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.

Legitimacy in financial markets: credit default swaps in the current crisis

The current financial crisis appears to be a moment of epochal change, an archetypal ‘legitimation crisis’. This paper examines the impact of this collapse on one particular section of the financial markets that concerned with credit default swaps. This paper shows how and why the markets for these products expanded and why they were integral to the financial crash. The consequence of the crash was a huge loss of legitimacy for these markets. This paper examines the processes whereby this legitimacy is being reconstructed. In particular, it distinguishes between the re-establishment of pragmatic legitimacy, which is the primary concern of the market participants, and the re-establishment of broader political legitimacy, which concerns governments and regulators. It argues that these two forms of re-establishing legitimacy work in different ways and proceed at different rates. It explores the tensions to which this leads in terms of reconstructing the financial system