Phenomenology of the interest rate curve

Jean-Philippe Bouchaud, Nicolas Sagna, Rama Cont, Nicole El-Karoui and Marc Potters ()
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Jean-Philippe Bouchaud: Science & Finance, Capital Fund Management
Rama Cont: Science & Finance, Capital Fund Management

No 500048, Science & Finance (CFM) working paper archive from 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.

JEL-codes: G10 (search for similar items in EconPapers)
Date: 1997-12
New Economics Papers: this item is included in nep-fin, nep-fmk and nep-mon
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Published in Applied Mathematical Finance, 6, 209, (1999)

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Working Paper: Phenomenology of the Interest Rate Curve (1997)
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Persistent link: https://EconPapers.repec.org/RePEc:sfi:sfiwpa:500048

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