A Base Model for Multifactor Specifications of the Term Structure

2011

SSRN Journal

Yield curve models within the popular Nelson and Siegel (hereafter NS) class are shown to arise from a formal low-order Taylor approximation to the generic Gaussian a¢ ne term structure model. That theoretical foundation provides an assurance that NS models correspond to a well-accepted framework for yield curve modeling. It further suggests that any yield curve from the GATSM class should be parsimoniously representable by an two-factor arbitrage-free NS model, which should prove useful for macro…nance applications. Such a model is derived and applied to provide evidence for changes in United States yield curve dynamics pre-and post-1988. JEL: E43, G12, C58 Keywords: yield curve; term structure of interest rates; Nelson and Siegel model; a¢ ne term structure models.

Section: Introductionmentioning

confidence: 99%

A Theoretical Foundation for the Nelson and Siegel Class of Yield Curve Models

2011

SSRN Journal

“…preferences, technology, consumption, inflation) within a general equilibrium model. For example, Cox et al () originally provided a general equilibrium basis for term structure models (including the one‐factor GATSM) based on a representative‐agent economy, and that approach has since been extended by many authors to provide theoretical foundations for multifactor GATSMs; see, for example, Berardi and Esposito () and Berardi (). Wu () also shows how GATSMs may be given an explicit foundation within dynamic stochastic general equilibrium models.…”

Section: The Generic Gaussian Affine Term Structure Modelmentioning

confidence: 99%

A Theoretical Foundation for the Nelson-Siegel Class of Yield Curve Models

2015

J. Appl. Econ.

Yield curve models within the popular Nelson-Siegel class are shown to arise from formal low-order Taylor approximations of the generic Gaussian affine term structure model. Extensive empirical testing on government and bank-risk yield curve datasets for the five largest industrial economies shows that the arbitrage-free three-factor (Level, Slope, Curvature) Nelson-Siegel model generally provides an acceptable representation of the data relative to the three-factor Gaussian affine term structure model. The combined theoretical foundation and empirical evidence means that Nelson-Siegel models may be applied and interpreted from the perspective of Gaussian affine term structure models that already have firm statistical and theoretical foundations in the literature. L. KRIPPNERThe purpose of this paper is to introduce a simple, parsimonious model that is flexible enough to represent the range of shapes generally associated with yield curves : monotonic, humped, and S shaped. (p. 473) A class of functions that readily generates the typical yield curve shapes is that associated with solutions to differential or difference equations. The expectations theory of the term structure provides heuristic motivation for investigating this class since, if spot rates are generated by a differential equation, then forward rates, being forecasts, will be the solution to the equations. (p. 474) A more parsimonious model that can generate the same range of shapes is given by the solution equation for the case of equal roots. (p. 475) Our objective in this paper has been to propose a class of models, motivated by but not dependent on the expectations theory of the term structure, that offers a parsimonious representation of the shapes traditionally associated with yield curves. (p. 488) Even the recent introduction of arbitrage-free NS models (e.g. Sharef and Filipović, 2004;Krippner, 2006;Christensen et al., 2009Christensen et al., , 2011, while at least imposing theoretical self-consistency by explicitly accounting for the effect of dynamics on the shape of the yield curve, still takes the NS Level, Slope and Curvature components as given latent factors. Specifically, for example, Christensen et al. (2011) footnote 4 states: 'Our strategy is to find the affine AF [arbitrage-free] model with factor loadings that match Nelson-Siegel exactly.' Justification for the components themselves, if supplied, inevitably appeals to the practical benefits of NS models, such as their ease of estimation, close fit to the yield curve data, intuitive estimated components (including the similarity of the Level, Slope and Curvature components to the first three principal components of the term structure) and their empirical success in past applications.Therefore, the fundamental question 'Why NS components?' remains an open question. As such, it represents a potential point of vulnerability in the widespread application of NS models and, by extension, their associated empirical results.Fortunately, I show in this article that the NS components and...

“…While GATSM summaries are readily available in many articles and textbooks, I generally use Chen (1995) as a convenient point of reference because it contains explicit multifactor expressions for GATSM bond and option prices. 12 However, I also refer to Berardi and Esposito (1999) and Berardi (2009) for their economic foundation and Dai and Singleton (2002) pp. 437-8 for the convenience of its matrix notation.…”

Section: The Generic Gatsm Term Structurementioning

confidence: 99%

Modifying Gaussian Term Structure Models When Interest Rates are Near the Zero Lower Bound

2012

SSRN Journal

With nominal interest rates currently at or near their zero lower bound (ZLB) in many major economies, it has become untenable to apply Gaussian a¢ ne term structure models (GATSMs) while ignoring their inherent non-zero probabilities of negative interest rates. In this article I modify GATSMs by representing physical currency as call options on bonds to establish the ZLB. The resulting ZLB-GATSM framework remains tractable, producing a simple closed-form analytic expression for forward rates and requiring only elementary univariate numerical integration (over time to maturity) to obtain interest rates and bond prices. I demonstrate the salient features of the ZLB-GATSM framework using a two-factor model. An illustrative application to U.S. term structure data indicates that movements in the model state variables have been consistent with unconventional monetary policy easings undertaken after the U.S. policy rate reached the ZLB in late 2008. JEL: E43, G12, G13 Keywords: zero lower bound; term structure of interest rates; Gaussian a¢ ne term structure models.