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Explaining The Forward Interest Rate Term Structure

Author

Listed:
  • ANDREW MATACZ

    (Science and Finance, 109-111 rue Victor Hugo, 92532 Levallois, France)

  • JEAN-PHILIPPE BOUCHAUD

    (Service de Physique de l'Etat Condensé CEA-Saclay, Orme des Merisiers, 91 191 Gif s/ Yvette, France)

Abstract

We present compelling empirical evidence for a new interpretation of the Forward Rate Curve (FRC) term structure. We find that the average FRC follows a square-root law, with a prefactor related to the spot volatility, suggesting a Value-at-Risk like pricing. We find a striking correlation between the instantaneous FRC and the past spot trend over a certain time horizon. This confirms the idea of an anticipated trend mechanism proposed earlier and provides a natural explanation for the observed shape of the FRC volatility. We find that the one-factor Gaussian Heath–Jarrow–Morton model calibrated to the empirical volatility function fails to adequately describe these features.

Suggested Citation

  • Andrew Matacz & Jean-Philippe Bouchaud, 2000. "Explaining The Forward Interest Rate Term Structure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 381-389.
    • Handle: RePEc:wsi:ijtafx:v:03:y:2000:i:03:n:s0219024900000243
    DOI: 10.1142/S0219024900000243
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    References listed on IDEAS

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    1. Andrew Matacz & Jean-Philippe Bouchaud, 1999. "An empirical investigation of the forward interest rate term structure," Science & Finance (CFM) working paper archive 500047, Science & Finance, Capital Fund Management.
    2. Carl Chiarella & Oh-Kang Kwon, 1999. "Classes of Interest Rate Models Under the HJM Framework," Research Paper Series 13, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. 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.
    4. 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..
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    Cited by:

    1. Baaquie, Belal E. & Pan, Tang, 2011. "Simulation of coupon bond European and barrier options in quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 263-289.
    2. 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.
    3. Baaquie, Belal E. & Tang, Pan, 2012. "Simulation of nonlinear interest rates in quantum finance: Libor Market Model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1287-1308.
    4. Baaquie, Belal E. & Liang, Cui, 2007. "Empirical investigation of a field theory formula and Black's formula for the price of an interest-rate caplet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 331-348.
    5. Baaquie, Belal E. & Liang, Cui, 2007. "Pricing American options for interest rate caps and coupon bonds in quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 285-316.
    6. 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.

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