Term Structure Of Interest Rates Research Articles

Bond supply expectations and the term structure of interest rates

This paper investigates the influence of forward-looking government bond supply information on changes in the term structure of interest rates. While traditional arbitrage-free models suggest that bond supply should not impact bond yields, models accounting for preferred-habitat investors and imperfect asset substitutability raise this possibility. By analysing debt supply expectations derived from Germany's Treasury press releases, we find that news about expected bond supply affects bond yields, supporting the notion that supply expectations influence current interest rates. Our study also extends macro-finance models, highlighting the significant role of supply expectations in term structure dynamics. Additionally, we provide insights into the puzzle of German government bond yields falling below the ECB deposit rate.

EXTRACTING PRICE SIGNALS FROM THE TERM STRUCTURE OF COMMODITY AND CREDIT MARKETS USING AUSTRIAN BUSINESS CYCLE THEORY

Austrian School economists first explained the significance of interest rates for the structure of production in time. Furthermore, they showed how manipulating the level of interest and the credit supply causes the business cycle (v.Böhm-Bawerk, 1891; v.Hayek, 1938; v.Hayek, 1941 and v.Mises, 1949). More recently, Austrian School economists have elaborated the relationship between the term structure of interest rates and the business cycle (Barnett and Block, 2009; Bagus and Howden, 2010; Bagus et al., 2018; Potuzak and Nemec, 2020; Alonso-Neira and Sanchez-Bayon, 2023). At the same time, market practitioners understand the potency of yield curve inversions as a predictor of future recessions as a result of experience and observation unrelated to Austrian Business Cycle Theory (ABCT). Reference textbooks (Stigum and Crescensi, 2007) explain that capital allocators are pricing in future cuts to the central bank discount rate, thus inverting the yield curve. This ignores the role of free-market price signals in credit, which result from supply and demand fundamentals, and are the link connecting ABCT to term structures.The term structure of commodities markets is also affected by actual or anticipated shortfalls in production over different time horizons. This is widely understood, perhaps because settlement by physical delivery is commonplace and tangible (Hull, 2022). Even though credit and derivatives may at first glance seem more abstract, the same underlying market principles are at work there. The theoretical foundations of and recent work on ABCT provide the necessary tools to analyse both markets through the same lens.

Revisiting the fitting of the Nelson–Siegel and Svensson models

The Nelson–Siegel and the Svensson models are two widely used models for the term structure of interest rates. These models are quite simple and intuitive, but fitting them to market data is numerically challenging and various difficulties have been reported. In this paper, we provide a novel mathematical analysis of the fitting problem based on parametric optimization. We formulate the fitting problem as a separable nonlinear least-squares problem, in which the linear parameters can be eliminated. We provide a thorough discussion on the conditioning of the inner part of the reformulated problem and show that many of the reported difficulties encountered when solving it are inherent to the problem formulation itself and cannot be tackled by choosing a particular optimization algorithm. Our stability analysis provides novel insights that we use to show that some of the ill-conditioning can be avoided, and that a suitably chosen penalty approach can be used to address the remaining ill-conditioning. Numerical results indicate that this approach has the expected impact while being independent of any choice of a particular optimization algorithm. We further establish smoothness properties of the reduced objective function, putting global optimization methods for the reduced problem on a sound mathematical basis.

Dynamic Asset Pricing in a Unified Bachelier–Black–Scholes–Merton Model

We present a unified, market-complete model that integrates both Bachelier and Black–Scholes–Merton frameworks for asset pricing. The model allows for the study, within a unified framework, of asset pricing in a natural world that experiences the possibility of negative security prices or riskless rates. Unlike the classical Black–Scholes–Merton, we show that option pricing in the unified model differs depending on whether the replicating, self-financing portfolio uses riskless bonds or a single riskless bank account. We derive option price formulas and extend our analysis to the term structure of interest rates by deriving the pricing of zero-coupon bonds, forward contracts, and futures contracts. We identify a necessary condition for the unified model to support a perpetual derivative. Discrete binomial pricing under the unified model is also developed. In every scenario analyzed, we show that the unified model simplifies to the standard Black–Scholes–Merton pricing under specific limits and provides pricing in the Bachelier model limit. We note that the Bachelier limit within the unified model allows for positive riskless rates. The unified model prompts us to speculate on the possibility of a mixed multiplicative and additive deflator model for risk-neutral option pricing.

U.S. macroeconomic news and low-frequency changes in bond yields in Canada, Sweden and the U.K.

This paper investigates the importance of U.S. macroeconomic news in driving low-frequency fluctuations in the term structure of interest rates in Canada, Sweden, and the U.K. We follow two complementary approaches: First, we apply a regression-based framework that aggregates the impact of daily macroeconomic news on bond yields to a lower quarterly frequency. Next, we estimate a macro-finance affine term structure model linking the daily news to lower-frequency changes in bond yields and its expectations and term premia components. Both approaches show that U.S. macroeconomic news is an important source of lower-frequency quarterly fluctuations in bond yields in these open economies, and even more important than their respective domestic macroeconomic news. Furthermore, the macro-finance model shows that U.S. macroeconomic news is particularly important in explaining low-frequency changes in the expectation components of the nominal, real, and break-even inflation rates.

A Smooth Shadow-Rate Dynamic Nelson-Siegel Model for Yields at the Zero Lower Bound

We propose a smooth shadow-rate version of the dynamic Nelson-Siegel (DNS) model to analyze the term structure of interest rates during a zero lower bound (ZLB) period. By relaxing the no-arbitrage restriction, our shadow-rate model becomes highly tractable with a closed-form yield curve expression. This permits the implementation of readily available DNS extensions such as allowing for time-varying parameters and the integration of macroeconomic variables. Using U.S. Treasury data, we provide clear evidence of a smooth transition of the yields entering and leaving the ZLB state. Moreover, we show that the smooth shadow-rate DNS model dominates the baseline DNS model and (shadow-rate) affine term structure models in terms of fitting and forecasting the yield curve, while it also produces plausible policy insights at the ZLB.

Testing rational expectations in a cointegrated VAR with structural change

The rational expectation hypothesis is widely used in finance and macroeconomics. A research question investigates whether models using this hypothesis can fit the data well. Researchers have been developing econometric procedures to test rational expectation models. Sargent and Hansen (1991) proposed how to test exact rational expectation restrictions. This study aims to achieve three objectives. The first objective is to extend Johansen and Swensen’s framework that test exact rational expectation restrictions to the case where the data-generating process is a cointegrated vector autoregressive model with abrupt structural change (CVAR-SC). The second goal is to highlight that the type of rational expectation restrictions analysed in this paper imply co-breaking, as defined by Hendry and Mizon (1998). Finally, the restrictions on the CVAR-SC parameters implied by the present value model and expectation hypothesis of the interest rate term structure are analysed, derived and tested. Three empirical exercises are reported. The first is Engsted (2002)’s dataset on share prices and dividends, the second uses a Brazilian term structure data set and the third uses a North American term structure dataset.

Near-term forward rate spread and commodity index relationship with real economic activity in Brazil

This study investigates the relationship between Brazilian economic cycles and two key indicators: the international S&P GSCI commodity index and the near-term forward spread derived from the Brazilian interest rate term structure. We find that the forward spread serves as a robust leading indicator of economic downturns in Brazil, offering recession forecasts up to four quarters in advance. This underscores a link between yield curve steepness and recession likelihood in Brazil. However, we uncover distinct cyclical behaviors in Brazil's term structure that diverge from patterns in the United States. Furthermore, our research reveals the significant influence of commodity price fluctuations on Brazil's economic performance, underscoring a strong correlation between commodity markets and economic outcomes. Examining term structure and commodity prices together provides novel insights into monitoring emerging market cycles. These indicators can assist policymakers and improve early warning systems, especially in developing economies like Brazil.

A Multicountry Model of the Term Structures of Interest Rates with a GVAR

Abstract Extant multicountry affine term structure models (ATSMs) handle global financial interdependence at the cost of increasing model dimensionality. To address this challenge, we propose a novel no-arbitrage ATSM with risk factor dynamics following a global vector-autoregressive (GVAR). Compared to referenced benchmarks, the GVAR − ATSM offers a more parsimonious representation, enables a faster estimation process, produces more precise model estimates, yields more plausible term premia dynamics, and improves bond yield out-of-sample forecasting. Furthermore, our empirical findings reveal the significant impact of China’s economic stances on Latin American yield curve dynamics, underscoring its importance as a global economic player.

Supply and Demand and the Term Structure of Interest Rates

Supply and Demand and the Term Structure of Interest Rates

Estimating time-varying factors’ variance in the string-term structure model with stochastic volatility

This paper presents a novel term structure of interest rate (TSIR) model with stochastic volatility and jumps (SVJ) that combines the market framework proposed by Brace et al. (1997) with the string-shock framework of Santa-Clara and Sornette (2001). In this model, the factors’ variance is estimated through the eigendecomposition of a variance–covariance matrix obtained with a measure of market volatility derived from out-of-the-money option prices and historical correlations of interest rates traded in the futures market. The stochastic evolution of the factors’ variance is governed by the 4/2 model developed by Grasselli (2017), including jumps. A novel method is employed to estimate the parameters of the SVJ model that minimizes the distance between the sample moments and the moments of a gamma distribution. The empirical application of the model in the Brazilian derivatives market demonstrates its effectiveness in accurately capturing the volatility smile of interest rate options.

A recursive method for fractional Hawkes intensities and the potential approach of credit risk

This article explores the potential approach for credit risk, which is an alternative to structural and reduced models. In the context of credit risk, it consists in assuming that the survival probability of a company is equal to the ratio of the expected value of a supermartingale divided by its initial value. This approach, that was previously used for modeling the term structure of interest rates, is extended by the use of a fractional self-exciting process, or fractional Hawkes process. This is a self-exciting process that is time-changed by the inverse of an alpha-stable subordinator. A self-exciting process allows to take into account the clustering of economic events such as defaults, whereas the time-change allows to properly fit highly convex survival probability curves. We derive a new recursive method that allows to compute all the moments of a self-exciting process intensity, as well as its time-changed counterpart. We show that this method can be used to approximate the survival probabilities in the potential approach. More specifically, we prove that the approximation converges and we provide a bound on the numerical error. Finally, we calibrate the model and show that it allows to properly fit survival probability curves that are highly convex.

Fixed-income average options: a pricing approach based on Gaussian mean-reverting cyclical models

This paper values fixed-income (discrete- and continuous-time) European Asian and Australian options. We assume that the term structure of interest rates is modelled by the specification proposed in Moreno et al. (Econ Model 72:140–150, 2018, https://doi.org/10.1016/j.econmod.2018.01.015). We obtain closed-form expressions for the premiums of geometric average options and, for arithmetic average options, premiums are computed by numerical methods. We also perform a sensitivity analysis with respect to different parameters for both (geometric and arithmetic) options.

A Theory of the Term Structure of Interest Rates under Limited Household Risk Sharing

Abstract We present a theory in which the interaction between limited sharing of idiosyncratic labor income risk and labor adjustment costs (that endogenously arise through search frictions) determines interest rate dynamics. In the general equilibrium, the interaction of these two ingredients relates bond risk premiums, cross-sectional skewness of income growth, and labor market tightness. Our model rationalizes an upward-sloping average yield curve and predicts a negative relation between labor market tightness and bond risk premiums. We provide evidence for our theory’s mechanism and predictions.

The Effects of Conventional and Unconventional Monetary Policy Shocks on US REITs Moments: Evidence from VARs with Functional Shocks

AbstractWe use a vector autoregressive model with functional shocks, capturing the shift of the entire term structure of interest rates on monetary policy announcement dates, to empirically evaluate the effects of conventional and unconventional monetary policy decisions on the Real Estate Investment Trusts (REITs) markets of the United States (US). Using 5-min interval intraday data, we analyze not only the impact on REITs returns, but also its realized variance (RV), realized jumps (RJ), realized skewness (RSK), and realized kurtosis (RKU) over the daily period of September 2008 to June 2021. While the effects of conventional monetary policy shocks on the moments of REITs returns tend to conform with economic theories, the same is not necessarily the case with unconventional monetary policy shocks. In addition, though monetary policy shocks have the most persistent and strongest effects on RJ, the extreme behaviour of the REITs market is also observed through RSK and RKU. Moreover, when we look into 10 REITs sectors, there is indeed heterogeneity in terms of the strength of the effect, but not so much in terms of the sign of responses of the various moments compared to the overall market. Our results have important implications for REITs market participants, given its exponential growth as an asset class.

The Relationship between SOFR and Market Yield of U.S. Treasury Securities

This paper introduces the characteristic of the new benchmark rate Secured Overnight Financing Rate (SOFR), explain its connection to the futures price, and show its potential to provide new insight into the argument on interest rate term structure. Based on the future price discovery theory, this study set up a hypothesis that short-term interest rates should contribute to forecasting long-term ones. The causality between interest rates in different terms of, which are separately represented by bilateral repurchase rate and the market yield of long-term U.S. government bonds, is explored in this research using the VAR model, as well as the Granger causality test. The conclusion of this research proves the hypothesis and indicates a single-direction causality between interest rate of different terms. However, the research also has drawbacks such as ignoring non-linear relations and evading the change of government policy. These problems need to be solved in the following study.

The term structure of interest rates and economic activity: Evidence from the COVID‐19 pandemic

AbstractThis paper tests the accuracy and predictability of two term structure models using both yields‐only and factor‐augmented specifications focusing on the recent COVID‐19 crisis. In addition, we test the predictive ability of the yield curve on economic activity for the United States and other advanced countries. We provide evidence that models with an enhanced information set, including COVID‐19 factors, improve interest rate forecasts for this period. Also, we point out that term structure models can determine future variations in economic activity but are time‐ and country‐sensitive. Finally, out‐of‐sample analysis reveals that the use of factor‐augmented term structure models, to reflect the current economic and market conditions, improves their forecasting accuracy.

Static term structure of interest rate construction with tension interpolation splines

<abstract><p>Traditional theories of term structure of interest rate consist of four major classical theories, including Pure Expectation Theory, Liquidity Preference Theory, Preferred Habitat Theory and Market Segmentation Theory. However, they cannot be well interpreted by the traditional static term structure of interest rate methods such as polynomial spline and exponential spline. To address problems on low precision and weak stability of traditional methods in constructing static interest rate term structure curve, in this paper, we introduce the tension interpolation spline based on a fourth-order differential equation with local tension parameters calculated by Generalized Reduced Gradient (GRG) algorithm. Our primary focus is to illustrate its better prediction effect and stability with an empirical study conducted using datum of treasury bonds. Then, we divided the datum into intra-sample datum for estimating tension parameters and out-of-sample datum for evaluating their robustness of predicting stochastics collected from Shanghai Stock Exchange on $ {2^{{\rm{nd}}}} $ February, 2019. According to the principle of total least squares and total least absolute deviations, the result shows that the tension interpolation spline model has better precision and stronger stability in prediction of out-of-sample treasury bonds prices compared with the model established by polynomial spline and exponential spline. In addition, it can better explain the Liquidity Preference Theory, which confirms that it is suitable for constructing the static term structure of interest rates in the securities exchange market.</p></abstract>

Accuracy of analytical approximation formula for bond prices in a three-factor convergence model of interest rates

We consider a convergence model of interest rates, in which the behaviour of the domestic instantaneous interest rate (so called short rate) depends on the short rate in a monetary union that the country is going to join. The short rate in the monetary union is modelled by a two-factor model, which leads to a three-factor model for the domestic rate. In this setting, term structures of interest rates are computed from bond prices, which are obtained as solutions to a parabolic partial differential equation. A closed-form solution is known only in special cases. An analytical approximation formula for the domestic bond prices has been proposed, with the error estimate only for certain parameter values, when the solution has a separable form. In this paper, we derive the order of accuracy in the general case. We also study a special case, which makes it possible to model the phenomenon of negative interest rates that were observed in the previous years. It turns out that it leads to a higher accuracy than the one achieved in the general case without restriction on parameters.

Монетарные сюрпризы и временная структура процентных ставок: идентификация посредством гетероскедатичности

How does an unexpected change in the Bank of Russia key rate affect the bond market? This article quantifies the impact of monetary surprises on government bond yields of various maturities. To estimate the causal effect with the joint dynamics of the key rate and bond yields (that is, to solve the problem of endogenous bias), we use the heteroscedasticity-driven identification method that requires weaker assumptions than other alternative methods used in the literature. The results confirm the significant impact of monetary policy surprises on the interest rate term structure, with a greater effect on short-term rates. In contrast to previous studies, the behavior of long-term rates is consistent with the expectations hypothesis: risk premia do not respond significantly to a monetary shock.