Question: I don't understand why a Monte Carlo simulation needs correlated random variables. Isn't each simulation thread independent?
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.
In the simulation, we setup a matrix of 1,000 draws from a 100 dimension joint normal distribution.
We posit 4 separate assumptions for pairwise correlation 0, 0.3, 0.6, 0.9
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 ?