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Yield Curve Modelling at the Bank of Canada

  • Bolder, David
  • Streliski, David

The primary objective of this paper is to produce a framework that could be used to construct a historical data base of zero-coupon and forward yield curves estimated from Government of Canada securities' prices. The secondary objective is to better understand the behaviour of a class of parametric yield curve models, specifically, the Nelson-Siegel and the Svensson methodologies. These models specify a functional form for the instantaneous forward interest rate, and the user must determine the function parameters that are consistent with market prices for government debt. The results of these models are compared with those of a yield curve model used by the Bank of Canada for the last 15 years. The Bank of Canada's existing model, based on an approach developed by Bell Canada, fits a so-called "par yield" curve to bond yields to maturity and subsequently extracts zero-coupon and "implied forward" rates. Given the pragmatic objectives of this research, the analysis focuses on the practical and deals with two key problems: the estimation problem (the choice of the best yield curve model and the optimization of its parameters); and the data problem (the selection of the appropriate set of market data). In the absence of a developed literature dealing with the practical side of parametric term structure estimation, this paper provides some guidance for those wishing to use parametric models under "real world" constraints. In the analysis of the estimation problem, the data filtering criteria are held constant (this is the "benchmark" case). Three separate models, two alternative specifications of the objective function, and two global search algorithms are examined. Each of these nine alternatives is summarized in terms of goodness of fit, speed of estimation, and robustness of the results. The best alternative is the Svensson model using a price-error-based, log-likelihood objective function and a global search algorithm that estimates subsets of parameters in stages. This estimation approach is used to consider the data problem. The authors look at a number of alternative data filtering settings, which include a more severe or "tight" setting and an examination of the use of bonds and/or treasury bills to model the short-end of the term structure. Once again, the goodness of fit, robustness, and speed of estimation are used to compare these different filtering possibilities. In the final analysis, it is decided that the benchmark filtering setting offers the most balanced approach to the selection of data for the estimation of the term structure. This work improves the understanding of this class of parametric models and will be used for the development of a historical data base of estimated term structures. In particular, a number of concerns about these models have been resolved by this analysis. For example, the authors believe that the log-likelihood specification of the objective function is an efficient approach to solving the estimation problem. In addition, the benchmark data filtering case performs well relative to other possible filtering scenarios. Indeed, this parametric class of models appears to be less sensitive to the data filtering than initially believed. However, some questions remain; specifically, the estimation algorithms could be improved. The authors are concerned that they do not consider enough of the domain of the objective function to determine the optimal set of starting parameters. Finally, although it was decided to employ the Svensson model, there are other functional forms that could be more stable or better describe the underlying data. These two remaining questions suggest that there are certainly more research issues to be explored in this area.

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File URL: http://www.bankofcanada.ca/en/res/tr/1999/tr84.pdf
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Paper provided by Bank of Canada in its series Technical Reports with number 84.

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Length: 69 pages
Date of creation: 1999
Date of revision:
Handle: RePEc:bca:bocatr:84
Contact details of provider: Postal: 234 Wellington Street, Ottawa, Ontario, K1A 0G9, Canada
Phone: 613 782-8845
Fax: 613 782-8874
Web page: http://www.bank-banque-canada.ca/

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  1. Svensson, L.E.O., 1994. "Estimating and Interpreting Foreward Interest Rates: Sweden 1992-1994," Papers 579, Stockholm - International Economic Studies.
  2. Litzenberger, Robert H & Rolfo, Jacques, 1984. " An International Study of Tax Effects on Government Bonds," Journal of Finance, American Finance Association, vol. 39(1), pages 1-22, March.
  3. Suits, Daniel B & Mason, Andrew & Chan, Louis, 1978. "Spline Functions Fitted by Standard Regression Methods," The Review of Economics and Statistics, MIT Press, vol. 60(1), pages 132-39, February.
  4. Caks, John, 1977. "The Coupon Effect on Yield to Maturity," Journal of Finance, American Finance Association, vol. 32(1), pages 103-15, March.
  5. Bolder, David & Boisvert, Serge, 1998. "Easing Restrictions on the Stripping and Reconstitution of Government of Canada Bonds," Working Papers 98-8, Bank of Canada.
  6. Vasicek, Oldrich A & Fong, H Gifford, 1982. " Term Structure Modeling Using Exponential Splines," Journal of Finance, American Finance Association, vol. 37(2), pages 339-48, May.
  7. Soderlind, P & Svensson, L-E-O, 1996. "New Techniques to Extract Market Expectations from Financial Instruments," Papers 621, Stockholm - International Economic Studies.
  8. Shea, Gary S., 1984. "Pitfalls in Smoothing Interest Rate Term Structure Data: Equilibrium Models and Spline Approximations," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(03), pages 253-269, September.
  9. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-89, October.
  10. Schich, Sebastian T., 1996. "Alternative specifications of the German term structure and its information content regarding inflation," Discussion Paper Series 1: Economic Studies 1996,08e, Deutsche Bundesbank, Research Centre.
  11. Serge Boisvert & Nancy Harvey, 1998. "The declining supply of treasury bills and the Canadian money market," Bank of Canada Review, Bank of Canada, vol. 1998(Summer), pages 53-69.
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