In order to account for simulations with multiple variables, it is possible to generate simulated variables that are related by a correlation coefficient. This process can be extended to more than two variables through a process known as the Cholesky factorization. However, the Cholesky factorization requires that the covariance matrix be positive-definite for this process to be effective. It is also possible to use principal components method to overcome difficulties in the Cholesky factorization method. Note that the Cox, Ingersoll, Ross (CIR) model is a one-factor model of interest rate dynamics. |
