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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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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Tong, Xiaojun & He, Zhuoqiong Chong & Sun, Dongchu, 2018. "Estimating Chinese Treasury yield curves with Bayesian smoothing splines," Econometrics and Statistics, Elsevier, vol. 8(C), pages 94-124.
    6. 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.
    7. Silverio Foresi & Alessandro Penati & George Pennacchi, 1997. "Estimating the cost of U.S. indexed bonds," Working Papers (Old Series) 9701, Federal Reserve Bank of Cleveland.
    8. Morini,S., 2003. "Estimación de la curva de tipos cupón-cero con polinomios de Legendre," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 21, pages 363-375, Agosto.
    9. 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.
    10. 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.
    11. 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.
    12. Guo, Feng & McCulloch, J.H., 2017. "Heterogeneous capital and misintermediation," Journal of Macroeconomics, Elsevier, vol. 53(C), pages 16-41.
    13. 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.
    14. 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.
    15. Koo, B. & La Vecchia, D. & Linton, O., 2019. "Nonparametric Recovery of the Yield Curve Evolution from Cross-Section and Time Series Information," Cambridge Working Papers in Economics 1916, Faculty of Economics, University of Cambridge.
    16. Faria, Adriano & Almeida, Caio, 2018. "A hybrid spline-based parametric model for the yield curve," Journal of Economic Dynamics and Control, Elsevier, vol. 86(C), pages 72-94.
    17. 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.
    18. George J. Hall & Thomas J. Sargent, 1997. "Accounting for the federal government's cost of funds," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 21(Jul), pages 18-28.
    19. Koo, Bonsoo & La Vecchia, Davide & Linton, Oliver, 2021. "Estimation of a nonparametric model for bond prices from cross-section and time series information," Journal of Econometrics, Elsevier, vol. 220(2), pages 562-588.

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