VaR for Options Portfolio

TMethod · Post by **TMethod** » Tue Mar 17, 2015 9:16 pm

I am trying to calculate Monte-Carlo 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?

il_vitorio · Post by **il_vitorio** » Tue Mar 17, 2015 11:56 pm

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,

TMethod · Post by **TMethod** » Mon Mar 23, 2015 6:22 pm

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 · Post by **chiral3** » Mon Mar 23, 2015 8:54 pm

uncorrelated r.v. -> correlated random variables using a cholesky decomposition? You could probably get the code online. Use Jaeckel or Glasserman are the books.

il_vitorio · Post by **il_vitorio** » Mon Mar 23, 2015 11:16 pm

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

radikal · Post by **radikal** » Tue Mar 24, 2015 2:57 am

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 co-depedent asset paths. Do again to appropriately correlated ATM/rho moves. You'll need skew model for each asset/tenure.

HankScorpio · Post by **HankScorpio** » Tue Mar 31, 2015 1:07 pm

You can use the code/algo from numerical recipes for finding the Cholesky pseudo-square-root matrix: www.aip.de/groups/soe/local/numres/bookfpdf/f2-9.pdf

Of course, this implies your correl matrix is positive-definite. 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.