Generating correlated random vars with Cholesky

panjerzy

New Member
Hi everyone,

Can somebody please explain to me what is the intuition behind the cholesky decomposition when generating correlated random variables? The funny thing is that i know how to calculate it, the thing is that I have no idea why it works.......

In my Monte Carlo simulator i generate a choleski deco on correlation matrix, mulitply it with vector of uncorelated standard normals , rescale the normals and get nice results...But why does multiplying Cholesky lower triangular by uncorelated vector gives me correlated one? I saw some simbolic, very general explanation but somehow I just dont get it.......

Many thanks

Jerzy

Dragan

Super Moderator
Hi everyone,

Can somebody please explain to me what is the intuition behind the cholesky decomposition when generating correlated random variables? The funny thing is that i know how to calculate it, the thing is that I have no idea why it works.......

In my Monte Carlo simulator i generate a choleski deco on correlation matrix, mulitply it with vector of uncorelated standard normals , rescale the normals and get nice results...But why does multiplying Cholesky lower triangular by uncorelated vector gives me correlated one? I saw some simbolic, very general explanation but somehow I just dont get it.......

Many thanks

Jerzy
Well, start with two variables. That is, given that X and E are iid standard normal, show that Y has correlation with X of r.

$$Y=rX+\sqrt{1-r^{2}}E$$