I've been trying to generate correlated random numbers for Pricing a Basket option (Monte Carlo) using MATLAB. Nonetheless, I am now a bit confused when I use Cholesky decomposition i.e. when I decompose correlation matrix, I get one price. But when I decompose covariance matrix, I get another (much lower) price (I believe this is because values of element in cov matrix are much lower which in turn yields lower epsilon). So my questions are:1) when generating random numbers and using Cholesky decomposition, can one use covariance and correlation matrix interchangably? (i.e. are they both "All positive definite"?) (It seems to me that most people are alway talking about correlation matrix.)2) let X is the correlated random variable vector with a dimension of (path * number of stocks), and my X isX = (C'*Z)', where C is Matrix obtained from Cholesky decomposition of E (where E is n*n square covariance matrix) and Z is a vector of normally distributed random variable with a dimension of (number of stock * path).Did I make any mistakes in this formula? PLease help advice.Cheers