A CONSTRAINED LEAST SQUARE METHOD FOR ESTIMATING A SMOOTH, NONNEGATIVE FORWARD RATE SEQUENCE

Hiroshi Konno () and Sumito Ito
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2005, vol. 08, issue 07, 989-998

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.

Keywords: Forward rate; term structure; Carleton–Cooper's method; least square method; convex minimization problem (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024905003293

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