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Testing term structure estimation methods

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  • Robert R. Bliss

Abstract

This paper tests and compares five distinct methods for estimating the term structure. The Unsmoothed Fama-Bliss method is an iterative method by which the discount rate function is built up by computing the forward rate necessary to price successively longer maturity bonds. The Smoothed Fama-Bliss "smooths out" these discount rates by fitting an approximating function to the "unsmoothed" rates. The McCulloch method fits a cubic spline to the discount function using an implicit smoothness penalty, while the Fisher-Nychka-Zervos method fits a cubic spline to the forward rate function and makes the smoothness penalty explicit. Lastly, the Extended Nelson-Siegel method, introduced in this paper, fits an exponential approximation of the discount rate function directly to bond prices. ; The tests demonstrate the dangers of in-sample goodness-of-fit as the sole criterion for judging term structure estimation methods. A series of residual analysis tests are introduced to detect misspecification of the underlying pricing equation relating the term structure to bond prices. These tests establish the presence of unspecified, but nonetheless systematic, omitted factors in the prices of long maturity notes and bonds. ; Comparisons of the five term structure estimation methods using these parametric and non-parametric tests finds that the Unsmoothed Fama-Bliss does best overall. Differences with some alternatives may not be economically significant given the much larger number of parameters this method estimates. Users seeking a parsimonious representation of the term structure should consider either the Smoothed Fama-Bliss or the Extended Nelson-Siegel methods. One method was found to be unacceptable. The Fisher-Nychka-Zervos cubic spline method performs poorly relative to the alternatives, both in- and out-of-sample. Furthermore, it systematically misprices short maturity issues and suffers from instability in the estimated term structure.

Suggested Citation

  • Robert R. Bliss, 1996. "Testing term structure estimation methods," FRB Atlanta Working Paper 96-12, Federal Reserve Bank of Atlanta.
  • Handle: RePEc:fip:fedawp:96-12
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    Cited by:

    1. Morini,S., 2003. "Estimación de la curva de tipos cupón-cero con polinomios de Legendre," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 21, pages 363-375, Agosto.
    2. Brennan, Michael J. & Xia, Yihong, 2004. "International Capital Markets and Foreign Exchange Risk," University of California at Los Angeles, Anderson Graduate School of Management qt53z0s29k, Anderson Graduate School of Management, UCLA.
    3. Gurkaynak, Refet S. & Sack, Brian & Wright, Jonathan H., 2007. "The U.S. Treasury yield curve: 1961 to the present," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2291-2304, November.
    4. repec:eee:dyncon:v:86:y:2018:i:c:p:72-94 is not listed on IDEAS
    5. Robert R. Bliss & Ehud I. Ronn, 1997. "Callable U.S. Treasury bonds: optimal calls, anomalies, and implied volatilities," FRB Atlanta Working Paper 97-1, Federal Reserve Bank of Atlanta.
    6. Dupacova, Jitka & Bertocchi, Marida, 2001. "From data to model and back to data: A bond portfolio management problem," European Journal of Operational Research, Elsevier, vol. 134(2), pages 261-278, October.
    7. David Jamieson 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.
    8. Baruník, Jozef & Malinská, Barbora, 2016. "Forecasting the term structure of crude oil futures prices with neural networks," Applied Energy, Elsevier, vol. 164(C), pages 366-379.
    9. Wong, Edwin & Lucia, Kathlyn & Price, Stephanie & Startz, Richard, 2011. "The changing relation between the Canadian and U.S. yield curves," Journal of International Money and Finance, Elsevier, vol. 30(6), pages 965-981, October.
    10. Refet S. Gürkaynak & Brian Sack & Jonathan H. Wright, 2010. "The TIPS Yield Curve and Inflation Compensation," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(1), pages 70-92, January.
    11. Silverio Foresi & Alessandro Penati & George Pennacchi, 1997. "Estimating the cost of U.S. indexed bonds," Working Paper 9701, Federal Reserve Bank of Cleveland.
    12. Gonzalo Cortazar & Eduardo S. Schwartz & Lorenzo F. Naranjo, 2007. "Term-structure estimation in markets with infrequent trading," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 12(4), pages 353-369.
    13. repec:eee:jmacro:v:53:y:2017:i:c:p:16-41 is not listed on IDEAS
    14. Backus, David & Foresi, Silverio & Mozumdar, Abon & Wu, Liuren, 2001. "Predictable changes in yields and forward rates," Journal of Financial Economics, Elsevier, vol. 59(3), pages 281-311, March.
    15. George J. Hall & Thomas J. Sargent, 1997. "Accounting for the federal government's cost of funds," Economic Perspectives, Federal Reserve Bank of Chicago, issue Jul, pages 18-28.
    16. Cortazar, Gonzalo & Schwartz, Eduardo S. & Naranjo, Lorezo, 2003. "Term Structure Estimation in Low-Frequency Transaction Markets: A Kalman Filter Approach with Incomplete Panel-Data," University of California at Los Angeles, Anderson Graduate School of Management qt56h775cz, Anderson Graduate School of Management, UCLA.

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    Keywords

    Financial markets ; Interest rates ; Prices;

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