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A simple and general approach to fitting the discount curve under no-arbitrage constraints

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  • Fengler, Matthias R.
  • Hin, Lin-Yee
Abstract
We suggest a simple and general approach to fitting the discount curve under no-arbitrage constraints based on a penalized shape-constrained B-spline. Our approach accommodates B-splines of any order and fitting both under the L1 and the L2 loss functions. Simulations and an empirical analysis of US STRIPS data from 2001-2009 suggest that an active knot search and splines of order three and four are mandatory to obtain reasonable fits. The loss function appears to be less relevant.

Suggested Citation

  • Fengler, Matthias R. & Hin, Lin-Yee, 2014. "A simple and general approach to fitting the discount curve under no-arbitrage constraints," Economics Working Paper Series 1423, University of St. Gallen, School of Economics and Political Science.
    • Handle: RePEc:usg:econwp:2014:23
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    References listed on IDEAS

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    1. 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.
    2. Vasicek, Oldrich A & Fong, H Gifford, 1982. "Term Structure Modeling Using Exponential Splines," Journal of Finance, American Finance Association, vol. 37(2), pages 339-348, May.
    3. 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.
    4. Chiu, Nan-Chieh & Fang, Shu-Cherng & Lavery, John E. & Lin, Jen-Yen & Wang, Yong, 2008. "Approximating term structure of interest rates using cubic L1 splines," European Journal of Operational Research, Elsevier, vol. 184(3), pages 990-1004, February.
    5. Leif Andersen, 2007. "Discount curve construction with tension splines," Review of Derivatives Research, Springer, vol. 10(3), pages 227-267, December.
    6. Alessandro Ramponi, 2003. "Adaptive And Monotone Spline Estimation Of The Cross-Sectional Term Structure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 195-212.
    7. Fengler, Matthias & Hin, Lin-Yee, 2011. "Semi-nonparametric estimation of the call price surface under strike and time-to-expiry no-arbitrage constraints," Economics Working Paper Series 1136, University of St. Gallen, School of Economics and Political Science, revised May 2013.
    8. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    9. Luca Barzanti & Corrado Corradi, 1999. "A note on direct term structure estimation using monotonic splines," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 22(1), pages 101-108, March.
    10. Mark Grinblatt & Francis A. Longstaff, 2000. "Financial Innovation and the Role of Derivative Securities: An Empirical Analysis of the Treasury STRIPS Program," Journal of Finance, American Finance Association, vol. 55(3), pages 1415-1436, June.
    11. Patrick Hagan & Graeme West, 2006. "Interpolation Methods for Curve Construction," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(2), pages 89-129.
    12. Poletti Laurini, Márcio & Moura, Marcelo, 2010. "Constrained smoothing B-splines for the term structure of interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 339-350, April.
    13. McCulloch, J Huston, 1975. "The Tax-Adjusted Yield Curve," Journal of Finance, American Finance Association, vol. 30(3), pages 811-830, June.
    14. He, Xuming & Shi, Peide, 1996. "Bivariate Tensor-Product B-Splines in a Partly Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 162-181, August.
    15. Jordan, Bradford D. & Jorgensen, Randy D. & Kuipers, David R., 2000. "The relative pricing of U.S. Treasury STRIPS: empirical evidence," Journal of Financial Economics, Elsevier, vol. 56(1), pages 89-123, April.
    16. Zhou S. & Shen X., 2001. "Spatially Adaptive Regression Splines and Accurate Knot Selection Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 247-259, March.
    17. Preve, Daniel & Medeiros, Marcelo C., 2011. "Linear programming-based estimators in simple linear regression," Journal of Econometrics, Elsevier, vol. 165(1), pages 128-136.
    18. Livio Marangio & Massimo Massimo & Alessandro Ramponi, 2002. "A Review Of Techniques For The Estimation Of The Term Structure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 189-221.
    19. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    20. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    21. 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.
    22. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    23. Ioannides, Michalis, 2003. "A comparison of yield curve estimation techniques using UK data," Journal of Banking & Finance, Elsevier, vol. 27(1), pages 1-26, January.
    24. 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.
    25. Fengler, Matthias R. & Hin, Lin-Yee, 2015. "Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints," Journal of Econometrics, Elsevier, vol. 184(2), pages 242-261.
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    More about this item

    Keywords

    Employment; B-splines; Discount curve; No-arbitrage constraints; Monotone estimation; Yield curve;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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