Modelling Interest Rates by Correlated Multi-Factor CIR-Like Processes
23 Pages Posted: 29 Jul 2008 Last revised: 31 Jul 2008
Date Written: July 24, 2008
Abstract
We investigate the joint description of the interest-rate term stuctures of Italy and an AAA-rated European country by mean of a - here proposed - correlated CIR-like bivariate model where one of the state variables is interpreted as a benchmark risk-free rate and the other as a credit spread. The model is constructed by requiring the strict positivity of interest rates and the asymptotic decoupling of the joint distribution of the two state variables on a long time horizon. The second condition is met by imposing the reversibility of the process with respect to a product measure, the first is then implemented by using the tools of potential theory. It turns out that these conditions select a class of non-affine models, out of which we choose one that is quadratic in the two state variables both in the drift and diffusion matrix. We perform a numerical analysis of the model by investigating a cross section of the term structures comparing the results with those obtained with an uncoupled bivariate CIR model.
Keywords: Interest rates, Multidimensional CIR processes, Potential theory
JEL Classification: E43
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