I am trying to simulate multivariate lognormal distribution values using means(mu), standard deviations(sigma), and correlations(rho) matrices. Does anyone have any source I can read about to simulate multivariate lognormal distribution?

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    $\begingroup$ Can you elaborate? Do you just want to have it where the individual components when logged have those properties. Even if that is the case, there is no "multivariate log normal" in the same way there is a multivariate normal. You can try using copulas. $\endgroup$ – Josh Feb 9 '18 at 22:19
  • $\begingroup$ Possible duplicate (although I am not sure) of multivariate log normal pdf $\endgroup$ – Peter Flom - Reinstate Monica Jul 14 '18 at 11:25

Simulate the multivariate normal, then take exponents of variables. Take a look at this parameterization of it. The means and covaraince matrix in this parameterization are of the logs of multivariate normals. The means and covarainces of lognormals can be easily calculated following the equations.

If your inputs are the mean and covariance matrix of the lognormals themselves, then you can convert them into normals, and proceed as I suggested

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    $\begingroup$ There's an ambiguity with this: what do the correlations refer to? Are they the correlations of the logarithms or the correlations of the original variables? Ditto for the variances. $\endgroup$ – whuber Feb 9 '18 at 22:29
  • $\begingroup$ @Aksakal Thank you very much for yor comment. Yea I agree that I can simulate multivariate normal and just take exponential. $\endgroup$ – Jun Jang Feb 9 '18 at 23:29
  • $\begingroup$ @Aksakal. Do you know how to simulate multivariate normal Monte Carlo using VBA? $\endgroup$ – Jun Jang Feb 9 '18 at 23:40
  • $\begingroup$ I don't code in VBA. If you know how to do Cholesky decomposition, then you can generate indpendent normals, then do matrix multiplication on the cholesky of covariance matrix $\endgroup$ – Aksakal Feb 10 '18 at 0:31

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