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Phenomenology of the Interest Rate Curve

Author

Listed:
  • J. -P. Bouchaud

    (SPEC-Saclay, Science & Finance, Ecole Polytechnique)

  • N. Sagna

    (SPEC-Saclay, Science & Finance, Ecole Polytechnique)

  • R. Cont

    (SPEC-Saclay, Science & Finance, Ecole Polytechnique)

  • N. El-Karoui

    (SPEC-Saclay, Science & Finance, Ecole Polytechnique)

  • M. Potters

    (SPEC-Saclay, Science & Finance, Ecole Polytechnique)

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

  • J. -P. Bouchaud & N. Sagna & R. Cont & N. El-Karoui & M. Potters, 1997. "Phenomenology of the Interest Rate Curve," Papers cond-mat/9712164, arXiv.org.
  • Handle: RePEc:arx:papers:cond-mat/9712164
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    References listed on IDEAS

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    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
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    Cited by:

    1. 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.
    2. D. Sornette, 1998. "``String'' formulation of the Dynamics of the Forward Interest Rate Curve," Papers cond-mat/9802136, arXiv.org.
    3. 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.
    4. 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.
    5. Jean-Philippe Bouchaud, 2002. "An introduction to statistical finance," Science & Finance (CFM) working paper archive 313238, Science & Finance, Capital Fund Management.
    6. Bouchaud, Jean-Philippe, 2002. "An introduction to statistical finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(1), pages 238-251.
    7. Belal E. Baaquie, 2001. "Quantum Field Theory of Forward Rates with Stochastic Volatility," Papers cond-mat/0110506, arXiv.org.
    8. 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.
    9. repec:wsi:ijtafx:v:08:y:2005:i:06:n:s0219024905003244 is not listed on IDEAS
    10. Eckhard Platen, 2005. "An Alternative Interest Rate Term Structure Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(06), pages 717-735.
    11. Markus Leippold & Liuren Wu, 2002. "Design and Estimation of Quadratic Term Structure Models," Finance 0207014, EconWPA.
    12. 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.
    13. Rama Cont, 1999. "Modeling interest rate dynamics: an infinite-dimensional approach," Papers cond-mat/9902018, arXiv.org.
    14. Rene Carmona & Michael Tehranchi, 2004. "A Characterization of Hedging Portfolios for Interest Rate Contingent Claims," Papers math/0407119, arXiv.org.
    15. 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.

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    JEL classification:

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

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