MODELING TERM STRUCTURE DYNAMICS: AN INFINITE DIMENSIONAL APPROACH

Rama Cont ()
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Rama Cont: Centre de Mathématiques Appliquées, Ecole Polytechnique, F-91128 Palaiseau, France

International Journal of Theoretical and Applied Finance (IJTAF), 2005, vol. 08, issue 03, 357-380

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.

Keywords: Term structure of interest rates; forward rates; multifactor models; Hilbert space; stochastic PDE; random field (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (14)

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DOI: 10.1142/S0219024905003049

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