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Exponentials, Polynomials, and Fourier Series: More Yield Curve Modelling at the Bank of Canada

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David Jamieson Bolder
Scott Gusba

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Paper provided by Bank of Canada in its series Working Papers with number 02-29.

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Length: 90 pages Abstract: This paper continues the work started by Bolder and Stréliski (1999) and considers two alternative classes of models for extracting zero-coupon and forward rates from a set of observed Government of Canada bond and treasury-bill prices. The first class of term-structure estimation methods follows from work by Fisher, Nychka, and Zervos (1994), Anderson and Sleath (2001), and Waggoner (1997). This approach employs a B-spline basis for the space of cubic splines to fit observed coupon-bond prices—as a consequence, we call these the spline-based models. This approach includes a penalty in the generalized least-squares objective function—following from Waggoner (1997)—that imposes the desired level of smoothness into the term structure of interest rates. The second class of methods is called function-based and includes variations on the work of Li et al. (2001), which uses linear combinations of basis functions, defined over the entire term-to-maturity spectrum, to fit the discount function. This class of function-based models includes the model proposed by Svensson (1994). In addition to a comprehensive discussion of these models, the authors perform an extensive comparison of these models' performance in the Canadian marketplace.
Date of creation: 2002
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Handle: RePEc:bca:bocawp:02-29

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Keywords: Interest rates; Econometric and statistical methods; Financial markets;

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Find related papers by JEL classification:
C0 - Mathematical and Quantitative Methods - - General
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming
E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
G1 - Financial Economics - - General Financial Markets

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. McCulloch, J Huston, 1971. "Measuring the Term Structure of Interest Rates," Journal of Business, University of Chicago Press, vol. 44(1), pages 19-31, January. [Downloadable!] (restricted)
  2. Mark Fisher, 2001. "Forces that shape the yield curve: Parts 1 and 2," Working Paper 2001-3, Federal Reserve Bank of Atlanta. [Downloadable!]
  3. Seppälä, Juha & Viertiö, Petri, 1996. "The Term Structure of Interest Rates: Estimation and Interpretation," Research Discussion Papers 19/1996, Bank of Finland. [Downloadable!]
  4. Shea, Gary S, 1985. " Interest Rate Term Structure Estimation with Exponential Splines: A Note," Journal of Finance, American Finance Association, vol. 40(1), pages 319-25, March. [Downloadable!] (restricted)
  5. O. Linton & E. Mammen & J. Nielsen & C. Tanggaard, . "Estimating Yield Curves by Kernel Smoothing Methods," Sonderforschungsbereich 373 1999-54, Humboldt Universitaet Berlin.
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  6. Robert R. Bliss, 1996. "Testing term structure estimation methods," Working Paper 96-12, Federal Reserve Bank of Atlanta. [Downloadable!]
  7. Andrew Mark Jeffrey & Oliver B. Linton, 2001. "Flexible Term Structure Estimation: Which Method Is Preferred?," Yale School of Management Working Papers ysm171, Yale School of Management. [Downloadable!]
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  8. Daniel F. Waggoner, 1997. "Spline methods for extracting interest rate curves from coupon bond prices," Working Paper 97-10, Federal Reserve Bank of Atlanta. [Downloadable!]
  9. Bolder, David & Streliski, David, 1999. "Yield Curve Modelling at the Bank of Canada," Technical Reports 84, Bank of Canada. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. René Garcia & Richard Luger, 2005. "The Canadian Macroeconomy and the Yield Curve: An Equilibrium-Based Approach," Working Papers 05-36, Bank of Canada. [Downloadable!]
    Other versions:
  2. Christensen, Ian & Frédéric Dion & Christopher Reid, 2004. "Real Return Bonds, Inflation Expectations, and the Break-Even Inflation Rate," Working Papers 04-43, Bank of Canada. [Downloadable!]
  3. C. Emre Alper & Aras Akdemir & Kazim Kazimov, 2004. "Estimating the Term Structure of Government Securities in Turkey," Working Papers 2004/03, Bogazici University, Department of Economics. [Downloadable!]
  4. David Jamieson Bolder, 2006. "Modelling Term-Structure Dynamics for Risk Management: A Practitioner's Perspective," Working Papers 06-48, Bank of Canada. [Downloadable!]
  5. David J. Bolder & Grahame Johnson & Adam Metzler, 2004. "An Empirical Analysis of the Canadian Term Structure of Zero-Coupon Interest Rates," Working Papers 04-48, Bank of Canada. [Downloadable!]
  6. David Jamieson Bolder & Yuliya Romanyuk, 2008. "Combining Canadian Interest-Rate Forecasts," Working Papers 08-34, Bank of Canada. [Downloadable!]
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