Modelling interest rates by correlated multi-factor CIR-like processes
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.
Cite
@article{arxiv.0807.3898,
title = {Modelling interest rates by correlated multi-factor CIR-like processes},
author = {L. Bertini and L. Passalacqua},
journal= {arXiv preprint arXiv:0807.3898},
year = {2008}
}