Abstract
This paper proposes a new nonparametric approach to the problem of inferring term structure estimates using coupon bond prices. The nonparametric estimator is defined on the basis of a penalized least squares criterion. The solution is a natural cubic spline, and the paper presents an iterative procedure for solving the non-linear first-order conditions. Besides smoothness, there are no a priori restrictions on the yield curve, and the position of the knots and the optimal smoothness can be determined from data. For these reasons the smoothing procedure is said to be completely data driven. The paper also demonstrates that smoothing a simple transformation of the yield curve greatly improves the stability of longer-term yield curve estimates.
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References
Chambers, D. R., W. T. Carleton, and D. W. Waldman. Anew approach to estimation of the term structure of interest rates, Journal of Financial and Quantitative Analysis, 19, 233–269 (1984).
Cox, J.,J. Ingersoll, and S. Ross. A theory of the term structure of interest rates, Econometrica, 53, 385–407 (1985).
Craven, P. and G. Wahba. Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross validation, Numerische Mathematik, 31, 377–403 (1979).
Delgado, M. A. and P. M. Robinson.Nonparametric and semiparametric methods for economic research, Journal of Economic Surveys, 6, 201–249 (1992).
Eubank, R. L. SplineSmoothing and Nonparametric Regression, Vol. 90 of Statistics, textbooks and monographs, Marcel Dekker (1988).
Härdle, W. Applied NonparametricRegression, Cambridge University Press (1990).
Hastie, T. J. and R. J. Tibshirani. Generalized Additive Models, Vol. 43 of Monographs on Statistics and Probability, Chapman and Hall (1990).
Magnus, J. R. andH. Neudecker. Matrix Differential Calculus with Applications in Statistics and Econometrics, Series in Probability and Mathematical Statistics, John Wiley & Sons (1988).
McCulloch, J. H. Measuring the term structure of interestrates, Journal of Business, XLIV, 19–31 (1971).
McCulloch, J.H. The tax-adjusted yield curve, The Journal of Finance, 30, 811–830 (1975).
Nelson, C. R. and A. F. Siegel. Parsimonious modeling of yieldcurves, Journal of Business, 60, 473–489 (1987).
Press, W. H.,S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in C, Cambridge University Press (1992).
Robinson, P. M. Semiparametriceconometrics: A survey, Journal of Applied Econometrics, 3, 35–51 (1988).
Shea, G. S. Pitfalls in smoothing interest rate term structure data:Equilibrium models and spline approximations, Journal of Financial and Quantitative Analysis, 19, 253–269 (1984).
Vasicek, O. A. and H.G. Fong. Term structure modeling using exponential splines, The Journal of Finance, 37, 339–356 (1982).
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Tanggaard, C. Nonparametric Smoothing of Yield Curves. Review of Quantitative Finance and Accounting 9, 251–267 (1997). https://doi.org/10.1023/A:1008231600688
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DOI: https://doi.org/10.1023/A:1008231600688