Term Structure Models

2017 ◽  
Author(s):  
Kerry E. Back
Keyword(s):  
Term Structure ◽  
Yield Curve ◽  
Model Parameters ◽  
Bond Yields ◽  
Expectations Hypothesis ◽  
Forward Rates ◽  
Affine Models ◽  
Deterministic Function ◽  
Root Model ◽  
Quadratic Models

Bond yields and forward rates are defined. The fundamental PDE is derived. Affine term strucure models are explained, including the Vasicek model and the Cox‐Ingersoll‐Ross square root model. Gaussian affine models, completely affine models, and multifactor CIR models are explained. Quadratic models are described. The various versions of the expectations hypothesis are explained. We can fit a given yield curve by adding a deterministic function of time to an interest rate model or allowing model parameters to be time varying. Heath‐Jarrow‐Morton models are explained, and it is shown that drifts of forward rates under the risk neutral probability are determined by their volatilities.

A Consumption Based Term Structure Model w ith Habit Utility

2018 ◽  
Vol 9 (6) ◽  
pp. 484-496
Author(s):  
Jun Lou ◽  
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Yield Curve ◽  
Bond Yields ◽  
Expectations Hypothesis ◽  
Term Structure Model ◽  
Bond Risk Premia ◽  
The Interest Rate ◽  
Bond Risk

This paper proposes a term structure of interest rates model that modifies and extends the Campbell and Cochrane (1999) surplus consumption framework. The distinguishing contributions are tractable, continuous-time analytical solutions for the term structure of interest rate generating a realistic upward sloping yield curve. Despite the focus on the term structure, the model matches plausible equity quantities. For the interest rate, the model is able to account for the moments of bond yields at numerous maturities and produce countercyclical bond risk premia as seen in the data. Moreover, the model captures reasonable time series fluctuation on real interest rates. However, the model has difficulties reproducing empirical deviations from the expectations hypothesis.

scholarly journals MODELING TERM STRUCTURE DYNAMICS: AN INFINITE DIMENSIONAL APPROACH

2005 ◽  
Vol 08 (03) ◽  
pp. 357-380 ◽  
Author(s):  
RAMA CONT
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Yield Curve ◽  
Dimensional Space ◽  
Forward Rate ◽  
Model Parameters ◽  
Stochastic Pde ◽  
Forward Rates ◽  
Infinite Dimensional ◽  
Average Shape

Motivated by stylized statistical properties of interest rates, we propose a modeling approach in which the forward rate curve is described as a stochastic process in a space of curves. After decomposing the movements of the term structure into the variations of the short rate, the long rate and the deformation of the curve around its average shape, this deformation is described as the solution of a stochastic evolution equation in an infinite dimensional space of curves. In the case where deformations are local in maturity, this equation reduces to a stochastic PDE, of which we give the simplest example. We discuss the properties of the solutions and show that they capture in a parsimonious manner the essential features of yield curve dynamics: imperfect correlation between maturities, mean reversion of interest rates, the structure of principal components of forward rates and their variances. In particular we show that a flat, constant volatility structures already captures many of the observed properties. Finally, we discuss parameter estimation issues and show that the model parameters have a natural interpretation in terms of empirically observed quantities.

The term structure of Eurozone peripheral bond yields: an asymmetric regime-switching equilibrium correction approach

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
Christos Avdoulas ◽  
Stelios Bekiros ◽  
Brian Lucey
Keyword(s):  
Term Structure ◽  
Regime Switching ◽  
Yield Curve ◽  
Bond Yields ◽  
Short Term ◽  
Economic Implications ◽  
Expectations Hypothesis ◽  
The Difference ◽  
The Business Cycle ◽  
Equilibrium Correction

AbstractSeveral studies have established the predictive power of the yield curve i.e. the difference between long and short-term bond rates and the role of asymmetries in the term structure of bond yields with respect to real economic activity. Using an extensive dataset, comprising 3-month, 1-year, 5-year and 10-year constant maturity Treasury bonds for the Eurozone southern periphery countries – the so-called “PIIGS” – from January 1999 to April 2019, we investigate the links between bond yields of different maturities for the Eurozone southern peripheral countries and we find they co-evolve in line with the predictions of the Expectations Hypothesis theory. We demonstrate the presence of nonlinearities in the term structure, and utilize a multivariate asymmetric two-regime Markov-switching VAR methodology to model them properly. Moreover, we address the economic reasoning behind the introduction of an equilibrium-correction regime-switching approach, hence providing potentially important insights on the behaviour of the entire yield curve. We reveal that the regime shifts are related to the state of the business cycle, particularly in economies in which monetary policy decisions are implemented via changes in short-term rates as a response to deviations of output from equilibrium levels. Our results may have important statistical and economic implications on the behaviour of the term structure of bond yields.

scholarly journals Does The Expectations Hypothesis Explain The Term Structure Of Treasury Bond Yields In Tunisia?

2015 ◽  
Vol 32 (1) ◽  
pp. 239
Author(s):  
Jamel Boukhatem
Keyword(s):  
Term Structure ◽  
Yield Curve ◽  
Aggregate Demand ◽  
Bond Market ◽  
Bond Yields ◽  
Monthly Data ◽  
Expectations Hypothesis ◽  
Cointegrated Var ◽  
Treasury Bond ◽  
One Year

<p><em>This paper tests the expectations hypothesis (EH) using monthly data for Treasury bond yields (TBYs) over the period 1994m5–2014m12 and ranging in maturity from one year to 10 years. We apply cointegrated-VAR jointly on more than one pair of yields. The results suggest rejection of the EH throughout the medium maturity spectrum. However, for longer maturities they suggest the validity of the EH for the TBYs. This indeed confirms the smooth functioning of Tunisian bond market which gives an indication that the yield curve should serve as an indicator to the monetary policymakers to manage inflation and to influence the aggregate demand in the economy.</em></p><p><strong> </strong></p>

An International Examination of Affine Term Structure Models and the Expectations Hypothesis

2007 ◽  
Vol 42 (1) ◽  
pp. 41-80 ◽  
Author(s):  
Huarong Tang ◽  
Yihong Xia
Keyword(s):  
Term Structure ◽  
Yield Curve ◽  
Expectations Hypothesis ◽  
Affine Term Structure ◽  
Forward Rates ◽  
Affine Term Structure Models ◽  
Term Structure Models ◽  
Affine Model ◽  
The U.S ◽  
Three Factor

AbstractWe examine the yield curve behavior and the relative performance of affine term structure models (ATSMs) using government bond yield data from Canada, Germany, Japan, the U.K., and the U.S. We find strong predictability of forward rates for excess bond returns and reject the expectations hypothesis in all five countries. A three-factor model is sufficient to capture movements in the yield curve of Canada, Japan, the U.K., and the U.S., but may not be enough for Germany. An exhaustive comparison among ATSMs with no more than three factors reveals that the three-factor essential affine model (A1(3)E), with only one factor affecting the volatility of the short rate but with all three factors affecting the price of risk, performs best in all five countries. Simulations provide inconclusive evidence on whether this best affine model can successfully generate the rich yield curve behavior observed in the data.

scholarly journals A Nonparametric Approach to Bond Portfolio Immunization

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1121
Author(s):  
Victor Lapshin
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Best Practice ◽  
Yield Curve ◽  
Model Parameters ◽  
Dimensional Manifold ◽  
Nonparametric Approach ◽  
Hedging Portfolio ◽  
Practice Approach ◽  
Low Dimensional

We consider the problem of short term immunization of a bond-like obligation with respect to changes in interest rates using a portfolio of bonds. In the case that the zero-coupon yield curve belongs to a fixed low-dimensional manifold, the problem is widely known as parametric immunization. Parametric immunization seeks to make the sensitivities of the hedged portfolio price with respect to all model parameters equal to zero. However, within a popular approach of nonparametric (smoothing spline) term structure estimation, parametric hedging is not applicable right away. We present a nonparametric approach to hedging a bond-like obligation allowing for a general form of the term structure estimator with possible smoothing. We show that our approach yields the standard duration based immunization in the limit when the amount of smoothing goes to infinity. We also recover the industry best practice approach of hedging based on key rate durations as another particular case. The hedging portfolio is straightforward to calculate using only basic linear algebra operations.

scholarly journals Testes da Hipótese de Expectativas na Estrutura a Termo das Taxas de Juros Brasileiras

2003 ◽  
Vol 1 (1) ◽  
pp. 19
Author(s):  
Benjamin Miranda Tabak ◽  
Sandro Canesso de Andrade
Keyword(s):  
Monetary Policy ◽  
Interest Rates ◽  
Term Structure ◽  
Risk Premium ◽  
Rational Expectations ◽  
Yield Curve ◽  
Single Equation ◽  
Expectations Hypothesis ◽  
Macro Modeling ◽  
Daily Data

We test the Expectations Hypothesis (EH) plus Rational Expectations (RE) in the Brazilian term-structure of interest rates, using maturities ranging from 1 month to 12 months, and daily data from 1995 to 2000. We rely on two methodologies based on single-equation regressions. Our results indicate a rejection of the EH plus RE, specially at the longer maturity. This may have important implications for the rational expectations macro-modeling currently being used to evaluate the conduct of monetary policy in Brazil. We also show the risk premium in the yield curve are positively related to the covered interest rate differential and to the volatility of interest rates.

Estimation of Peru’s sovereign yield curve: the role of macroeconomic and latent factors

2019 ◽  
Vol 46 (3) ◽  
pp. 533-563
Author(s):  
Alejandra Olivares Rios ◽  
Gabriel Rodríguez ◽  
Miguel Ataurima Arellano
Keyword(s):  
Term Structure ◽  
Risk Premium ◽  
Yield Curve ◽  
International Markets ◽  
Bond Yields ◽  
Content Type ◽  
Vector Autoregressive ◽  
Term Structure Model ◽  
No Arbitrage ◽  
Unobservable Factors

PurposeFollowing Ang and Piazzesi’s (2003) study, the authors use an affine term structure model to study the relevance of macroeconomic (domestic and foreign) factors for Peru’s sovereign yield curve in the period from November 2005 to December 2015. The paper aims to discuss this issue.Design/methodology/approachRisk premia are modeled as time-varying and depend on both observable and unobservable factors; and the authors estimate a vector autoregressive model considering no-arbitrage assumptions.FindingsThe authors find evidence that macro factors help to improve the fit of the model and explain a substantial amount of variation in bond yields. However, their influence is very sensitive to the specification model. Variance decompositions show that macro factors explain a significant share of the movements at the short and middle segments of the yield curve (up to 50 percent), while unobservable factors are the main drivers for most of the movements at the long end of the yield curve (up to 80 percent). Furthermore, the authors find that international markets are relevant for the determination of the risk premium in the short term. Higher uncertainty in international markets increases bond yields, although this effect vanishes quickly. Finally, the authors find that no-arbitrage restrictions with the incorporation of macro factors improve forecasts.Originality/valueTo the authors’ knowledge this is the first application of this type of models using data from an emerging country such as Peru.

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