I'm relatively new in this field, so I have a couple of points that I need to clarify.
I would like to know how I can estimate the correlation matrix necessary to implement a Cholesky decomposition for a model that has two different sources of risk.
Let's take for example an Heston model where we have two Brownian motions, $W_{s}$ and $W_{v}$.
In the case of a portfolio composed by two stocks, in order to be able to simulate correlated paths:
How do I estimate the correlation matrix of the variance process for the two stocks? Moving average std or other methods?
Because in Heston model $W_{s}$ and $W_{v}$ are correlated, so that we have $\rho_{1}=corr(W_{1s},W_{1v})$ for the first asset and $\rho_{2}=corr(W_{2s},W_{2v})$ for the second asset, do I have to get two different matrixes of dimension $2\times2$ (one for each stock) or one matrix of dimension $4\times4$?
Thank you in advance!