# 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.

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