IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v6y1999i3p209-232.html
   My bibliography  Save this article

Phenomenology of the interest rate curve

Author

Listed:
  • Jean-Philippe Bouchaud
  • Nicolas Sagna
  • Rama Cont
  • Nicole El-Karoui
  • Marc Potters

Abstract

The paper contains a phenomenological description of the whole US forward rate curve (FRC), based on data in the period 1990-1996. It is found that the average deviation of the FRC from the spot rate grows as the square-root of the maturity, with a prefactor which is comparable to the spot rate volatility. This suggests that forward rate market prices include a risk premium, comparable to the probable changes of the spot rate between now and maturity, which can be understood as a 'Value-at-Risk' type of pricing. The instantaneous FRC, however, departs from a simple square-root law. The deformation is maximum around one year, and reflects the market anticipation of a local trend on the spot rate. This anticipated trend is shown to be calibrated on the past behaviour of the spot itself. It is shown that this is consistent with the volatility 'hump' around one year found by several authors (which is confirmed). Finally, the number of independent components needed to interpret most of the FRC fluctuations is found to be small. This is rationalized by showing that the dynamical evolution of the FRC contains a stabilizing second derivative (line tension) term, which tends to suppress short-scale distortions of the FRC. This shape-dependent term could lead to arbitrage. However, this arbitrage cannot be implemented in practice because of transaction costs. It is suggested that the presence of transaction costs (or other market 'imperfections') is crucial for model building, for a much wider class of models becomes eligible to represent reality.1

Suggested Citation

  • Jean-Philippe Bouchaud & Nicolas Sagna & Rama Cont & Nicole El-Karoui & Marc Potters, 1999. "Phenomenology of the interest rate curve," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 209-232.
  • Handle: RePEc:taf:apmtfi:v:6:y:1999:i:3:p:209-232
    DOI: 10.1080/135048699334546
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/135048699334546
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/135048699334546?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Rendleman, Richard J, Jr & Carabini, Christopher E, 1979. "The Efficiency of the Treasury Bill Futures Market," Journal of Finance, American Finance Association, vol. 34(4), pages 895-914, September.
    2. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    4. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    5. Raphaël Douady, 2013. "Yield Curve Smoothing and Residual Variance of Fixed Income Positions," Post-Print hal-00666751, HAL.
    6. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    7. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    8. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(2), pages 235-254, June.
    9. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
    10. Longstaff, Francis A & Schwartz, Eduardo S, 1992. "Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-1282, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Constantin Mellios, 2001. "Valuation of Interest Rate Options in a Two-Factor Model of the Term Structure of Interest Rate," Working Papers 2001-1, Laboratoire Orléanais de Gestion - université d'Orléans.
    2. David K. Backus & Stanley E. Zin, 1994. "Reverse Engineering the Yield Curve," Working Papers 94-09, New York University, Leonard N. Stern School of Business, Department of Economics.
    3. Tiziana Di Matteo & Tomaso Aste, 2002. "How Does The Eurodollar Interest Rate Behave?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 107-122.
    4. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    5. repec:uts:finphd:40 is not listed on IDEAS
    6. Moreno, Manuel & Platania, Federico, 2015. "A cyclical square-root model for the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 241(1), pages 109-121.
    7. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    8. Giuseppe Arbia & Michele Di Marcantonio, 2015. "Forecasting Interest Rates Using Geostatistical Techniques," Econometrics, MDPI, vol. 3(4), pages 1-28, November.
    9. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    10. Jean-Philippe BOUCHAUD & Rama CONT & Nicole EL KAROUI & Marc POTTERS & Nicolas SAGNA, 1997. "Phenomenology of the interest curve," Finance 9712009, University Library of Munich, Germany.
    11. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018.
    12. Dennis Kristensen, 2004. "A Semiparametric Single-Factor Model of the Term Structure," FMG Discussion Papers dp501, Financial Markets Group.
    13. Jin-Chuan Duan & Kris Jacobs, 2001. "Short and Long Memory in Equilibrium Interest Rate Dynamics," CIRANO Working Papers 2001s-22, CIRANO.
    14. Duan, Jin-Chuan & Jacobs, Kris, 2008. "Is long memory necessary? An empirical investigation of nonnegative interest rate processes," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 567-581, June.
    15. Vetzal, Kenneth R., 1997. "Stochastic volatility, movements in short term interest rates, and bond option values," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 169-196, February.
    16. R.C. Stapleton & Marti G. Subrahmanyam, 1999. "The Term Structure of Interest Rate-Futures Prices," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-045, New York University, Leonard N. Stern School of Business-.
    17. Jury Falini, 2009. "Pricing caps with HJM models: the benefits of humped volatility," Department of Economics University of Siena 563, Department of Economics, University of Siena.
    18. Gibson, Rajna & Lhabitant, Francois-Serge & Talay, Denis, 2010. "Modeling the Term Structure of Interest Rates: A Review of the Literature," Foundations and Trends(R) in Finance, now publishers, vol. 5(1–2), pages 1-156, December.
    19. Dai, Qiang & Singleton, Kenneth J., 2003. "Fixed-income pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 20, pages 1207-1246, Elsevier.
    20. repec:wyi:journl:002108 is not listed on IDEAS
    21. Michael W. Brandt & Amir Yaron, 2003. "Time-Consistent No-Arbitrage Models of the Term Structure," NBER Working Papers 9458, National Bureau of Economic Research, Inc.
    22. Juan M. Moraleda & Ton Vorst, 1996. "The Valuation of Interest Rate Derivatives: Empirical Evidence from the Spanish Market," Tinbergen Institute Discussion Papers 96-170/2, Tinbergen Institute.

    More about this item

    Keywords

    Forward Rate Curve; Spot Rate; Risk Premium; 'value-at-risk' Pricing; Volatility Hump; Deformation;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    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:taf:apmtfi:v:6:y:1999:i:3:p:209-232. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAMF20 .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.