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Phenomenology of the interest rate curve

Author

Listed:
  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

  • Nicolas Sagna
  • Rama Cont

    (Science & Finance, Capital Fund Management)

  • Nicole El-Karoui
  • Marc Potters

    (Science & Finance, Capital Fund Management)

Abstract

This paper contains a phenomenological description of the whole U.S. forward rate curve (FRC), based on an data in the period 1990-1996. We find that the average FRC (measured 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 form a simple square-root law. The distortion 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. We show that this is consistent with the volatility `hump' around one year found by several authors (and which we confirm). Finally, the number of independent components needed to interpret most of the FRC fluctuations is found to be small. We rationalize this 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, in principle, to arbitrage. However, this arbitrage cannot be implemented in practice because of transaction costs. We suggest 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.

Suggested Citation

  • Jean-Philippe Bouchaud & Nicolas Sagna & Rama Cont & Nicole El-Karoui & Marc Potters, 1997. "Phenomenology of the interest rate curve," Science & Finance (CFM) working paper archive 500048, Science & Finance, Capital Fund Management.
  • Handle: RePEc:sfi:sfiwpa:500048
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    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. Schloegl, Erik & Daniel Sommer, 1997. "Factor Models and the Shape of the Term Structure," Discussion Paper Serie B 395, University of Bonn, Germany.
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    7. 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.
    8. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    9. 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(02), pages 235-254, June.
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    Cited by:

    1. Cajueiro, Daniel O. & Tabak, Benjamin M., 2007. "Long-range dependence and multifractality in the term structure of LIBOR interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 603-614.
    2. Markus Leippold & Liuren Wu, 2002. "Design and Estimation of Quadratic Term Structure Models," Finance 0207014, EconWPA.
    3. Eckhard Platen, 2003. "An Alternative Interest Rate Term Structure Model," Research Paper Series 97, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Belal Baaquie & Jean-Philippe Bouchaud, 2004. ""Stiff" Field Theory of Interest Rates and Psychological Future Time," Science & Finance (CFM) working paper archive 500064, Science & Finance, Capital Fund Management.
    5. Belal E. Baaquie, 2001. "Quantum Field Theory of Forward Rates with Stochastic Volatility," Papers cond-mat/0110506, arXiv.org.
    6. Roncoroni, Andrea & Galluccio, Stefano & Guiotto, Paolo, 2010. "Shape factors and cross-sectional risk," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2320-2340, November.
    7. Bouchaud, Jean-Philippe, 2002. "An introduction to statistical finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(1), pages 238-251.
    8. Rama Cont, 1999. "Modeling interest rate dynamics: an infinite-dimensional approach," Papers cond-mat/9902018, arXiv.org.
    9. Zhou, Wei-Xing & Sornette, Didier, 2004. "Causal slaving of the US treasury bond yield antibubble by the stock market antibubble of August 2000," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(3), pages 586-608.
    10. repec:wsi:ijtafx:v:08:y:2005:i:06:n:s0219024905003244 is not listed on IDEAS
    11. D. Sornette, 1998. "``String'' formulation of the Dynamics of the Forward Interest Rate Curve," Papers cond-mat/9802136, arXiv.org.
    12. Rene Carmona & Michael Tehranchi, 2004. "A Characterization of Hedging Portfolios for Interest Rate Contingent Claims," Papers math/0407119, arXiv.org.
    13. Baaquie, Belal E. & Yang, Cao, 2009. "Empirical analysis of quantum finance interest rates models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(13), pages 2666-2681.
    14. Jean-Philippe Bouchaud, 2002. "An introduction to statistical finance," Science & Finance (CFM) working paper archive 313238, Science & Finance, Capital Fund Management.
    15. Baaquie, Belal E. & Liang, Cui & Warachka, Mitch C., 2007. "Hedging LIBOR derivatives in a field theory model of interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 730-748.

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    JEL classification:

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

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