# Why do we need correlated random variables in a Monte Carlo simulation?

Question: I don't understand why a Monte Carlo simulation needs correlated random variables. Isn't each simulation thread independent?

Background:

Specifically, I'm referring to the below example on pg 319 in the Malz text (http://ca.wiley.com/WileyCDA/WileyTitle/productCd-0470481803.html).

He describes a Monte Carlo simulation with 1,000 simulation threads to calculate credit losses on a CDO with 100 underlying credits.

### #1.

In the simulation, we setup a matrix of 1,000 draws from a 100 dimension joint normal distribution.

### #2.

We posit 4 separate assumptions for pairwise correlation 0, 0.3, 0.6, 0.9

### #3.

For each correlation assumption, the matrix of 1,000 random normals is transformed into matrix of 1,000 correlated random normals (which of course are still 100 dimensional normals).

I don't understand why we need to transform the matrix of uncorrelated random normals into correlated ones? Isn't each simulation thread independent of the previous ?