Modeling Term Structure Dynamics: An Infinite Dimensional Approach
Motivated by stylized statistical properties of interest rates, we propose a modeling approach in which the forward rate curve is described as a stochastic process in a space of curves. After decomposing the movements of the term structure into the variations of the short rate, the long rate and the deformation of the curve around its average shape, this deformation is described as the solution of a stochastic evolution equation in an infinite dimensional space of curves. 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, the structure of principal components of forward rates and their variances. In particular we show that a flat, constant volatility structures already captures many of the observed properties. Finally, we discuss parameter estimation issues and show that the model parameters have a natural interpretation in terms of empirically observed quantities.
Volume (Year): 08 (2005)
Issue (Month): 03 ()
|Contact details of provider:|| Web page: http://www.worldscinet.com/ijtaf/ijtaf.shtml|
|Order Information:|| Email: |
References listed on IDEAS
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.:
- 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.
- Michael J. Brennan and Eduardo S. Schwartz., 1979. "A Continuous-Time Approach to the Pricing of Bonds," Research Program in Finance Working Papers 85, University of California at Berkeley.
- Brennan, Michael J. & Schwartz, Eduardo S., 1979. "A continuous time approach to the pricing of bonds," Journal of Banking & Finance, Elsevier, vol. 3(2), pages 133-155, July.
- 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.
- J. -P. Bouchaud & N. Sagna & R. Cont & N. El-Karoui & M. Potters, 1997. "Phenomenology of the Interest Rate Curve," Papers cond-mat/9712164, arXiv.org.
- Jean-Philippe Bouchaud & Nicolas Sagna & Rama Cont & Nicole El-Karoui & Marc Potters, 1997. "Phenomenology of the interest rate curve," Science & Finance (CFM) working paper archive 500048, Science & Finance, Capital Fund Management.
- Ballocchi, Giuseppe & Dacorogna, Michel M. & Hopman, Carl M. & Muller, Ulrich A. & Olsen, Richard B., 1999. "The intraday multivariate structure of the Eurofutures markets," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 479-513, December.
- Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
- Jonathan E. Ingersoll Jr. & Philip H. Dybvig & Stephen A. Ross, 1998.
"Long Forward and Zero-Coupon Rates Can Never Fall,"
Yale School of Management Working Papers
ysm45, Yale School of Management.
- Giovanni Di Masi & Tomas Björk & Wolfgang Runggaldier & Yuri Kabanov, 1997.
"Towards a general theory of bond markets (*),"
Finance and Stochastics,
Springer, vol. 1(2), pages 141-174.
- Björk, Tomas & di Masi, Giovanni & Kabanov, Yuri & Runggaldier, Wolfgang, 1996. "Towards a General Theory of Bond Markets," SSE/EFI Working Paper Series in Economics and Finance 143, Stockholm School of Economics.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Schloegl, Erik & Daniel Sommer, 1997. "Factor Models and the Shape of the Term Structure," Discussion Paper Serie B 395, University of Bonn, Germany.
When requesting a correction, please mention this item's handle: RePEc:wsi:ijtafx:v:08:y:2005:i:03:p:357-380. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tai Tone Lim)
If references are entirely missing, you can add them using this form.