I'm trying to simulate correlated assets under Heston model. I coded the QE scheme for a single asset but i dont understand the next step: How should i set the correlation matrix given my n-asset independent stock and variance paths ? Should i generate those paths first given my asset-variance correlation, then decorrelate my subsystem (i mean from the same asset-variance system) or what ? And if so, how ? My question is really what's the first step ? From what i read in the papers below ill have to then calibrate my asset-asset correlation given the historical one but that's an another issue. I read wadman, dimitroff and De Innocentis but I'm still struggling. Help would be appreciated. Many thanks
Wadman, 2010: an advanced Monte Carlo for the multi asset Heston model
Dimitroff: a parsimonious multi asset Heston model: calibration and derivative pricing
De Innocentis: Efficient simulation of the multi asset Heston model