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A Constrained Least Square Method For Estimating A Smooth, Nonnegative Forward Rate Sequence

Author

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  • HIROSHI KONNO

    (Department of Industrial and Systems Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan)

  • SUMITO ITO

    (Department of Industrial and Systems Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan)

Abstract

We will develop an efficient method for estimating a smooth nonnegative forward rate sequence using the market price of riskless bonds. This method is an improvement of the classical Carleton–Cooper's method based on standard least square method, which often generates a non-smooth forward rate sequence and hence is not used in practice. The method to be proposed in this paper is intended to resolve this difficulty. We will impose a smoothness condition while maintaining the fitting error within an acceptable level. The resulting optimization problem is shown to be convex in the region of interest. Therefore, we can calculate a globally optimal solution very fast by standard nonlinear programming algorithms. We will demonstrate that this method generates a smooth forward rate sequence at the expense of a very small increase of fitting error.

Suggested Citation

  • Hiroshi Konno & Sumito Ito, 2005. "A Constrained Least Square Method For Estimating A Smooth, Nonnegative Forward Rate Sequence," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(07), pages 989-998.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:07:n:s0219024905003293
    DOI: 10.1142/S0219024905003293
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    Cited by:

    1. Lazar Fred & Prisman Eliezer Z., 2012. "Constructing Historical Yield Curves from Very Sparse Spot Rates: A Methodology and Examples from the 1920s Canadian Market," Journal of Business Valuation and Economic Loss Analysis, De Gruyter, vol. 7(1), pages 1-24, May.
    2. Koji Kato & Hiroshi Konno, 2007. "Studies on a general stock-bond integrated portfolio optimization model," Computational Management Science, Springer, vol. 4(1), pages 41-57, January.

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