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Discount Curve Estimation By Monotonizing Mcculloch Splines

Author

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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)

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.

Suggested Citation

  • Holger Dette & Daniel Ziggel, 2008. "Discount Curve Estimation By Monotonizing Mcculloch Splines," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 529-544.
    • Handle: RePEc:wsi:ijtafx:v:11:y:2008:i:05:n:s0219024908004919
    DOI: 10.1142/S0219024908004919
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    References listed on IDEAS

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    1. Svensson, Lars E O, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992-4," CEPR Discussion Papers 1051, C.E.P.R. Discussion Papers.
    2. Svensson, L.E.O., 1994. "Estimating and Interpreting Foreward Interest Rates: Sweden 1992-1994," Papers 579, Stockholm - International Economic Studies.
    3. Mark Deacon & Andrew Derry, 1994. "Estimating the Term Structure of Interest Rates," Bank of England working papers 24, Bank of England.
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