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

TL;DR

This paper introduces a novel correlated bivariate CIR-like model for jointly describing interest rate term structures of Italy and a AAA-rated European country, emphasizing positivity and long-term decoupling.

Contribution

It proposes a non-affine, quadratic bivariate CIR-like model with specific properties, including positivity and asymptotic independence, using potential theory and reversibility constraints.

Findings

Model effectively captures joint interest rate dynamics.

Comparison shows improved fit over uncoupled models.

Numerical analysis validates theoretical properties.

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.