Modeling interest rate dynamics: an infinite-dimensional approach

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Title: Modeling interest rate dynamics: an infinite-dimensional approach
Authors: Cont, R
Item Type: Journal Article
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. © World Scientific Publishing Company.
Issue Date: 1-May-2005
URI: http://hdl.handle.net/10044/1/10541
DOI: http:dx.doi.org/10.1142/S0219024905003049
ISSN: 0219-0249
Publisher: World Scientific
Start Page: 357
End Page: 380
Journal / Book Title: International Journal of Theoretical and Applied Finance
Issue: 3
Copyright Statement: © World Scientific Publishing Company. Electronic version of an article published as International Journal of Theoretical and Applied Finance, Volume 8, Issue 3, 2005, Pages 357–380. Article DOI 10.1142/S0219024905003049
Volume: 8
Notes: Keywords: interest rates, stochastic PDE, term structure models, stochastic processes in Hilbert space. Other related works may be retrieved on http://www.eleves.ens.fr:8080/home/cont/papers.html
Publisher URL: http://dx.doi.org/10.1142/S0219024905003049
Appears in Collections:Financial Mathematics



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