Gaussian Dynamic Term Structure Model Research Articles

International linkages of term structures: US and Korea Treasury bond yields

This study analyzes the international linkages of term structures between the United States (US) and Korea using a Gaussian dynamic term structure model. The empirical analysis shows that the US level factor makes the most important contribution to the Korean term structure fluctuations. When two separate channels (i.e., policy and risk-compensation) are considered for propagating structural shocks into Korean bond yields, the policy channel dominates for the short-term rates, whereas for the long-term yield, the policy channel is dominant for the US level shock, but the risk channel is dominant for other shocks. These results are sensitive to whether or not small-sample bias is corrected. With a help of the bias correction, term premium estimates in the US and Korea exhibit substantial countercyclicality with respect to the US output gap. The US slope factor, which also has a significant impact on Korean long-term yields, is closely related to the global liquidity conditions for Korean bond returns.

Interest Rate Volatility and No-Arbitrage Affine Term Structure Models

Within the affine framework, many have observed a tension between matching conditional first and second moments in dynamic term structure models (DTSMs). Although the existence of this tension is generally accepted, less understood is the mechanism that underlies it. We show that no arbitrage along with the rich information in the cross section of yields has strong implications for both the dynamics of volatility and the forecasts of yields. We show that this link implied by the absence of arbitrage—and not the factor structure per se—underlies the tension between first and second moments found in the literature. Adding to recent research that has suggested that no-arbitrage restrictions are nearly irrelevant in Gaussian DTSMs, our results show that no-arbitrage restrictions are potentially relevant when there is stochastic volatility. This paper was accepted by Gustavo Manso, finance.

Unifying Gaussian dynamic term structure models from a Heath–Jarrow–Morton perspective

In this paper, we show that most existing Gaussian dynamic term structure models (GDTSMs) can be nested as special cases under a unified Heath–Jarrow–Morton (HJM)-based framework of GDTSM construction. Our study provides not only a systematic way to examine the commonality of many seemingly distinct GDTSMs, but also a novel and convenient approach to constructing GDTSMs that are otherwise unavailable or intractable under the traditional approach. In our empirical study using the Euro area forward rates, we conduct a specification analysis based on this novel approach. The analysis reveals that the traditional models impose restrictive constraints limiting their flexibility in capturing key features of the correlations and volatilities of the forward rates.

PRINCIPAL-COMPONENT-BASED GAUSSIAN AFFINE TERM STRUCTURE MODELS: CONSTRAINTS AND THEIR FINANCIAL IMPLICATIONS

This work builds on the work by Joslin et al. [(2011) A new perspective on Gaussian dynamic term structure Models, The Review of Financial Studies 24, 926–970] on the affine dynamics of portfolios of yields and addresses the unresolved issues of ‘internal consistency’ mentioned in the same paper. It shows the unexpected constraints that have to be satisfied by the [Formula: see text]-measure evolution of the yield curve if the portfolio of yields has to be interpreted as their principal components. This choice of state variables is common in the recent literature and so our findings are intrinsically interesting. However, we show that our results also extend to a wide class of choices for state variables, when these are chosen as linear combinations of yields. We show that these constraints have important financial consequences, which, to our knowledge, have not been appreciated. In particular, this paper highlights some puzzling issues of compatibility between the [Formula: see text]- and [Formula: see text]-measure dynamics of Gaussian dynamic term structure models when principal components are chosen as state variables, once the constraints we derive are taken into account.

Defining and Exploiting Value in US Treasury Bonds

In this article, the authors propose a definition of value in Treasury bonds that, the authors believe, is more satisfactory than definitions found in the recent literature, and that allows for statistically significant and economically relevant predictions of cross-sectional excess returns. The authors’ value pricing factor exploits the differences between the market and the theoretical values of Treasury bonds, where the theoretical value is assessed using an economically-justifiable Gaussian dynamic term structure model. The authors show that the profitability of the strategy they build using their value signal is statistically and economically significant and is closely linked to the Treasury market volatility. The authors provide an explanation for this strong link using arguments similar to what can be found in the recent literature on liquidity in Treasuries; and the authors show that their value signal is not subsumed by the best-known return-predicting factors. With an eye to practical applications, the authors also present a long-only version of their strategy. TOPICS:Analysis of individual factors/risk premia, factor-based models, style investing

The influence of real interest rates and risk premium effects on the ability of the nominal term structure to forecast inflation

Based on an empirically attractive Gaussian dynamic term structure model and data on the short-term real interest rate and per capita real consumption, this paper examines the information content of the nominal term structure of interest rates with respect to inflation, real interest rates and risk premium effects. The paper finds a number of interesting results, which have monetary policy implications. First, it shows that the suggested model fits well the data and provides estimates of real interest rates and expected inflation rates which are very close to those given by survey data. Second, it provides clear cut evidence that the nominal term structure is mainly determined by movements in real interest rates and, to a lesser extent, by inflation and risk premium effects. These results mean that term spreads between long and short-term nominal rates fail to forecast future changes in inflation rates because are dominated by real term structure effects, which are not orthogonal to inflation rate shocks (changes). Third, to retrieve information from the term spread models of nominal interest rates about future inflation rate changes, the paper suggests a regression model which adjusts the nominal interest rates term spreads for the real term structure effects.

Unifying Gaussian Dynamic Term Structure Models from an HJM Perspective

We show that the unified HJM-based approach of constructing Gaussian dynamic term structure models developed by Li, Ye, and Yu (2016) nests most existing GDTSMs as special cases. We also discuss issues of interest rate derivatives pricing under this approach and using integration to construct Markov representations of HJM models.

A New Approach to Measuring Market Expectations and Term Premia

This article develops a novel approach for measuring market expectations and term premia in the term structure of interest rates. Key components of this approach are generic impact measures of state variables in a Gaussian dynamic term structure model. These measures are inherent in a particular state variable regardless of how other state variables are defined within the model. With the help of these measures, the approach gives rise to market expectations that predict yield changes well, and term premia with a legitimate impact on the forward curve. In my empirical analysis, I show the generic impact of the short rate on the yield curve, and present observations of the historical dynamics of market expectations and term premia. The calibrated model is also employed to study the impacts of recent unconventional monetary policies.

Term spread regressions of the rational expectations hypothesis of the term structure allowing for risk premium effects

AbstractThis paper suggests a new empirical methodology of testing the predictions of the term spread between long and short-term interest rates about future changes of the former allowing for term premium effects, according to the rational expectations hypothesis of the term structure. To capture the effects of a time-varying term premium on the term spread, the paper relies on an empirically attractive affine Gaussian dynamic term structure model which assumes that the term structure of interest rates is spanned by three unobserved state variables. To retrieve accurate values of these variables from interest rates series, the paper suggests a new method which can overcome the effects of measurement (or pricing) errors inherent in these series on the estimates of the model. This method is assessed by a Monte Carlo study. Ignoring these errors will lead to biased estimates of term structure models. The empirical results of the paper provide support for the suggested term structure model. They show that this model can efficiently capture the time-varying term premium effects embodied in long-term interest rates, which can explain the failures of term spread to forecast future changes in long-term rates.

Retrieving Inflation Expectations and Risk Premia Effects from the Term Structure of Interest Rates

This paper suggests an empirically attractive Gaussian dynamic term structure model to retrieve estimates of real interest rates and in‡flation expectations from the nominal term structure of interest rates which are net of in‡flation risk premium effects. The paper shows that this model is consistent with the data and that time-variation of infl‡ation risk premium and real interest rates can explain the puzzling behavior of the spread between long and short-term nominal interest rates to forecast changes in in‡flation rates, especially over short-term horizons. The estimates of in‡flation risk premium effects retrieved by the model tend to be negative and signi ficant, which implies that investors in the bond market require less compensation for holding nominal bonds compared to in‡flation-indexed bonds. This is more evident during the recent fi nancial crisis.

A New Linear Estimator for Gaussian Dynamic Term Structure Models

This article proposes a novel regression-based approach to the estimation of Gaussian dynamic term structure models. This new estimator is an asymptotic least-square estimator defined by the no-arbitrage conditions upon which these models are built. Further, we note that our estimator remains easy-to-compute and asymptotically efficient in a variety of situations in which other recently proposed approaches might lose their tractability. We provide an empirical application in the context of the Canadian bond market.

Term Spread Regressions of the Rational Expectations Hypothesis of the Term Structure Allowing for Risk Premium Effects

This paper suggests term spread regression based tests allowing for time-varying term premium effects, with the aim of explaining the empirical failures of the term spread to forecast future movements in interest rates. To capture the e¤ects of a time-varying term premium on the term spread, the paper relies on a simple and empirically attractive arbitrage-free Gaussian dynamic term structure model, which assumes that the term structure of interest rates is spanned by three unobserved factors. To retrieve these factors from the data, the paper suggests a new empirically methodology which can overcome the effects of measurement (or pricing) errors on the estimates of the unobserved factors, and our tests. The results of the paper indicate that term spread regressions allowing for a time-varying term premium effects can provide unbiased estimates of future changes of long-term interest rates, as predicted by the rational expectations hypothesis of the term structure.

Modeling Yields at the Zero Lower Bound: Are Shadow Rates the Solution?

Recent U.S. Treasury yields have been constrained to some extent by the zero lower bound (ZLB) on nominal interest rates. In modeling these yields, we compare the performance of a standard affine Gaussian dynamic term structure model (DTSM), which ignores the ZLB, and a shadow-rate DTSM, which respects the ZLB. We find that the standard affine model is likely to exhibit declines in fit and forecast performance with very low interest rates. In contrast, the shadow-rate model mitigates ZLB problems significantly and we document superior performance for this model class in the most recent period.

A Unified Heath-Jarrow-Morton Approach to Gaussian Dynamic Term Structure Models

Motivated by an extensive literature showing that government bond yields exhibit a strong non-Markov property, in the sense that moving averages of long-lagged yields significantly improve the predictability of excess bond returns. We then develop a systematic approach of constructing non-Markov Gaussian dynamic term structure models (GDTSMs) under the Heath-Jarrow-Morton (HJM) framework. Compared to the current literature, our approach is more flexible and parsimonious, enabling us to estimate an economically significant non-Markov effect that helps predict excess bond returns both in-sample and out-of-sample.

Market Expectations of the Short Rate and the Term Structure of Interest Rates: A New Perspective from the Classic Model

This paper develops a novel approach to measure the market expectations and term premia in the term structure of interest rates. Key components of this approach are generic impact measures of state variables in a Gaussian dynamic term structure model. These measures are inherent in a particular state variable regardless of how other state variables are defined within the model. With the help of these measures, the approach gives rise to market expectations predicting yield changes well, and term premia having a legitimate impact on the forward curve. In the empirical analysis, I show the generic impact of the short rate on the yield curve, and historical dynamics of market expectations and term premia. The calibrated model is also employed to study the impacts of recent unconventional monetary policies.

A New Perspective on Gaussian Dynamic Term Structure Models

In any canonical Gaussian dynamic term structure model (GDTSM), the conditional forecasts of the pricing factors are invariant to the imposition of no-arbitrage restrictions. This invariance is maintained even in the presence of a variety of restrictions on the factor structure of bond yields. To establish these results, we develop a novel canonical GDTSM in which the pricing factors are observable portfolios of yields. For our normalization, standard maximum likelihood algorithms converge to the global optimum almost instantaneously. We present empirical estimates and out-of-sample forecasts for several GDTSMs using data on U.S. Treasury bond yields. (JEL E43, G12, C13) Dynamic models of the term structure often posit a linear factor structure for a collection of yields, with these yields related to underlying factors P through a no-arbitrage relationship. Does the imposition of no-arbitrage in a Gaussian dynamic term structure model (GDTSM) improve the out-of-sample forecasts of yields relative to those from the unconstrained factor model, or sharpen model-implied estimates of expected excess returns? In practice, the answers to these questions are obscured by the imposition of over-identifying restrictions on the risk-neutral (Q) or historical (P) distributions of the risk factors, or on their market prices of risk, in addition to the cross-maturity restrictions implied by no-arbitrage. 1

A New Perspective on Gaussian Dynamic Term Structure Models

In any canonical Gaussian dynamic term structure model (GDTSM), the conditional forecasts of the pricing factors are invariant to the imposition of no-arbitrage restrictions. This invariance is maintained even in the presence of a variety of restrictions on the factor structure of bond yields. To establish these results, we develop a novel canonical GDTSM in which the pricing factors are observable portfolios of yields. For our normalization, standard maximum likelihood algorithms converge to the global optimum almost instantaneously. We present empirical estimates and out-of-sample forecasts for several GDTSMs using data on U.S. Treasury bond yields. Taken together, our results shed new light on estimation and interpretation of GDTSMs, as well as the eff ects of di fferent specifi cations of the risk premiums and the risk-neutral distribution of bond yields on the observed dynamics of the yield curve.

Kalman filtering of consistent forward rate curves: a tool to estimate and model dynamically the term structure

This work explores an original methodology to specify Gaussian dynamic term structure models and estimate them efficiently from time series data. The emphasis is on the cross-sectional dimension of the problem. The form of the term premium is chosen so as to take into account the recent contributions that provide evidence in favor of time-varying market prices of risk. A model based on a widely used family of forward curves is then estimated from time series of eight UK interest rates. An extensive diagnostic check is carried out to assess the fit of the model.