DISCOUNT CURVE ESTIMATION BY MONOTONIZING MCCULLOCH SPLINES

Holger Dette () and Daniel Ziggel ()
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Holger Dette: Department of Statistics, Ruhr-University of Bochum, Universitätsstraße 150, 44780 Bochum, Germany
Daniel Ziggel: Department of Statistics, Ruhr-University of Bochum, Universitätsstraße 150, 44780 Bochum, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2008, vol. 11, issue 05, 529-544

Abstract: In this paper a new method for monotone estimation of discount curves is proposed. The main idea of this approach is a simple modification of the commonly used (unconstrained) McCulloch Spline. We construct an integrated density estimate from the predicted values of the discount curve. It can be shown that this statistic is an estimate of the inverse of the discount function and the final estimate can be obtained by a numerical inversion. The resulting procedure is simple and we have implemented it in Excel and VBA, respectively. The performance is illustrated by several examples, in which the curve was previously estimated with an unconstrained McCulloch Spline.

Keywords: Monotone discount curve; McCulloch splines; nonnegative forward rates (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1142/S0219024908004919

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