure model (DTSM) 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. Agents are assumed to know

This paper 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). Moreover, we allow the market price of risk Λt, linking the risk-neutral and historical distributions of X, to depend generally on the state Xt. The conditional likelihood functions for coupon bond yields for the resulting nonlinear models under the historical measure are known exactly in closed form. As an illustration of our approach, we estimate a three factor model with a cubic term in the drift of the stochastic volatility factor and compare it to a model with a linear drift. Our results show that inclusion of a cubic term in the drift significantly improves the models statistical fit as well as its out-of-sample forecasting performance. 1

Abstract: The authors study time-variation in the co-movements between daily stock and Treasury bond returns over 1986 to 2000. Their innovation is to examine whether variation in stock-bond return dynamics can be linked to non-return-based measures of stock market uncertainty, specifically the implied volatility (IV) from equity index options and detrended stock turnover (DTVR). The authors investigate two empirical questions suggested by recent literature on stock market uncertainty and cross-market hedging. First, from a forward-looking perspective, they find that the levels of IV and DTVR are both negatively associated with the future correlation between stock and bond returns. The probability of a negative correlation between daily stock and bond returns over the next month is several times greater following relatively high values of IV and DTVR. Second, from a contemporaneous perspective, the authors find that bond returns tend to be relatively high (low) during days when IV increases (decreases) and during days when stock turnover is unexpectedly high (low). Their findings suggest that stock market uncertainty has cross-market pricing influences that play an important role in understanding joint stock-bond price formation. Further, our results imply that stock-bond diversification benefits increase with stock market uncertainty.

international diversification We thank Cam Harvey for providing data and Theo Nijman for helpful comments on the research proposal. This research is funded by a grant from INQUIRE Europe. We thank seminar participants at a joint INQUIRE Europe- INQUIRE UK meeting. Andrew Ang: aa610@columbia.edu; Geert Bekaert:

The term structure of interest rates is often summarized using a handful of yield factors that capture shifts in the shape of the yield curve. In this paper, we develop a comprehensive model for volatility dynamics in the level, slope, and curvature factors that simultaneously includes level and GARCH effects along with regime shifts. We show that the level of the short-rate is useful in modeling the volatility of the three yield factors and that there is significant GARCH effects present even after including a level effect. We also study the effect of interest rate volatility on the level of the yield factors and report evidence that is consistent with a ”flight-to-cash”. Furthermore, we show that allowing for regime shifts in the factor volatilities dramatically improves the model’s fit and strengthens the level effect. Finally, we discuss how the dynamics of yield factors we identify could potentially be used to discriminate between alternative term structure models.

A regime switching vector autoregression (RS-VAR) is defined as a vector autoregression in which the parameters of the vector autoregression are functions of a set of discrete indices, which consitute the regimes. This process can be applied to interest rate models, default models, and other financial models. This can be done in the "objective" or P-measure or the risk-neutral or Q-measure of finance or other measures. One set of applications include calculation of prices, cashflows, capital, reserves, defaults, and other variables. Another set includes transactions using these including purchases and sales, producing and/or sending reports, advisory services, portfolio strategy, etc.

In an unobservable regime-switching model, investors ’ learning of the state of future real funda-mentals from current inflation leads to dramatic variation in asset valuations and is able to partially resolve five credit risk puzzles: (i) the high level of credit spreads for firms with average solvency ratios and volatility calibrated to their credit rating, (ii) the high volatility of credit spreads, (iii) the positive and slow response of credit spreads to shocks in the short rate (the ‘momentum ’ effect), (iv) the inability of default risk measures to explain the variation in corporate bond returns, and (v) the changing sign of the risk-return relationship for corporate bond excess returns across the past three decades. ∗ A previous draft of this paper was circulated under the title “Dynamics of The Credit Risk Premium: The Effects of