Yield Curve Dynamics Research Articles

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.

Specification Analysis of International Treasury Yield Curve Factors

We show how to compute patterns of variation over time, both among and within countries, that determine the international term structure of interest rates, using maximum likelihood within a linear Gaussian state-space framework. The simultaneous estimation of common factors (shared by all countries) and local factors (specific to one country) requires development of a normalization procedure beyond that of ordinary factor analysis. By jointly estimating common and local factors we avoid sequential estimation effects that may explain the lack of agreement in the multi-country term structure literature regarding not only the total number of latent factors required to explain the joint dynamics of yield curves, but also the number of common and of local factors. Using data on international yield curves of U.S., Germany, U.K. and Japan from January 1986 to December 2009, we generally find (analyzing yields in level and in difference) that a model with two common factors and three correlated local factors is preferred to a model (of similar complexity) that includes one common factor only or a model with only correlated local factors. In addition, each common factor closely mimics (or is similar to) a local factor extracted from a pure local factor model. We also reach the conclusion that dependence across international yield curves are driven, first, by the instantaneous correlation between local factors of different countries and, then, by the (full) autoregressive matrix of latent factors and by the matrix of common loadings.

Comments on ‘Global and Regional Yield Curve Dynamics and Interactions: The Case of Some Asian Countries’ by Byung Yoon Bae & Dong Heon Kim

Comments on ‘Global and Regional Yield Curve Dynamics and Interactions: The Case of Some Asian Countries’ by Byung Yoon Bae & Dong Heon Kim

Global and Regional Yield Curve Dynamics and Interactions: The Case of Some Asian Countries

Since the Asian financial crisis in 1997–98, Asian countries have made continuous efforts to promote monetary and financial cooperation for developing regionally well-established bond markets. This paper empirically evaluates the developments of bond markets in the East-Asia region based on the recently developed empirical methodology of dynamic cross-country bond yield interactions. To this end, we use a two-step state space model to examine the existence of the global and regional factor and analyze the effect of both factors on four Asian countries’ yield curves. We find that both global and regional factors play an important role in explaining these countries’ yield factors, although the regional factor appears to have a smaller role than the global factor and that this result seems to be robust to different subsamples. We interpret this result as evidence on the existence of the regional commonality and on endeavors toward Asian bond markets.

Credit and Liquidity Risks in Euro Area Sovereign Yield Curves

In this paper, we propose a model of the joint dynamics of euro-area sovereign yield curves. The arbitrage-free valuation framework involves five factors and two regimes, one of the latter being interpreted as a crisis regime. These common factors and regimes explain most of the fluctuations in euro-area yields and spreads. The regime-switching feature of the model turns out to be particularly relevant to capture the rise in volatility experienced by fixed-income markets over the last years. In our reduced-form set up, each country is characterized by a hazard rate, specified as some linear combinations of the factors and regimes. The hazard rates incorporate both liquidity and credit components, that we aim at disentangling. The estimation suggests that a substantial share of the changes in euro-area yield differentials is liquidity-driven. Our approach is consistent with the fact that sovereign default risk is not diversifiable, which gives rise to specific risk premia that are incorporated in spreads. Once liquidity-pricing effects and risk premia are filtered out of the spreads, we obtain estimates of the actual – or real-world – default probabilities. The latter turn out to be significantly lower than their risk-neutral counterparts.

Explaining Yield Curve Dynamics

Yield curve dynamics are usually analyzed in terms of the unobservable components—level, slope, and curvature. The factor-augmented vector autoregression (FAVAR) framework applied in this article has become increasingly popular for forecasting interest rates. To link these two strands of research, the authors operate in the space of latent yield and latent macroeconomic factors to analyze the relationship between the term structure of interest rates and the macroeconomic aggregates. They predict the yield curve dynamics by directly forecasting the unobservable yield curve factors. They use the FAVAR methodology to encompass a data-rich environment and to identify dynamic responses of the yield curve to the macroeconomic variables. The empirical results suggest that parsimonious FAVAR models with a few latent macroeconomic factors and a reduced lag order show superior short-horizon forecast performance over simple VAR systems and univariate autoregressions. <b>TOPICS:</b>Fixed-income portfolio management, statistical methods, factor-based models

The Term Structure of Interest Rates and Macro-Portfolio Returns

The paper presents an arbitrage-free yield model based on macro-portfolio dynamics. Apart from a level factor, detrended portfolio values serve as factors for the yield model. Using trend-balanced portfolios and parameters in terms of the instantaneous mean-variance frontier, risk premia and yield curve dynamics are modeled in a natural, integrated, parsimonious way. Positivity constraints on parameters and factors are formulated that guarantee the model is well posed. In an empirical analysis a four-factor model is applied to daily US Treasury yields. We estimate by quasi-maximum likelihood using the unscented Kalman filter. The model fits well, while the estimates of both parameters and factors satisfy the positivity constraints. The analysis reveals a strong link between business cycle variation in yields and risk premia.

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.

Yield Curve Dynamics: Regional Common Factor Model

In this paper, we focus on thorough yield curve modelling. We build on extended classical NelsonSiegel model, which we further develop to accommodate unobserved regional common factors. We centre our discussion on Central European currencies’ yield curves: CZK, HUF, PLN and SKK. We propose a model to capture regional dynamics purely based on state space formulation. The contribution of this paper is twofold: we examine regional yield curve dynamics and we quantify regional interdependencies amongst considered currencies’ yield curves. We conclude that the CZK yield curve possesses its own dynamics corresponding to country specifi c features, whereas other currencies’ yield curves are strongly infl uenced by the regional level, the regional slope factor or both.

Yield Curve Dynamics and Spillovers in Central and Eastern European Countries

This paper applies the models used to study yield curve dynamics and spillovers in the U.S. and other countries to Central and Eastern European countries (CEE countries). Using the Diebold, Rudebusch, and Aruoba (2006) dynamic version of the Nelson-Siegel representation of the yield curve, the paper finds that the two-way relationship between macroeconomic and financial variables in the CEE countries is similar to the one in mature economies. However, inflation shocks have very little persistence in the CEE countries, owing to the strong convergence trends in these countries-which tend to re-anchor expectations faster. Increased convergence in policies and market integration over time are associated with a stronger correlation between the levels of the yield curves, while the curves slopes are more driven by idiosyncratic factors. Shifts in the euro yield curve are transmitted both to interest rates and inflation expectations in the CEE countries-and transmission is stronger after 2004.

Yield Curve Dynamics and Spillovers in Central and Eastern European Countries

This paper applies the models used to study yield curve dynamics and spillovers in the U.S. and other countries to Central and Eastern European countries (CEE countries). Using the Diebold, Rudebusch, and Aruoba (2006) dynamic version of the Nelson-Siegel representation of the yield curve, the paper finds that the two-way relationship between macroeconomic and financial variables in the CEE countries is similar to the one in mature economies. However, inflation shocks have very little persistence in the CEE countries, owing to the strong convergence trends in these countries-which tend to re-anchor expectations faster. Increased convergence in policies and market integration over time are associated with a stronger correlation between the levels of the yield curves, while the curves slopes are more driven by idiosyncratic factors. Shifts in the euro yield curve are transmitted both to interest rates and inflation expectations in the CEE countries-and transmission is stronger after 2004.

Empirical Yield-Curve Dynamics, Scenario Simulation and VAR

This paper has two objectives. First we will construct a general model for the variation in the term structure of interest rates, or to put it another way, we will define a general model for the shift function. Secondly, I will specify a VAR model which uses the shift function derived in the first part of the paper as its main building block.Firstly, using Principal Component Analysis (PCA) we show that it takes a 4 factor model (which, in principle, can very well be considered a 3 factor model due to the limited effect of factor four (4)) to explain the variation in the term structure of interest rates over the period from the beginning of 1990 to mid-1998. These 3 factors can be called a Level factor, a Slope factor and a Curvature factor, where this is in line with what is generally reported in the literature, see among others Litterman and Scheinkmann (1988).Secondly, we specify a VAR model which relies on the scenario simulation procedure of Jamshidian and Zhu (1997). The general idea behind the scenario simulation procedure is to limit the number of portfolio evaluations by using the factor loadings derived in the first part of paper and then specify particular intervals for the Monte Carlo simulated random numbers and assign appropriate probabilities to these intervals (states).We find that the scenario simulation procedure is computational efficient, because we with a limited number of states is capable of deriving robust approximations of the probability distribution. We also find that it is very useful for non-linear securities (Danish MBBs), and argue that the method is feasible for large portfolios of highly complex non-linear securities for example Danish MBBs.

A 3-Factor Model for the Yield-Curve Dynamics - The Case of Stochastic Spot-Rate, Market Price of Risk and Volatility

This paper proposes a new 3-factor model for the dynamic in the yield-curve which belongs to the Affine class of term structure models. Using a yield-factor approach combined with a maximum likelihood estimation technique we conclude the following using Danish bond data over the period 2 January 1990 - 30 June 1998: 1: We find all the parameters to be significant and when comparing the model generated interest rate series against the actual (observed) interest rate series we find for all maturity dates that we cannot reject the hypothesis that both samples have been randomly selected from the same distribution. 2: We also find that there is a high degree of correlation between the predicted interest rates and the observed interest rates - given the state-variables. We also analyse the implied state-variables - that is the state-variables that arise when converting the model into a yield-factor model - and find that there are three dominant factors that govern the dynamic in the term structure of interest rates which can be recognized as, a Short-factor (sometimes called a Steepness-factor), a Level-factor and a Curvature-factor. This is in line with what is generally reported in the literature, see among others Litterman and Scheinkmann (1991). As is generally the case we also find evidence that the Level-factor is close to being nonstationary.

Time‐varying yield curve dynamics and monetary policy

AbstractMonetary policy, the yield curve and the private sector behaviour of the US economy are modelled as a time‐varying structural vector autoregression. The monetary policy shocks of the early 1980s explain a large portion of the persistence of inflation and the level of the term structure. Changes in inflation expectations implied by the yield curve account for the persistence of the federal funds rate. Failures of the expectations hypothesis are rare, and coincided with the credibility building of Paul Volcker's Fed tenure at the beginning of the 1980s and the sequence of consecutive policy rate cuts around the time of the early 1990s recession. Copyright © 2009 John Wiley &amp; Sons, Ltd.

An Option Theory Based Yield Curve Model

The Black-Scholes option theory provides a simple analytical model about the yields of corporate bonds. We extend the theory to model the yields of default free government bonds from a simple observation. From the purchasing power perspective, the values of corporate and government bonds follow similar patterns. The option theory based model of the term structure of interest rates explains major empirical patterns on the shapes and dynamics of yield curves. Compared with existing theories on yield curves, this theory provides a simple analytical theory without additional assumptions about risk, liquidity and preference. It greatly simplifies the understanding and teaching of yield curves.

Stationarity and the Term Structure of Interest Rates: A Characterisation of Stationary and Unit Root Yield Curves

The nature of yield curve dynamics and the determinants of the integration order of yields are investigated using a benchmark economy in which the logarithmic expectations theory holds and the regularity condition of a limiting yield and limiting term premium is satisfied. By considering a zero-coupon yield curve with a complete term structure of maturities, a linear vector autoregressive process is constructed that provides an arbitrarily accurate moving average representation of the complete yield curve as its cross-sectional dimension (n) goes to infinity. We use this to prove the following novel results. First, any I(2) component vanishes owing to the almost sure (a.s) convergence of the innovations to yields as n goes to infinity. Second, the yield curve is stationary if and only if the innovations to log discount bond prices converge a.s.; otherwise yields are I(1). A necessary condition for either stationarity or the absence of arbitrage is that the limiting yield is constant over time. Since the time-varying component of term premia is small in various fixed-income markets, these results provide insight into the critical determinants of the stationarity properties of the term structure.

The Yield Curve and Macroeconomic Dynamics*

We show that microfounded DSGE models with nominal rigidities can be successful in replicating features of bond yield data, including sizeable term premia and volatile long-term yields, which have previously been considered puzzling in general equilibrium frameworks. At the same time, sample moments of consumption growth and inflation can be fit relatively well. The improved model performance does not arise directly from the presence of nominal rigidities. However, this feature introduces (short-run) monetary non-neutrality, so that monetary policy affects consumption dynamics and bond prices. A high degree of 'interest rate smoothing' in the policy rule is essential for our results. At the core of dynamic macroeconomic models, we find equilibrium relationships which describe the allocation of quantities (e.g. consumption and investment) and, when imperfect competition prevails, the setting of prices. These equations are typically valid across time and across states of nature, and financial assets form the tool that is supposed to ensure their validity. Financial assets are therefore an integral part of macroeconomic models. Any well-specified model should be able to match financial data as well as macro data. It is therefore problematic that microfounded models have had a hard time explaining key features of asset prices. The most famous example of this difficulty is the equity premium puzzle but various features of bond yield data have also been char acterised as puzzling in the literature. A number of papers, including Backus et al. (1989), Donaldson et al. (1990), Den Haan (1995) and Chapman (1997), have con cluded that general equilibrium models cannot generate term premia of a magnitude comparable to what we observe in actual data - and may not even be capable of producing positive term premia. For equity, one could argue that fundamentals (the expected future profitability of individual firms) are unobservable and difficult to evaluate. Equity prices may therefore be thought to be subject to fluctuations disconnected from the real economy (information acquisition, fads, etc.) and one could hope that the inability of macroeconomic models to match equity prices does not represent a signal of misspecification. This argument is more difficult to construct for bonds. Bond yields should ultimately reflect expectations of future monetary policy decisions which, at least in recent years, are arguably more predictable than equity fundamentals. Thus, the ability of macroeconomic models to explain bond prices represents an important test of their empirical performance. In this article, we revisit the relationship between bond prices and macroeconomic fundamentals. Contrary to the papers cited above, that rely on flexible price models, we

Global yield curve dynamics and interactions: A dynamic Nelson–Siegel approach

The popular Nelson-Siegel (1987) yield curve is routinely fit to cross sections of intra-country bond yields, and Diebold and Li (2006) have recently proposed a dynamized version. In this paper we extend Diebold-Li to a global context, modeling a potentially large set of country yield curves in a framework that allows for both global and country-specific factors. In an empirical analysis of term structures of government bond yields for the Germany, Japan, the U.K. and the U.S., we find that global yield factors do indeed exist and are economically important, generally explaining significant fractions of country yield curve dynamics, with interesting differences across countries.

Global term structure modelling using principal component analysis

Principal component analysis (PCA) is a technique commonly applied to the interest rate markets to describe yield curve dynamics in a parsimonious manner. Despite an increase in global investing and the growing interconnectedness of the international markets, PCA has not been widely applied to decomposing joint structure of global yield curves. Our objective is to describe the joint structure with a model that can potentially be used for scenario analysis and for estimating the risk of interest rate-sensitive portfolios. In this study, we examine three variations of the PCA technique to decompose global yield curve and interest rate implied volatility structure. We conclude that global yield curve structure can be described with 15–20 factors, whereas implied volatility structure requires at least 20 global factors. The procedure that we identify as preferable is a two-step PCA, with local curves decomposed in the first step and combined local PCs decomposed into a joint structure (PCA of PCs) in the second step. This procedure has a key advantage in that it makes any scenario analysis more meaningful by keeping local PCA factors, which have important economic interpretations as shift, twist and butterfly moves of the yield curve.

Conundrum or Complication: A Study of Yield Curve Dynamics Under Unusual Economic Conditions and Monetary Policies

The definition of the decline of long term yields in the light of increasing short term yields as a conundrum by Chairman Greenspan in February 2005 has generated a significant amount of research. This paper presents a study of yield curve dynamics over this period using economic surprise data as the diagnostic tool. Results are presented for both US and Japanese data which indicate a non-linear response of the yield curve to economic data and monetary policy over the period in question. Further, a limited model is presented that is consistent with the observations. This can lead to an explanation of the conundrum in terms of a non-linear yield response to expected long term inflation and a variable expected long term real rate.