How to simulate a multivariate diffusion?

[aaps]

I'd like to know how to simulate a d-dimensional or multivariate diffusion, such as a multivariate version of the Heston model. Can anyone recommend a useful reference for me?

Thanks a lot!:tiphat:

 

[parisjohn]

You must use Monte Carlo model if you want to simule multivariate heston
In a first time you can just make a Euler scheme for the diffusion and the only problem is to reduce the matrix covariance between S1,V1,S2,V2 you can use cholevski decomposition
In a second time for the diffusion you can use L.Andersen scheme but the Variance with multivariate process is quite difficult to find.
You can go here The Quantitative Finance Library to find documentation for monte-carlo method

 

[aaps]

Thanks. I think I will simulate a multivariate discrete stochastic volatility model, such as Harvey, Ruiz and Shepard 1992, RFS. It is much easier and I will save a lot of work.