An intertemporally-consistent and arbitrage-free version of the Nelson and Siegel class of yield curve models

This article derives a generic, intertemporally-consistent, and arbitrage-free version of the popular class of yield curve models originally introduced by Nelson and Siegel (1987). The derived model has a theoretical foundation (conferred via the Heath, Jarrow and Morton (1992) framework) that allows it to be used in applications that involve an implicit or explicit time-series context. As an example of the potentialapplication of the model, the intertemporal consistency is exploited to derive a theoretical time-series process that may be used to forecast the yield curve. The empirical application of the forecasting framework to United States data results in out-of-sample forecasts that outperform the random walk over a sample period of almost 50 years, for forecast horizons ranging from six months to three years

Modelling the yield curve with Orthonormalised Laguerre Polynomials: A consistent cross-sectional and inter-temporal approach

This article proposes the orthonormalised Laguerre polynomial (OLP) model of the yield curve, a generic linear model that is both cross-sectionally consistent (that is, it reliably fits the yield curve at a given point in time), and inter-temporally consistent (that is, the cross-sectional parameters are shown to be consistent over time within the expectations hypothesis framework). The OLP model generalises the exponential-polynomial model for a single yield curve, as originally proposed by Nelson and Siegel (1987), and also allows for the simultaneous modelling of other same-currency yield curves that have instrument-specific differences (such as default risk), as in Houweling, Hoek and Kleibergen (2001). New Zealand data is used to illustrate the empirical application of the OLP model

A yield curve perspective on uncovered interest parity

This article uses a dynamic multi-factor model of the yield curve with a rational-expectations, general-equilibrium-economy foundation to investigate the uncovered interest parity hypothesis(UIPH). The yield curve model is used to decompose the interest rate data used in the UIPH regressions into components that reflect rationally-based expectations of the cyclical and fundamental components of the underlying economy. The UIPH is not rejected based on the fundamental components of interest rates, but is soundly rejected based on the cyclical components. These results provide empirical support for suggestions in the existing theoretical literature that rationally-based interest rate and exchange rate dynamics associated with cyclical inter-linkages between the economy and financial markets may contribute materially to the UIPH puzzle

A new framework for yield curve, output and inflation relationships

This article develops a theoretically-consistent and easy-to-apply framework for interpreting, investigating, and monitoring the relationships between the yield curve, output, and inflation. The framework predicts that steady-state inflation plus steady-state output growth should be cointegrated with the long-maturity level of the yield curve as estimated by a arbitrage-free version of the Nelson and Siegel (1987) model, while the shape of the yield curve model from that model should correspond to the profile (that is, the timing and magnitude) of expected future inflation and output growth. These predicted relationships are confirmed empirically using 51 years of United States data. The framework may be used for monitoring expectations of inflation and output growth implied by the yield curve. It should also provide a basis for using the yield curve to value and hedge derivatives on macroeconomic data

Investigating the relationships between the yield curve, output and inflation using an arbitrage-free version of the Nelson and Siegel class of yield curve models

This article provides a theoretical economic foundation for the popular Nelson and Siegel (1987) class of yield curve models (which has been absent up to now). This foundation also offers a new framework for investigating and interpreting the relationships between the yield curve, output and inflation that have already been well-established empirically in the literature. Specifically, the level of the yield curve as measured by the VAO model is predicted to have a cointegrating relationship with inflation, and the shape of the yield curve as measured by the VAO model is predicted to correspond to the profile (that is, timing and magnitude) of future changes in the output gap (that is, output growth less the growth in potential output). These relationships are confirmed in the empirical analysis on 50 years of United States data

Attributing returns and optimising United States swaps portfolios using an intertemporally-consistent and arbitrage-free model of the yield curve

This paper uses the volatility-adjusted orthonormalised Laguerre polynomial model of the yield curve (the VAO model) from Krippner (2005), an intertemporally-consistent and arbitrage-free version of the popular Nelson and Siegel (1987) model, to develop a multi-dimensional yield-curve-based risk framework for fixed interest portfolios. The VAO model is also used to identify relative value (i.e. potential excess returns) from the universe of securities that define the yield curve. In combination, these risk and return elements provide an intuitive framework for attributing portfolio returns ex-post, and for optimising portfolios ex-ante. The empirical applications are to six years of daily United States interest rate swap data. The first application shows that the main sources of fixed interest portfolio risk (i.e. unanticipated variability in ex-post returns) are first-order (‘duration’) effects from stochastic shifts in the level and shape of the yield curve; second-order (‘convexity’) effects and other contributions are immaterial. The second application shows that fixed interest portfolios optimised ex-ante using the VAO model risk/relative framework significantly outperform a naive evenly-weighted benchmark over time

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

Yield curve models of the Nelson and Siegel (1987) class have proven themselves popular empirical tools in finance and economics, but they lack a formal theoretical justification. Hence, this article uses a multifactor version of the Cox, Ingersoll and Ross (1985a) continuous-time general-equilibrium economy to derive a macroeconomic foundation for a theoretically-consistent version of the Nelson and Siegel class of yield curve models. It is established that the level and shape of the yield curve as represented by NS models may be explained succinctly in terms of expectations of inflation and real output growth within an underlying economic model. This theoretically-rigorous yet parsimonious and intuitive framework is applicable as a macro-finance tool, and the application in this article provides a ready interpretation of a series of empirical results from the macro-finance literature that relate the level and slope of the yield curve to output growth and inflation.yield curve; term structure of interest rates; macro-finance; Nelson and Siegel model; Heath-Jarrow-Morton framework

Modifying Gaussian term structure models when interest rates are near the zero lower bound (this is a revised version of CAMA working paper 36/2011)

With nominal interest rates near the zero lower bound (ZLB) in many major economies, it has become untenable to apply Gaussian affine term structure models (GATSMs) while ignoring their inherent theoretical deficiency of non-zero probabilities of negative interest rates. In this article I propose correcting that deficiency by adjusting the entire GATSM term structure with an explicit function of maturity that represents the optionality associated with the present and future availability of physical currency. 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.

The Derivation and Application of a Theoretically and Economically Consistent Version of the Nelson and Siegel Class of Yield Curve Models

A popular class of yield curve models is based on the Nelson and Siegel (1987) (hereafter NS) approach of fitting yield curve data with simple functions of maturity. However, NS models are not theoretically consistent and they also lack an economic foundation, which limits their wider application in finance and economics. This thesis derives an intertemporally-consistent and arbitrage-free version of the NS model, and provides an explicit macroeconomic foundation for that augmented NS (ANS) model. To illustrate the general applicability of the ANS model, it is then applied to four distinct topics spanning finance and economics, each of which are active areas of research in their own right: i.e (1) forecasting the yield curve; (2) investigating relationships between the yield curve and the macroeconomy; (3) fixed interest portfolio management; and (4) investigating the uncovered interest parity hypothesis (UIPH). In each application, the ANS model allows the formal derivation of a parsimonious theoretical framework that captures the essence of the topic under investigation and is readily applicable in practice. Respectively: (1) the intertemporal consistency embedded in the ANS model results in a vector-autoregressive equation that projects the future yield curve from the current yield curve, and forecasts from that model outperform the random-walk benchmark; (2) the economic foundation for the ANS model leads to a single-equation relationship between the current shape of the yield curve and the magnitude and timing of future output growth, and empirical estimations confirm that the theoretical relationship holds in practice; (3) the ANS model provides a theoretically-consistent framework for quantifying risk and returns in fixed interest portfolios, and portfolios optimised ex-ante using that framework outperform a passive benchmark; and (4) the ANS model allows interest rates to be decomposed into a component related to economic fundamentals in the underlying economy, and a component related to cyclical influences. Empirical tests based on the fundamental interest rate components do not reject the UIPH, while the UIPH is rejected based on the cyclical interest rate components. This provides empirical support for suggestions in the theoretical literature that interest rate and exchange rate dynamics associated with cyclical interlinkages between the economy and financial markets under rational expectations may contribute materially to the UIPH puzzle

Modelling the yield curve with Orthonomalised Laguerre Polynomials: An intertemporally consistent approach with an economic interpretation

This article provides theoretical foundations for the popular orthonormalised Laguerre polynomial (OLP) model of the yield curve, as originally introduced by Nelson and Siegel (1987). Intertemporal consistency is provided by deriving the volatility-adjusted OLP (VAO) model of the yield curve using the risk-neutral Heath, Jarrow and Morton (1992) framework, and including an allowance for term premia as noted in Duffee (2002). An economic interpretation is provided by deriving the relationship between the VAO model and the Berardi and Esposito (1999) yield curve model that is based on a generic general equilibrium model of the economy. In empirical applications using almost 50 years of United States data, the VAO model outperforms the random walk when used to forecast the yield curve out of sample, and the level of the yield curve as measured by the VAO model is shown to be cointegrated with CPI inflation, as predicted