Modeling Term Structure Dynamics: An Infinite Dimensional Approach

CMAPX Internal Report No. 402

32 Pages Posted: 25 Feb 1999

Date Written: July 2004

Abstract

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.

JEL Classification: C5, C13, E43, E47

Suggested Citation

Cont, Rama, Modeling Term Structure Dynamics: An Infinite Dimensional Approach (July 2004). CMAPX Internal Report No. 402, Available at SSRN: https://ssrn.com/abstract=148408 or http://dx.doi.org/10.2139/ssrn.148408

Rama Cont (Contact Author)

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://https://www.maths.ox.ac.uk/people/rama.cont

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