Modelling interest rates by correlated multi-factor CIR-like processes

L. Bertini; L. Passalacqua

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arXiv · 0807.3898

Modelling interest rates by correlated multi-factor CIR-like processes

L. Bertini·L. Passalacqua

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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.

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L. Bertini, L. Passalacqua. 2008-07-24. Modelling interest rates by correlated multi-factor CIR-like processes. https://arxiv.org/abs/0807.3898

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