TMethod


Total Posts: 11 
Joined: Oct 2014 


I am trying to calculate MonteCarlo VaR for an options portfolio(5d99%). I am having difficulty grappling with the correlation across strikes. Aggregating the risk of each individual strike seems incorrect. Could anyone offer advise or resources I could seek out to build this risk system? 




How do you simulate your MC? Are your Processes correlated? It is crutial to have your processes correlated in order to see the "difersification benefit", if you simulate uncorrelated processes it is wrong.
Regards, 
One of my most productive days was throwing away 1000 lines of code. 

TMethod


Total Posts: 11 
Joined: Oct 2014 


I guess that is the piece that I am missing, I don't understand how to set up correlated processes. Is there documentation that you might direct me to on this topic, or is it simple enough that you might explain the methodology here?
Thanks 



chiral3

Founding Member

Total Posts: 4985 
Joined: Mar 2004 


uncorrelated r.v. > correlated random variables using a cholesky decomposition? You could probably get the code online. Use Jaeckel or Glasserman are the books. 
Nonius is Satoshi Nakamoto. 物の哀れ 


As @chiral3, Glasserman book is pretty excelent in the subject, there is some theoretical aspects of it in the Shreve Vol 2 Book.
And here is on math exchange that could give you the intuition.
Regards 
One of my most productive days was throwing away 1000 lines of code. 


radikal


Total Posts: 253 
Joined: Dec 2012 


Correlation across strikes? Or across assets?
If just across strikes...
Fit model to your skew either slice by slice or globally.
Define simplest possible correlation matrix of:
[1 rho1 0 rho1 1 rh02 0 rho2 1]
where rho1 = correlation of index and vol rho2 = correlation of index and short rate
generate your N steps by T paths of independent steps x 3 Dot with cholesky decomp of your assumed cov matrix
Now you've got asset paths and ATM vol and IR at each step. You need to perturb your skew model by the shift in ATM vol. Lots of ways you can do this. Start with parallel shift.
If I'm misinterpreting your question, you need to instead just start with an empirical covariance matrix of each asset, use cholesky decomp to get your codepedent asset paths. Do again to appropriately correlated ATM/rho moves. You'll need skew model for each asset/tenure. 
There are no surprising facts, only models that are surprised by facts 


You can use the code/algo from numerical recipes for finding the Cholesky pseudosquareroot matrix: www.aip.de/groups/soe/local/numres/bookfpdf/f29.pdf
Of course, this implies your correl matrix is positivedefinite. If you have some really small (or large for that matter) but negative eigenvalues then the matrix is not PD and the method won't work. In that case you'll need to "massage" the correl matrix via something like R's nearPD() function found in the R Matrix package.
As others have already mentioned, Glasserman should be a good reference for this. 


