Nelson and Siegel Curves

The technique for curve fitting presented by Nelson and Siegel and variants on it described by Svensson (1994), Wiseman (1994) and Bjork and Christensen (1997) have a small number of parameters, and generally one obtains a relatively close approximation to the yield curve with them. As we saw above, the Nelson and Siegel curve contains four parameters while the Svensson curve has six parameters. The curve presented by Wiseman contains 2x( +l) parameters, given by f)j, kj]j=o.n- The curve is f2(1 ) ... 

The original Nelson and Siegel curve does not produce close approximations for all types of yield curves, because the small number of parameters limits... 

The Svensson model, proposed in Svensson (1994), is aversion of the Nelson and Siegel curve with an adjustment for the hump in the yield curve. This is accomplished by expanding (5.12) as (5.13). 

As approximations. Nelson and Siegel curves are appropriate for noarbitrage applications. They are popular in the market because they are straightforward to calculate. Jordan and Mansi (2000) imputes two further advant es to them they force the long-date forward curve into a horizontal asymptote, and the user is not required to specify knot points, whose choice determines how effective the cubic spline curves are. The... 

As it is used as a predictive indicator, the spot yield curve needs to be fitted as accurately as possible. This is an area that has been extensively researched (see McCulloch, 1975 Deacon and Derry, 1994 Schaefer, 1981 Waggoner, 1997 Nelson and Siegel, 1987 Svensson, 1994, 1995 inter alia). Invariably researchers use the government debt market as the basis for modelling the term structure. This is because the government market is the most liquid debt market... 

The Bank of England uses a variation of the Svensson yield curve model, a one-dimensional paranetric yield curve model. This is similar to the Nelson and Siegel model and defines the forward rate curve/(/n) as a function of a set of unknown parameters, which are related to the short-term interest rate and the slope of the yield curve. The model is summarised in Appendix B. Anderson and Sleath (1999) assess parametric models, including the Svensson model, against spline-based methods such as those described by Waggoner (1997), and we summarise their results later in this chapter. 

FIGURE 5.1 A Nelson and Siegel fitted yield curve and gilt redemption yield curve. 

In the Nelson and Siegel (1987) method, we may model the implied forward rate yield curve along the entire term stmcture using the following function ... 

C.R. Nelson and A.F. Siegel, Parsimonious Modelling of Yield Curves, Journal of Business 60 (1987). 

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