This quick blog entry to share an excellent article of Thijs van den Berg entitled Generating Correlated Random Numbers.

This author describes in a nicely way how to generate sequences of correlated random numbers using the Cholesky decomposition, and a Eigenvector decomposition as well. (I worked out matrices with QuantLib some time ago.)  A piece of Matlab code follows.

This short article is a good opportunity for the reader to get back to some essential statisticals tools/concepts, such as Eigenvectors and Eigenvalues. One can have a look at MathWorld, for example.

The reader like myself that doesn’t have a Matlab license might be tempted to write equivalent code in R language. I recommend the Matrix Algebra in R documentation if you need a  refresh on matrices using R.

Example R code using a Cholesky decomposition:
In-a-shot, the code corresponding to the Matlab snippet of the original article might be as follows :

Mat <- matrix(c(1,0.6,0.3,0.6,1,0.5,0.3,0.5,1.0),nrow=3) # matrix creation
Chol <- chol(Mat) # cholesky decomposition
set.seed(123) # sets seed for random number generator
V1 <- rnorm(10, 0, 1)
V2 <- rnorm(10, 0, 1)
V3 <- rnorm(10, 0, 1)
VFin <- cbind(V1, V2, V3) # 3 vectors of 10 rand. norm. numbers
ans <- VFin %*% Chol