An Estimation of the term structure of interest rates: the exponential-polynomial Nelson-Siegel model

Purpose: The macroeconomic models have had difficulties in matching the macroeconomic and financial data. The inability of macroeconomic models to match equity prices could be that fact that the expected future profitability of individual firms is unobservable and difficult to evaluate. In contrast, the term structure of interest rates incorporates expectations of future monetary policy decisions are relatively well predictable. The last decades have produced major advances in theoretical models of the term structure as well as their econometric estimation, yet the resulting models vary in form and fit. This paper examines the estimation of the term structure of interest rates with the exponential-polynomial Nelson-Siegel Model. Originality: The term structure of interest rates describes the relationship between interest rates (spot rate on zero-coupon bonds) and time to maturity. Various methods have been proposed to estimate the term structure from quoted bond prices. A popular approach is the bootstrapping procedure which deduce price of the zero-coupon bond and transform it into the zero-coupon bond yield. However, this technique can only provide the zero-coupon bond yield for the payment dates of the traded bonds. Therefore, we need other methods which could estimate the entire zero-coupon bond yield function parametrically from observed data at any time to maturity. There are two popular parameterization techniques, namely spline interpolation and the Nelson-Siegel parameterization. Spline interpolation chooses the polynomial pieces such that they fit smoothly together. This technique is extremely sensitive to the number and precise location of knot point and it is not flexible enough to describe the whole family of observed term structure shapes. The Nelson and Siegel model derives a continuous zero-coupon bond yield curve in terms of three linear factors commonly referred to as the level factor, the slope factor and the curvature factor, together with a nonlinear factor, which represents a time-scale. Among other methods, it is extensively used by monetary policy makers and practitioners due to the fact that it posses desirable properties, such as flexibility, parsimony and economic interpretability. Therefore, this study focuses solely on the Nelson-Siegel models. Key literature/theoretical perspective: The exponential-polynomial Nelson-Siegel model is a simple parameterization of the term structure, which has become quite popular. Nelson and Siegel described the yield curve in terms of three linear factors commonly referred to as the level factor, the slope factor and the curvature factor, together with a nonlinear factor, which represents a time-scale. Their technique derives a continuous zero-coupon bond yield curve with desirable properties from a finite set of observed bond prices at different maturities. It is extensively used by monetary policy makers and practitioners due to the fact that it possess desirable properties, such as flexibility (i.e. it must be able to reproduce the various observed shapes of the yield curve, such as upward-sloping, downward-sloping, hump-shaped), parsimony (i.e. it must usefully summarize the features of the term structure using a limited set of parameters) and economic interpretability. Design/methodology/approach: At any given time, we fit the exponential-polynomial Nelson-Siegel Model. Then, the Nelson-Siegel model will be reformulated as a dynamic factor model with vector autoregressive factors. It will be extended by treating the loading parameter as a stochastically time-varying latent factor and introducing time-varying volatility in the variance specification of the disturbances. Findings: This study replicated the Nelson-Siegel model for fitting and forecasting the yield curve. We showed that the three coefficients in the Nelson-Siegel curve could be interpreted as latent level, slope and curvature factors. We estimated the forecasting performance of the Nelson-Siegel model. We concluded that the Nelson-Siegel model is a valid model for forecasting the yield curve.