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cholesky decomposition
I am trying to simulate 10 random correlated returns and I am using the Cholesky decomposition. (I have determined the Cholesky matrix both using eviews and excel->the result being identical). The correlation matrix for the simulated variables is not similar at all with the initial one. Does anyone know why this might happen? I know it's silly thing but I just can't figure it out
cholesky decomposition
you aren't giving us much information ... which uniform rng are you using ? how you generating the normal deviates ? finally, and I would start with this if I were you, test it for two, three, four etc correlated normals and see if any work.
knowledge comes, wisdom lingers
cholesky decomposition
I am using the normal distribution for the simulations with 0 mean but different sigmas. Could this be the source of the problem? I simply generate them using =normsinv(rand(),0,sigma) in excel.
cholesky decomposition
rand() is notoriously poor ... but before dismissing it try the two and three asset cases
knowledge comes, wisdom lingers
cholesky decomposition
I did, the problem is the same. I also tried an add in. Do you have any suggestions for better MC sim?
cholesky decomposition
which addin did you use ? I have tried it with two assets using rand() and my implementation of Mersenne Twister. Seems rand() is more slightly worse than MT... but I recover a correlation that is not too far from my input. for example, if I use a correlation of 0.1 I get values of around 0.13
knowledge comes, wisdom lingers
cholesky decomposition
the answer you are seeking for Excel is detailed here:Generating Correlated Normally Distributed Random Numbers in Excel(to the extent i understand what you are trying to achieve)you will find a nice how-to for Matlab, here:Generating Correlated Random Numbersand, a code snippet for similar results with R, here:Generation of correlated random numbers: blablabla
Last edited by tags on August 21st, 2012, 10:00 pm, edited 1 time in total.
cholesky decomposition
and one can find help here:Cholesky Decompositionbut i now have much doubt this is what you are seeking ????
Last edited by tags on August 21st, 2012, 10:00 pm, edited 1 time in total.
cholesky decomposition
I am sure you have done this but do you recover the original covariance matrix when you multiply your upper and lower triangular decomposed matrices?What number of simulations are you using?Is here a scaling issue of some sort that is distorting your results? Not busy today so if you PM me your results I am happy to take a look.
cholesky decomposition
I generate random correlated returns using the normsinv(rand(),0,sigma). I wanted to incorporate somehow in this that the distribution is not quite normal, so I calculate a special sigma that is equal to the stdev*(bootstrap alpha)/(normal alpha). The standard deviation is different for each asset so I simulate somehow correlated returns but "differently distributed". I am thinking this is probably the source of the distortion.Thanks a lot for your help. Also you can fin the addin I used here: http://www.esnips.com/displayimage.php? ... id=6025801
cholesky decomposition
OK. The simulated random variates you need to use are standard normal and independent. The volatility and correlation data is embedded in the decomposition you don't need to adjust the simulated variates for this. The other thing to watch for is getting the time scaling correct. Post an example on here if this doesn't help and I'll try to see where is the problem.