4 Modeling the term structure

doi:10.1016/S0169-7161(96)14006-2

Handbook of Statistics

Volume 14, 1996, Pages 91-118

https://doi.org/10.1016/S0169-7161(96)14006-2 Get rights and content

Publisher Summary

This chapter describes the methods of modeling the term structure that are to be found in the econometrics and finance literatures. By utilizing a factor representation, the chapter shows that there are many similarities in the two approaches. However, there are also some differences. Within the econometrics literature, it is common to assume that yields are integrated processes and that spreads constitute the co-integrating relations. Although the finance literature takes the stance that yields are near integrated, but stationary, it emerges that the models used in that literature would not predict that the spreads are co-integrating errors if one actually replaced the stationarity assumption by one of a unit root. The reason for this outcome is found to lie in the assumption that the conditional volatility of yields is a function of the level of the yields. Empirical work tends to support such a hypothesis and suggests that the consequences of such a relationship can be profound for testing propositions about the term structure. The chapter also presents a number of stylized facts about a set of data on yields that prove useful in assessing the likely adequacy of many of the models that are used in finance for capturing the term structure.

References (55)

AminK.I. et al.
Implied volatility functions in arbitrage-free term structure models
J. Financ. Econom.
(1994)
BaillieR.T. et al.
Prediction in dynamic models with time-dependent conditional variances
J. Econometrics
(1992)
BrennanM.J. et al.
A continuous time approach to the pricing of bonds
J. Banking Finance
(1979)
BrownR.H. et al.
The term structure of real interest rates and the Cox, Ingersoll and Ross model
J. Financ. Econom.
(1994)
EngstedT. et al.
Cointegration and the US term structure
J. Banking Finance
(1994)
EvansM.D.D. et al.
Do stationary risk premia explain it all? Evidence from the term structure
J. Monetary Econom.
(1994)
JohansenS.
Statistical analysis of cointegrating vectors
J. Econom. Dynamic Control
(1988)
AbkenP.A.
Generalized method of moments tests of forward rate processes
AndersonH.M.
Transaction costs and nonlinear adjustment towards equilibrium in the US treasury bill market
(1994)
BaillieR.T. et al.
Fractionally integrated autoregressive conditional heteroskedasticity
(1993)

BollerslevT. et al.

Common persistence in conditional variances: Definition and representation

Econometrica

(1993)

BoudoukhJ.

An equilibrium model of nominal bond prices with inflation-output correlation and stochastic volatility

J. Money, Credit and Banking

(1993)

BrennerR.J. et al.

Another look at alternative models of the short-term interest rate

(1994)

BrownS.J. et al.

The empirical implications of the Cox-Ingersoll-Ross theory of the term structure of intestest rates

J. Finance

(1986)

BrozeL.O. Scaillet et al.

Testing for continuous-time models of the short-term interest rates

CORE Discussion Paper 9331

(1993)

CampbellJ.Y. et al.

Yield spreads and interest rate movements: A bird's eye view

Rev. Econom. Stud.

(1991)

CanovaF. et al.

Reconciling the term structure of interest rates with the consumption based ICAP model

(1993)

ChanK.C. et al.

An empirical comparison of alternative models of the short-term interest rate

J. Finance

(1992)

ChenR.R. et al.

Pricing interest rate options in a two factor Cox-Ingersoll-Ross model of the term structure

Rev. Financ. Stud.

(1992)

ChenR.R. et al.

Maximum likelihood estimation for a multifactor equilibrium model of the term structure of interest rates

J. Fixed Income

(1993)

ConleyT. et al.

Estimating subordinated diffusions from discrete time data

(1994)

ConstantinidesG.

A theory of the nominal structure of interest rates

Rev. Financ. Stud.

(1992)

CoxJ.C. et al.

A theory of the term structure of interest rates

Econometrica

(1985)

DuffieD. et al.

A yield-factor model of interest rates

(1993)

DybvigP.H.

Bonds and bond option pricing based on the current term structure

EdmisterR.O. et al.

Informational content in interest rate term structures

Rev. Econom. Statist.

(1993)

EggintonD.M. et al.

An investigation of the effect of funding on the slope of the yield curve

Cited by (34)

Nonparametric cointegration analysis of fractional systems with unknown integration orders
2010, Journal of Econometrics
Citation Excerpt :
The restrictions laid down by the expectations hypothesis in terms of cointegration rank are tested within the fractional cointegration framework. For a general overview of term structure theory, see e.g. the survey by Pagan et al. (1996). In Fig. 1 the four interest rates are plotted.
In this paper a nonparametric variance ratio testing approach is proposed for determining the cointegration rank in fractionally integrated systems. The test statistic is easily calculated without prior knowledge of the integration order of the data, the strength of the cointegrating relations, or the cointegration vector(s). The latter property makes it easier to implement than regression-based approaches, especially when examining relationships between several variables with possibly multiple cointegrating vectors. Since the test is nonparametric, it does not require the specification of a particular model and is invariant to short-run dynamics. Nor does it require the choice of any smoothing parameters that change the test statistic without being reflected in the asymptotic distribution. Furthermore, a consistent estimator of the cointegration space can be obtained from the procedure. The asymptotic distribution theory for the proposed test is non-standard but easily tabulated or simulated. Monte Carlo simulations demonstrate excellent finite sample properties, even rivaling those of well-specified parametric tests. The proposed methodology is applied to the term structure of interest rates, where, contrary to both fractional- and integer-based parametric approaches, evidence in favor of the expectations hypothesis is found using the nonparametric approach.
Simulated Score Methods and Indirect Inference for Continuous-time Models
2010, Handbook of Financial Econometrics, Vol 1
This chapter describes a simulated method of moments estimator that is implemented by choosing the vector valued moment function to be the expectation under the structural model of the score function of an auxiliary model, where the parameters of the auxiliary model are eliminated by replacing them with their quasi-maximum likelihood estimates. This leaves a moment vector depending only on the parameters of the structural model. Structural parameter estimates are those parameter values that put the moment vector as closely to zero as possible in a suitable generalized method of moments metric. This methodology can also be interpreted as a practical computational strategy for implementing indirect inference. One argues that considerations from statistical science dictate that the auxiliary model should approximate the true data-generating process as closely as possible and show that using the seminonparametric model is one means to this end. When the view of close approximation is accepted in implementation, the methodology described here is usually referred to as Efficient Method of Moments in the literature because the estimator is asymptotically as efficient as maximum likelihood under correct specification and the detection of model error is assured under incorrect specification.
The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach
2009, Computational Statistics and Data Analysis
The dynamics for interest rate processes within the well-known multi-factor Heath, Jarrow and Morton (HJM) specification are considered. Despite the flexibility of and the notable advances in theoretical research about the HJM model, the number of empirical studies of it is still very sparse. This paucity is principally due to the difficulties in estimating models in this class, which are not only high-dimensional, but also nonlinear and involve latent state variables. The estimation of a fairly broad class of HJM models as a nonlinear filtering problem is undertaken by adopting the local linearization filter, which is known to have some desirable statistical and numerical features, so enabling the estimation of the model via the maximum likelihood method. The estimator is then applied to the US, the UK and the Australian markets. Different two- and three-factor models are found to be the best for each market, with the factors being the level, the slope and the “twist” effect. The contribution of each factor towards overall variability of the interest rates and the financial reward each factor claims are found to differ considerably from one market to another.
Forecasting the term structure of government bond yields
2006, Journal of Econometrics
Despite powerful advances in yield curve modeling in the last 20 years, comparatively little attention has been paid to the key practical problem of forecasting the yield curve. In this paper we do so. We use neither the no-arbitrage approach nor the equilibrium approach. Instead, we use variations on the Nelson–Siegel exponential components framework to model the entire yield curve, period-by-period, as a three-dimensional parameter evolving dynamically. We show that the three time-varying parameters may be interpreted as factors corresponding to level, slope and curvature, and that they may be estimated with high efficiency. We propose and estimate autoregressive models for the factors, and we show that our models are consistent with a variety of stylized facts regarding the yield curve. We use our models to produce term-structure forecasts at both short and long horizons, with encouraging results. In particular, our forecasts appear much more accurate at long horizons than various standard benchmark forecasts.
Interest rates hierarchical structure
2005, Physica A: Statistical Mechanics and its Applications
We propose a general method to study the hierarchical organization of financial data by embedding the structure of their correlations in metric graphs in multi-dimensional spaces. An application to two different sets of interest rates is discussed by constructing triangular embeddings on the sphere. Three-dimensional representations of these embeddings with the correct metric geometry are constructed and visualized. The resulting graphs contain the minimum spanning tree as a sub-graph and they preserve its hierarchical structure. This produces a clear cluster differentiation and allows us to compute new local and global topological quantities.
An interest rates cluster analysis
2004, Physica A: Statistical Mechanics and its Applications
An empirical analysis of interest rates in money and capital markets is performed. We investigate a set of 34 different weekly interest rate time series during a time period of 16 years between 1982 and 1997. Our study is focused on the collective behavior of the stochastic fluctuations of these time series which is investigated by using a clustering linkage procedure. Without any a priori assumption, we individuate a meaningful separation in 6 main clusters organized in a hierarchical structure.

View all citing articles on Scopus

: * We are grateful for comments on previous versions of this paper by John Robertson, Peter Phillips and Ken Singleton. All computations were performed with a beta version of MICROFIT 4 and GAUSS 3.2

View full text

4 Modeling the term structure

Publisher Summary

J. Financ. Econom.

J. Econometrics

J. Banking Finance

J. Financ. Econom.

J. Banking Finance

J. Monetary Econom.

J. Econom. Dynamic Control

Generalized method of moments tests of forward rate processes

Transaction costs and nonlinear adjustment towards equilibrium in the US treasury bill market

Fractionally integrated autoregressive conditional heteroskedasticity

Common persistence in conditional variances: Definition and representation

Econometrica

An equilibrium model of nominal bond prices with inflation-output correlation and stochastic volatility

J. Money, Credit and Banking

Another look at alternative models of the short-term interest rate

The empirical implications of the Cox-Ingersoll-Ross theory of the term structure of intestest rates

J. Finance

Testing for continuous-time models of the short-term interest rates

CORE Discussion Paper 9331

Yield spreads and interest rate movements: A bird's eye view

Rev. Econom. Stud.

Reconciling the term structure of interest rates with the consumption based ICAP model

An empirical comparison of alternative models of the short-term interest rate

J. Finance

Pricing interest rate options in a two factor Cox-Ingersoll-Ross model of the term structure

Rev. Financ. Stud.

Maximum likelihood estimation for a multifactor equilibrium model of the term structure of interest rates

J. Fixed Income

Estimating subordinated diffusions from discrete time data

A theory of the nominal structure of interest rates

Rev. Financ. Stud.

A theory of the term structure of interest rates

Econometrica

A yield-factor model of interest rates

Bonds and bond option pricing based on the current term structure

Informational content in interest rate term structures

Rev. Econom. Statist.

An investigation of the effect of funding on the slope of the yield curve