 Abstract
Motivated by several stylized statistical empirical 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 then described as a 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 and the structure of principal
components of term structure deformations. 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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Modeling term structure dynamics: an infinite dimensional approach
http://www.institut-europlace.com/files/pdf/doc836013.pdf
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