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An Orthogonal Polynomial Approach to Estimate the Term Structure of Interest Rates

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  • Hans-Jürg Büttler

Abstract

In this paper, we introduce a new algorithm to estimate the term structure of interest rates. It is obtained from a constrained optimization, where the objective is to minimize the integral of squared first derivatives of the instantaneous forward interest rate subject to the condition that the estimated bond prices lie within the range of observed bid and ask prices. We use a finite series of ordinary Laguerre polynomials to approximate the unknown function of the instantaneous forward interest rate. The objective function can be written explicitly as a quadratic form of the Laguerre constants and the nonlinear constraints can be obtained from a recurrence relationship. The estimation error is less than one basis point, given a sufficient number of bonds.

Suggested Citation

  • Hans-Jürg Büttler, 2007. "An Orthogonal Polynomial Approach to Estimate the Term Structure of Interest Rates," Working Papers 2007-08, Swiss National Bank.
    • Handle: RePEc:snb:snbwpa:2007-08
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    References listed on IDEAS

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    5. David Bolder & Scott Gusba, 2002. "Exponentials, Polynomials, and Fourier Series: More Yield Curve Modelling at the Bank of Canada," Staff Working Papers 02-29, Bank of Canada.
    6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
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    More about this item

    Keywords

    Term structure of interest rates; orthogonal polynomial;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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