IDEAS home Printed from https://ideas.repec.org/p/usg/econwp/201423.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://ux-tauri.unisg.ch/RePEc/usg/econwp/EWP-1423.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Preve, Daniel & Medeiros, Marcelo C., 2011. "Linear programming-based estimators in simple linear regression," Journal of Econometrics, Elsevier, vol. 165(1), pages 128-136.
    7. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    8. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    9. 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.
    10. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, December.
    11. Leif Andersen, 2007. "Discount curve construction with tension splines," Review of Derivatives Research, Springer, vol. 10(3), pages 227-267, December.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Patrick Hagan & Graeme West, 2006. "Interpolation Methods for Curve Construction," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(2), pages 89-129.
    20. 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.
    21. 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.
    22. McCulloch, J Huston, 1975. "The Tax-Adjusted Yield Curve," Journal of Finance, American Finance Association, vol. 30(3), pages 811-830, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cousin, Areski & Maatouk, Hassan & Rullière, Didier, 2016. "Kriging of financial term-structures," European Journal of Operational Research, Elsevier, vol. 255(2), pages 631-648.

    More about this item

    Keywords

    Employment; B-splines; Discount curve; No-arbitrage constraints; Monotone estimation; Yield curve;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:usg:econwp:2014:23. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Martina Flockerzi). General contact details of provider: http://edirc.repec.org/data/vwasgch.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.