Phenomenology of the Interest Curve: A Statistical Analysis of Term Structure Deformations

32 Pages Posted: 10 Feb 1998

See all articles by Jean-Philippe Bouchaud

Jean-Philippe Bouchaud

Capital Fund Management

Nicholas Sagna

Credit Suisse First Boston Fixed Income Research

Rama Cont

University of Oxford

Nicole El Karoui

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees

Marc Potters

Capital Fund Management; Capital Fund Management

Date Written: December 1997

Abstract

This paper contains a statistical description of the whole U.S. forward rate curve (FRC), based on data from the period 1990-1996. We find that the average deviation of the FRC from the spot rate grows as the square-root of the maturity, with a proportionality constant 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 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 behavior 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, suggesting an analogy with the motion of a vibrating string subject to random perturbations. 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.

JEL Classification: E43, C51

Suggested Citation

Bouchaud, Jean-Philippe and Sagna, Nicolas and Cont, Rama and El Karoui, Nicole and Potters, Marc and Potters, Marc, Phenomenology of the Interest Curve: A Statistical Analysis of Term Structure Deformations (December 1997). Available at SSRN: https://ssrn.com/abstract=58470 or http://dx.doi.org/10.2139/ssrn.58470

Jean-Philippe Bouchaud (Contact Author)

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France
+33 1 49 49 59 20 (Phone)

Nicolas Sagna

Credit Suisse First Boston Fixed Income Research ( email )

11 Madison Avenue
New York, NY 10010
United States

Rama Cont

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://www.maths.ox.ac.uk/people/rama.cont

Nicole El Karoui

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees ( email )

Palaiseau Cedex, 91128
France
(33) 1 69 33 41 48 (Phone)
(33) 1 69 33 70 31 (Fax)

Marc Potters

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

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