Generating correlated random vars with Cholesky

#1
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
#2
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.

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