Introduce correlation in exact multivariate CIR simulation

Develop an intuitive and exact method to introduce cross-series correlation when simulating multivariate Cox–Ingersoll–Ross (CIR) processes using the “exact” distribution algorithm based on normal and chi-square components, instead of relying on Euler discretization to impose correlation between series.

Background

The paper simulates bivariate interest rate series using the CIR model. While the one-dimensional CIR process has an exact transition law that can be sampled via a normal–chi-square mixture, the authors note difficulty in introducing correlation directly within this exact sampling framework for multiple series.

As a practical workaround, they correlate the series by switching to Euler discretization, acknowledging that a conceptually clear, exact approach to incorporate cross-series correlation is not evident. Establishing such a methodology would enable exact correlated sampling without sacrificing the benefits of the exact transition law.