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Constrained Smoothing Splines for the Term Structure of Interest Rates

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  • Laurini, Márcio P.
  • Moura, Marcelo

Abstract

The constrained smoothing B-splines (COBS) is proposed as a nonparametric approach to estimate the term structure of interest rate. Compared to the existing methods in the literature, COBS' main innovation lies in its incorporation of important constraints imposed by no-arbitrage, such as monotonically decreasing and boundary conditions for the discount function, positive forward and spot rates. In addition, by estimating the conditional median function, COBS is less sensible to outliers in reduced samples than other common methods in the literature. Estimation for high and low liquidity markets together with simulation exercises puts COBS in an intermediate position between usual parametric and nonparametric methods in the literature. It has more flexibility than parametric methods and, compared to other nonparametric methods, satisfies no-arbitrage constraints and generates parsimonious shapes of the term structure of interest rates.

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Paper provided by Insper Working Paper, Insper Instituto de Ensino e Pesquisa in its series Insper Working Papers with number wpe_100.

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Date of creation: Oct 2007
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Handle: RePEc:ibm:ibmecp:wpe_100

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  1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  2. repec:wop:humbsf:1999-54 is not listed on IDEAS
  3. Svensson, L.E.O., 1994. "Estimating and Interpreting Foreward Interest Rates: Sweden 1992-1994," Papers 579, Stockholm - International Economic Studies.
  4. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
  5. Jarrow, Robert & Ruppert, David & Yu, Yan, 2004. "Estimating the Interest Rate Term Structure of Corporate Debt With a Semiparametric Penalized Spline Model," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 57-66, January.
  6. Pham, Toan M., 1998. "Estimation of the term structure of interest rates: an international perspective," Journal of Multinational Financial Management, Elsevier, vol. 8(2-3), pages 265-283, September.
  7. McCulloch, J Huston, 1971. "Measuring the Term Structure of Interest Rates," The Journal of Business, University of Chicago Press, vol. 44(1), pages 19-31, January.
  8. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
  9. Barzanti, Luca & Corradi, Corrado, 1998. "A note on interest rate term structure estimation using tension splines," Insurance: Mathematics and Economics, Elsevier, vol. 22(2), pages 139-143, June.
  10. 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.
  11. Svensson, Lars E O, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992-4," CEPR Discussion Papers 1051, C.E.P.R. Discussion Papers.
  12. Bosch, Ronald J. & Ye, Yinyu & Woodworth, George G., 1995. "A convergent algorithm for quantile regression with smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 19(6), pages 613-630, June.
  13. 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.
  14. Barzanti, Luca & Corradi, Corrado, 1998. "Erratum to: "A note on interest rate term structure estimation using tension splines" [Insurance: Mathematics and Economics 22 (1998) 139-143]," Insurance: Mathematics and Economics, Elsevier, vol. 23(2), pages 179-180, November.
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Cited by:
  1. Yallup, Peter J., 2012. "Models of the yield curve and the curvature of the implied forward rate function," Journal of Banking & Finance, Elsevier, vol. 36(1), pages 121-135.
  2. Márcio Poletti Laurini, 2014. "Dynamic functional data analysis with non-parametric state space models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(1), pages 142-163, January.
  3. Gyorgy Varga, 2009. "Teste de Modelos Estatísticos para a Estrutura a Termo no Brasil," Revista Brasileira de Economia, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 63(4), pages 227-260, December.

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