Abstract
Nelson and Siegel curves are widely used to fit the observed term structure of interest rates in a particular date. By the other hand, several interest rate models have been developed such their initial forward rate curve can be adjusted to any observed data, as the Ho-Lee and the Hull and White one factor models. In this work we study the evolution of the forward curve process for each of these models assuming that the initial curve is of Nelson-Siegel type. We conclude that the forward curve process produces curves belonging to a parametric family of curves that can be seen as extended Nelson and Siegel curves. We show that the forward rate curve evolution has a linear or an exponential growth, depending on the particular short rate interest model. We applied the results to Argentinian short and forward rates obtained from the Lebac’s bills yields using the Hull and White short rate model, showing a good estimation of the observed forward rate curve for near dates when the initial forward curve is adjusted with a Nelson and Siegel one.
Highlights
A standard procedure when dealing with concrete interest rate models is to calibrate the initial forward curve with the market observed data
In this work we show that in this particular case, the following forward rate curves move on a manifold generated by specific parametric forward curves that can be written as a sum of a Nelson and Siegel curve and a linear or an exponential function, depending upon the short rate model
We prove that the forward rate curves produced by the Ho-Lee model and the Hull and White models when starting with a Nelson and Siegel curve is decomposed in four factors
Summary
A standard procedure when dealing with concrete interest rate models is to calibrate the initial forward curve with the market observed data. With z1, z2, z3 and λ being specified parameters This means that it is possible to choose the Ho-Lee and Hull-White models parameters in such a way that the initial forward rate curve fits with a specific Nelson and Siegel curve. In this work we show that in this particular case, the following forward rate curves move on a manifold generated by specific parametric forward curves that can be written as a sum of a Nelson and Siegel curve and a linear or an exponential function, depending upon the short rate model. We prove that the forward rate curves produced by the Ho-Lee model and the Hull and White models when starting with a Nelson and Siegel curve is decomposed in four factors. In particular we prove that each of these two short rate models is consistent with a forward curve manifold λ , for each λ > 0
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