Modeling Term Structure Dynamics: An Infinite Dimensional Approach
AbstractMotivated 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.
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Bibliographic InfoArticle provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.
Volume (Year): 08 (2005)
Issue (Month): 03 ()
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- J. -P. Bouchaud & N. Sagna & R. Cont & N. El-Karoui & M. Potters, 1997.
"Phenomenology of the Interest Rate Curve,"
- 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.
- 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.
- Björk, Tomas & di Masi, Giovanni & Kabanov, Yuri & Runggaldier, Wolfgang, 1996.
"Towards a General Theory of Bond Markets,"
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.
- 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.
- Schloegl, Erik & Daniel Sommer, 1997. "Factor Models and the Shape of the Term Structure," Discussion Paper Serie B 395, University of Bonn, Germany.
- 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.
- 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.
- 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.
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