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Im looking for a quick way (as in runs quick, not necessarily is quick to implement) of simulating multiple square root processes for a stochastic volatility model, flexible enough to allow for correlation between the brownian motions driving the underlying and the ones driving the factors.

Any help would be appreciated.

Edit: The dynamics are $$dX_t = \sum_{i=1}^n \sqrt{V_{it}} dW_{it}$$ and $$dV_{it}=\kappa_i(\omega_i-V_{it})dt +\eta_i dW_{(i+n)t}$$ where i would like to be able to potentially have for $i\in\{1,\dots,n\}$ $<dW_{i\cdot },dW_{i+n\cdot }>=\rho_i \neq 0$. In particular im trying to do a three factor model.

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could you please write down the model-dynamics ? - for the standard case of the Heston-Model Anderson devised the quadratic exponential scheme that has become a market standard –  Probilitator Apr 22 at 8:31
    
I am a bit confused y the notation with respect to $V_it$ what does $W_{(i+n)t}$ mean ? - If I am understanding you correctly we are talking about 6 sources of noise for the three factor case - correct ? –  Probilitator Apr 22 at 8:52
    
Yep exactly, could not figure out a neater way to write it. –  Henrik Apr 22 at 8:53
    
do you need it to be just fast or accurate as well ? - are you aware fo Kloeden and Platens work ? –  Probilitator Apr 22 at 8:53
    
Speed is most important, but I think it also need to be fairly accurate. I am googling it right now , otherwise no:) But i'm no stranger to simulating SDE's. I've already done Euler, Milstein and the Kaya Broadie for a one factor (which is of course useless here, but interesting). –  Henrik Apr 22 at 8:57

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