Simulating Multivariate Distribution

stirlitz · July 11th, 2005, 2:22 pm

Hi All Experts out there,I am doing a monte-carlo. I need to simulate several random variables which are correlated. I have estimated a correlation matrix.I also have means and volatilities of the individual random variables.I am looking for a piece of computer code (math algorithm, in C++ or VBA) that would generate correlated random variables.From past life in linear algebra and stats, I remember something about eigenvalues of the var-covar mx, but I am in a total hazehow to apply this (it was so long ago... I should have read my books at school).Anyway - is it a trivial problem for some of you?Can you suggest a solution?ThanksStiz

Antonio · July 11th, 2005, 3:15 pm

There have been many threads on this topic. TypeCholesky in the search form and you will find your answer.

chiranjiv · July 11th, 2005, 3:44 pm

Quick Google Search + Quick hacking produced this one. In the first prompt use mouse to select the corr matrix. There is lot of scope for improvement e.g. routines to "correct" the corr. matrix/better random number genetaion/faster eigen vlaues.. For that use Wilmott threads and Peter Jaeckel's book!!Ciao!!

umpbumpfizz · July 12th, 2005, 4:28 am

hi,use copula to generate correlated random number. any copula will do ir.for example if u have to generate correlated uniform random numbers follow the following steps-suppose correlation matrix is R and we r using gaussian copula-1) Find any suitable decomposition of R( say cholesky) R=AA'2) draw z n dimension random vector from uncorrelated standard normal distribution.3) x=z'A4)u=phi(x); phi is norm distu is n dimensional correlated unifor numbers

stirlitz · July 13th, 2005, 9:39 am

Thanks everybody.Particularly, thanks Chiranjiv for the VBA code. I tried it, and with enough simulations the simulated random variables have the correlation matrix close to the original.Two further questions on the file:(a) is there a limit on the size of the corr. matrix?(b) is the code using the Excel random number generator?Thx, Stiz

QGenius · July 13th, 2005, 10:48 am

umpbumpfizz : your vector x will indeed have the desired corr. matrix R, but how about u ? this is the vector for which we want the desired R!

chiranjiv · July 13th, 2005, 3:20 pm

Hi Stiz,To answer to ur questions..1) There is no upper limit on the size of the correl matrix...but with bigger matrices you might see the programme take much longer to run...2) Yes, it uses VBA's RND function to generate Uniform Random numbers which it then converts to Normal Variates..if you are unhappy with it..consider using this implementation of Mersenne Twister Mersenne Twister in VBABonne Chance!!Manu