Phenomenology of the interest rate curve

Jean-Philippe Bouchaud, Nicolas Sagna, Rama Cont, Nicole El-Karoui and Marc Potters ()

Applied Mathematical Finance, 1999, vol. 6, issue 3, 209-232

Abstract: The paper contains a phenomenological description of the whole US forward rate curve (FRC), based on data in the period 1990-1996. It is found that the average deviation of the FRC 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 from a simple square-root law. The deformation 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. It is shown that this is consistent with the volatility 'hump' around one year found by several authors (which is confirmed). Finally, the number of independent components needed to interpret most of the FRC fluctuations is found to be small. This is rationalized 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 to arbitrage. However, this arbitrage cannot be implemented in practice because of transaction costs. It is suggested 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.1

Keywords: Forward Rate Curve; Spot Rate; Risk Premium; 'value-at-risk' Pricing; Volatility Hump; Deformation (search for similar items in EconPapers)
Date: 1999
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (22)

Downloads: (external link)
http://www.tandfonline.com/doi/abs/10.1080/135048699334546 (text/html)
Access to full text is restricted to subscribers.

Related works:
Working Paper: Phenomenology of the Interest Rate Curve (1997)
Working Paper: Phenomenology of the interest rate curve (1997)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:apmtfi:v:6:y:1999:i:3:p:209-232

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/RAMF20

DOI: 10.1080/135048699334546

Access Statistics for this article

Applied Mathematical Finance is currently edited by Professor Ben Hambly and Christoph Reisinger

More articles in Applied Mathematical Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().