Yield-factor volatility models

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 of the yield curve 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 are significant GARCH effects present even after including a level effect. Further, we find that allowing for regime shifts in the factor volatilities dramatically improves the model’s fit and strengthens the level effect. We also show that a regime-switching model with level and GARCH effects provides the best out-of-sample forecasting performance of yield volatility. We argue that the auxiliary models often used to estimate term structure models with simulation-based estimation techniques should be consistent with the main features of the yield curve that are identified by our model.     

An Unobserved Components Model of the Yield Curve

We develop an unobserved component model in which the short‐term interest rate is composed of a stochastic trend and a stationary cycle. Using the Nelson–Siegel model of the yield curve as inspiration, we estimate an extremely parsimonious state‐space model of interest rates across time and maturity. The time‐series process suggests a specific functional form for the yield curve. We use the Kalman filter to estimate the time‐series process jointly with observed yield curves, greatly improving empirical identification. Our stochastic process generates a three‐factor model for the term structure. At the estimated parameters, trend and slope factors matter while the third factor is empirically unimportant. Our baseline model fits the yield curve well. Model generated estimates of uncertainty are positively correlated with estimated term premia. An extension of the model with regime switching identifies a high‐variance regime and a low‐variance regime, where the high‐variance regime occurs rarely after the mid‐1980s. The term premium is higher, and more so for yields of short maturities, in the high‐variance regime than in the low‐variance regime. The estimation results support our model as a simple and yet reliable framework for modeling the term structure.     

Reduced-form Models with Regime Switching: An Empirical Analysis for Corporate Bonds

Empirical evidence shows that there is a close link between regime shifts and business cycle fluctuations. A standard term structure of interest rates, such as the Cox et al. (1985 Econometrica, 53, 385–407; CIR) model, is sharply rejected in the Treasury bond data. Only Markov regime-switching models on the entire yield curve of the Treasury bond data can account for the observed behavior of the yield curve. In this paper, we examine the impact of regime shifts on AAA-rated and BBB-rated corporate bonds through the use of a reduced-form model. The model is estimated by the Efficient Method of Moments (EMM). Our empirical results suggest that regime-switching risk has significant implications for corporate bond prices and hence has a material impact on the entire corporate bond yield curve, providing evidence for the approach of rating through the cycle employed by rating agencies.     

Term Structure of Interest Rates with Regime Shifts

We develop a term structure model where the short interest rate and the market price of risks are subject to discrete regime shifts. Empirical evidence from efficient method of moments estimation provides considerable support for the regime shifts model. Standard models, which include affine specifications with up to three factors, are sharply rejected in the data. Our diagnostics show that only the regime shifts model can account for the well–documented violations of the expectations hypothesis, the observed conditional volatility, and the conditional correlation across yields. We find that regimes are intimately related to business cycles.     

A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables

We describe the joint dynamics of bond yields and macroeconomic variables in a Vector Autoregression, where identifying restrictions are based on the absence of arbitrage. Using a term structure model with inflation and economic growth factors, together with latent variables, we investigate how macro variables affect bond prices and the dynamics of the yield curve. We find that the forecasting performance of a VAR improves when no-arbitrage restrictions are imposed and that models with macro factors forecast better than models with only unobservable factors. Variance decompositions show that macro factors explain up to 85% of the variation in bond yields. Macro factors primarily explain movements at the short end and middle of the yield curve while unobservable factors still account for most of the movement at the long end of the yield curve.     

The Term Structure with Semi-credible Targeting

The Federal Reserve sets targets for interest rates which it enforces through direct market intervention. These targets are changed periodically. In this paper, we develop a term structure model in which the short rate is subject to a control which keeps it close to a target which changes from time to time. The probability of target changes is not constant in the model, but changes as a function of observables. The model performs well at explaining the shifts in the yield curve that accompany target changes.     

Corporate credit risk modeling and the macroeconomy

Despite a surge in the research efforts put into modeling credit and default risk during the past decade, few studies have incorporated the impact that macroeconomic conditions have on business defaults. In this paper, we estimate a duration model to explain the survival time to default for borrowers in the business loan portfolio of a major Swedish bank over the period 1994–2000. The model takes both firm-specific characteristics, such as accounting ratios and payment behaviour, loan-related information, and the prevailing macroeconomic conditions into account. The output gap, the yield curve and consumers’ expectations of future economic development have significant explanatory power for the default risk of firms. We also compare our model with a frequently used model of firm default risk that conditions only on firm-specific information. The comparison shows that while the latter model can make a reasonably accurate ranking of firms’ according to default risk, our model, by taking macro conditions into account, is also able to account for the absolute level of risk.     

Nonlinear equilibrium adjustment dynamics and predictability of the term structure of interest rates

We analyze money market dynamics under a long-run equilibrium framework where commonly-monitored spreads serve as error correction terms, derived from a structural model incorporating autocorrelated risk premia, interest rate smoothing and monetary policy feedback. Using a dataset of monthly observations of the spot next and four-, thirteen-, twenty six- and fifty two-week Treasury Bills rates for the United States, Germany and United Kingdom from January 1999 to April 2016, we investigate the power of the expectations hypothesis theory of interest rates taking into account long-run deviations from equilibrium and inherent nonlinearities. We reveal short-run dynamic adjustments for the term structure of the USA, Germany and the UK, which are subject to regime switches. When forecastability is tested during May 2016–October 2017, the MSIH-VECM outperforms systematically the VECM. This is the first attempt to explore the possibility of parameter instability as a crucial factor in deriving the rejection of the restricted version of the cointegration space. Moreover, we investigate the dynamic out-of-sample forecasts of the term structure to assess the effectiveness of nonlinear MS-VECM modeling in capturing the after-effects of the global crisis. Overall, our results suggest that regime shifts in the mean and variance of the term structure may be intertwined with changes in fundamentals, that play a role in driving interest rate regimes, in particular business cycle and inflation fluctuations.     

U.S. Monetary Policy Surprises: Identification with Shifts and Rotations in the Term Structure

We develop a model to extract measures of monetary policy surprises from the maturity structure of the yield curve. The model endogenously allows for the fact that the yield curve may either shift or rotate in response to monetary policy shocks. A latent factor model approach with identification through heteroskedasticity harnesses the term structure to extract monetary policy shocks. The approach offers informational advantages over event studies. Results from the U.S. term structure from 1994 strongly support the hypothesis that differing term structure responses are reactions to different types of monetary policy shock, rather than differing reactions to the same policy shock.     

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

This article develops and empirically implements an arbitrage-free,dynamic term structure model with "priced" factor and regime-shiftrisks. The risk factors are assumed to follow a discrete-timeGaussian process, and regime shifts are governed by a discrete-timeMarkov process with state-dependent transition probabilities.This model gives closed-form solutions for zero-coupon bondprices, an analytic representation of the likelihood functionfor bond yields, and a natural decomposition of expected excessreturns to components corresponding to regime-shift and factorrisks. Using monthly data on U.S. Treasury zero-coupon bondyields, we show a critical role of priced, state-dependent regime-shiftrisks in capturing the time variations in expected excess returns,and document notable differences in the behaviors of the factorrisk component of the expected returns across high and low volatilityregimes. Additionally, the state dependence of the regime-switchingprobabilities is shown to capture an interesting asymmetry inthe cyclical behavior of interest rates. The shapes of the termstructure of volatility of bond yield changes are also verydifferent across regimes, with the well-known hump being largelya low-volatility regime phenomenon.     

Multi-factor Affine Term Structure Model with Single Regime Shift: Real Term Structure under Zero Interest Rate

In this paper, we extend the one-factor, single regime shift, affine term structure model with time-dependent regime-shift probability to a multi-factor model. We model the nominal interest rate and the expected inflation rate, and estimate the term structure of the real interest rate in the Japanese government bond market using inflation-indexed bond data under zero interest rates. Incorporating the economic structure that the Bank of Japan terminates the zero interest rate when the expected inflation rate gets out of deflationary regime, we estimate the yield curve of the real interest rate for less than 10 years, consistent with the expectation of the market participants in the Japanese government bond market, where inflation-indexed bonds are traded for only around 10 years.     

The Term Structure of Real Rates and Expected Inflation

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 in the United States is fairly flat around 1.3%. In one real rate regime, the real term structure is steeply downward sloping. An inflation risk premium that increases with maturity fully accounts for the generally upward sloping nominal term structure.     

General equilibrium pricing with multiple dividend streams and regime switching

In this paper, we investigate a regime switching Lucas economy in continuous time, with multiple dividend streams and labour income. We determine the asset prices in equilibrium in the economy with regime switching, and derive a system of partial differential equations for the asset prices and the short interest rate. The solutions for the endogenous short interest rate, the bond price and the yield of the bond are obtained. We also consider applications of the equilibrium model and show that the model implies a rich framework for the term structure of interest rates. We demonstrate how the regime switching economy helps to improve the model-implied annual excess rate of return. This assists in explaining the famous equity premium puzzle.     

人口学特征与利率期限结构:老年社会平缓的收益率曲线

本文将刻画人口结构的生命周期模型引入消费-资本资产定价模型,考察人口结构对利率期限结构的影响。模型表明,人口结构及其家庭生命周期特征不仅决定利率水平,而且将通过人对债券期限的不同偏好,影响利率期限结构。少年人口占比对利率期限结构的影响为正,中年和老年人口占比的影响为负。相比少年人口,中老年人口更偏好长期债券,使长期收益率下降,期限结构的斜率更为平缓。基于全球数据的经验研究验证了这一结论。少年人口占比增加期限利差,中老年人口占比则起反向作用。因此,在年长的经济体中,期限利差更小,呈现更平缓的收益率曲线特征。在更换人口结构变量、期限利差变量、估计方法、赋权样本和处理遗漏变量后,结果表现稳健。本文从人口学视角拓宽了利率期限结构的决定因素,揭示了老年经济体可能面临一个平缓的收益率曲线,而这说明老龄化还可能通过抑制短期投机和促进长期投资来提高长期经济发展质量。     

Regime Shifts in Price‐Dividend Ratios and Expected Stock Returns: A Present‐Value Approach

We incorporate regime shifts in the mean of price‐dividend ratios into the present value model of van Binsbergen and Koijen (2010) who propose a latent variable approach to modeling expected returns and dividend growth rates. We find that accounting for regime shifts results in much lower persistence of expected returns and higher volatility of expected returns, and thus higher in‐sample predictability, when compared to the results from the van Binsbergen and Koijen (2010) model. We also show that the main source of the increase in the mean of price‐dividend ratios in the mid‐1990s is a decrease in the mean of expected returns.     

Term structure modelling with observable state variables

This paper proposes and implements a parsimonious three-factor model of the term structure whose dynamics is driven uniquely by observable state variables. This approach allows comparing alternative views on the way state variables – macroeconomic variables, in particular – influence the yield curve dynamics, avoids curse of dimensionality problems, and provides more reliable inference by using both the cross-sectional and the time series dimension of the data. I simulate the small-sample properties of the procedure and conduct in- and out-of-sample studies using a comprehensive set of US data. I show that even a parsimonious model where the level, slope and curvature factors of the term structure are driven by, respectively, inflation, monetary policy and economic activity consistently outperforms the (latent-variable) benchmark model in an out-of-sample study.     

Forecasting the term structure of Chinese Treasury yields

This paper is the first to study the forecasting of the term structure of Chinese Treasury yields. We extend the Nelson–Siegel class of models to estimate and forecast the term structure of Chinese Treasury yields. Our empirical analysis shows that the models fit the data very well, and that more flexible specifications dramatically improve in-sample fitting performance. In particular, the model which enhances slope fitting is the best in capturing the Chinese yield curve dynamics. We also demonstrate that time-varying factors of the models may be interpreted as the level, slope and curvature of the yield curve. Furthermore, we use five dynamic processes for the time-varying factors to forecast the term structure at both short and long horizons. Our forecasts are much more accurate than the random walk, the Cochrane–Piazzesi regression and the AR(1) benchmark models at long horizons.     

The term structure of inflation expectations

We use information in the term structure of survey-based forecasts of inflation to estimate a factor hidden in the nominal yield curve. We construct a model that accommodates forecasts over multiple horizons from multiple surveys and Treasury real and nominal yields by allowing for differences between risk-neutral, subjective, and objective probability measures. We establish that model-based inflation expectations are driven by inflation, output, and one latent factor. We find that this factor affects inflation expectations at all horizons but has almost no effect on the nominal yields; that is, the latent factor is hidden. We show that this hidden factor is not related to either current and past inflation or the standard set of macro variables studied in the literature. Consistent with the theoretical property of a hidden factor, our model outperforms a standard macro-finance model in its forecasting of inflation and yields.