Modeling interest rate dynamics: an infinite-dimensional approach
AbstractWe present a family of models for the term structure of interest rates which describe the interest rate curve as a stochastic process in a Hilbert space. We start by decomposing the deformations of the term structure into the variations of the short rate, the long rate and the fluctuations of the curve around its average shape. This fluctuation is then described as a solution of a stochastic evolution equation in an infinite dimensional space. In the case where deformations are local in maturity, this equation reduces to a stochastic PDE, of which we give the simplest example. We discuss the properties of the solutions and show that they capture in a parsimonious manner the essential features of yield curve dynamics: imperfect correlation between maturities, mean reversion of interest rates and the structure of principal components of term structure deformations. Finally, we discuss calibration issues and show that the model parameters have a natural interpretation in terms of empirically observed quantities.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number cond-mat/9902018.
Date of creation: Feb 1999
Date of revision:
Publication status: Published in International Journal of Theoretical and Applied Finance Vol. 8, No. 3 (2005) 357--380
Contact details of provider:
Web page: http://arxiv.org/
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Jean-Philippe Bouchaud & Nicolas Sagna & Rama Cont & Nicole El-Karoui & Marc Potters, 1998. "Strings Attached," Science & Finance (CFM) working paper archive 500049, Science & Finance, Capital Fund Management.
- D. P. Kennedy, 1994. "The Term Structure Of Interest Rates As A Gaussian Random Field," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 247-258.
- J. -P. Bouchaud & N. Sagna & R. Cont & N. El-Karoui & M. Potters, 1997.
"Phenomenology of the Interest Rate Curve,"
- Dybvig, Philip H & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1996.
"Long Forward and Zero-Coupon Rates Can Never Fall,"
The Journal of Business,
University of Chicago Press, vol. 69(1), pages 1-25, January.
- repec:fth:inseep:9611 is not listed on IDEAS
- Schaefer, Stephen M & Schwartz, Eduardo S, 1987. " Time-Dependent Variance and the Pricing of Bond Options," Journal of Finance, American Finance Association, vol. 42(5), pages 1113-28, December.
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-52.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.