suppose I have a large portfolio consisting of stock, bond, and derivative, and I use delta-gamma method to calculate its VaR, I also want to know the marginal VaR of individual asset, my method is:Define the portfolio's VaR as V(old), then change the investment amount of the individual asset a small ratio and re-compute VaR of the new portfolio, V(new), marginal VaR=(V(old)-V(new))/amount change. the question is if the portfolio is large enough, the above method is time-consuming, is there any method to speed up the calculation? same problem with component VaR. thanks a lot.

any help? thank you.

I am not a quant, but I believe you are looking for d(VaR)/d(i-th weight)?From Jorion, the delta gamma formula is, written with vectors, (deltas)*(weights*changes in underlyings) + 1/2*(weights*changes in underlyings)*(gammas)*(weights*changes in underlyings), where the latter term is a quadratic form, and "gamma" is a matrix of gammas and cross gammas on the off-diagonal positions? cf. Jorion p.214. Differentiating this with respect to the i-th weight leaves only (i-th weight)*(i-th delta)*(change in i-th underlying) + (weights*change in underlyings)*row i [gammas]where row i [gammas] is the i-th row of the gamma matrix. I don't know if this will speed up anything, but the curse of dimensionality in matrices is at work here too, as Jorion notes:"the delta gamma method is not practical with many sources of risk, because of the amount of data required" [in the gamma matrix]. One way to speed it up is to consider all off-diagonal terms 0, but "Monte Carlo provides a more direct route to VaR for large portfolios" (Jorion).I hope this helps?

Sorry, I wrote:(i-th weight)*(i-th delta)*(change in i-th underlying) + (weights*change in underlyings)*row i [gammas]but the first term shouldn't have a weight on it, I believe:(i-th delta)*(change in i-th underlying) + (weights*change in underlyings)*row i [gammas]

Also, Glyn Holton has criticized this approach severely:"During the mid-1990s, there was attention paid to the development of a "delta-gamma" (or "quadratic") methodology for calculating value-at-risk. This work culminated in Rouvinez's (1997) published model, which appeared in RISK Magazine. Jorion (2000) appears either to be unaware of that result or to not understand it. His "delta-gamma" methodology is a simplistic VaR measure that sometimes works if a portfolio's value depends on a single key factor. It does not generalize to higher dimensions, so it is largely useless. His "delta-gamma-delta" methodology is a crude approximation that substitutes a symmetric normal distribution for an asymmetric chi-squared distribution. The resulting error is significant. For more on Rouvinez's successful quadratic VaR measure, see the glossary article http://www.riskglossary.com/articles/qu ... mation.htm. It includes a reference to Rouvinez's original article as well as subsequent published research. For an explanation and examples of how to implement Rouvinez's methodology, see my book http://www.value-at-risk.net"

thanks, in your case, the first difference can be calculated analytically. but I use a cornish-fisher expansion to increase the accuracy of delta-gamma methodology, where the expansion kills me when I wanna differentiate it with i-th weight.QuoteOriginally posted by: PatrickMI am not a quant, but I believe you are looking for d(VaR)/d(i-th weight)?From Jorion, the delta gamma formula is, written with vectors, (deltas)*(weights*changes in underlyings) + 1/2*(weights*changes in underlyings)*(gammas)*(weights*changes in underlyings), where the latter term is a quadratic form, and "gamma" is a matrix of gammas and cross gammas on the off-diagonal positions? cf. Jorion p.214. Differentiating this with respect to the i-th weight leaves only (i-th weight)*(i-th delta)*(change in i-th underlying) + (weights*change in underlyings)*row i [gammas]where row i [gammas] is the i-th row of the gamma matrix. I don't know if this will speed up anything, but the curse of dimensionality in matrices is at work here too, as Jorion notes:"the delta gamma method is not practical with many sources of risk, because of the amount of data required" [in the gamma matrix]. One way to speed it up is to consider all off-diagonal terms 0, but "Monte Carlo provides a more direct route to VaR for large portfolios" (Jorion).I hope this helps?

hi, you can try this. compute marginal variance of the asset which is equal to correlation between the asset return and the portfolio return with that asset. this will give marginal variance, and use this to compute to marginal var.

Thanks you all, I find a way out.