Marginal VaR of Swap position

[Yan He]

Is it possible VaR of a single name swap can increase total VaR in a portfolio. I don't quite sure where the risk comes from as to a SWAP...:sos:

 

[PatM]

Hi,

It is certainly possible. Single name equity swap? The marginal VaR is usually calculated with the covariance matrix E -- the portfolio variance is w'Ew, and then you scale up the square root of that by some coefficient to get portfolio VaR (95%, 99%, 1 day, 10 day, etc).
The derivative of this portfolio variance is a vector 2Ew, which should be the vector of marginal variances from each position. From there you work back to marginal VaRs.

For single name credit default swaps or asset swaps, the covariance matrix method is not used as much. Monte Carlo is another way to get VaR, but it is more difficult to get marginal contributions -- you can run 2 portfolios on the same random paths, one portfolio with, and one without, the swap, and the VaR difference might be considered "incremental VaR" of the swap. But that is pretty costly for such a number.

 

[alain]

I don't quite sure where the risk comes from as to a SWAP...:sos:

if your counterparty defaults, you are stuck holding a leg of a swap and not getting anything.

 

[Yan He]

Hi,

It is certainly possible. Single name equity swap? The marginal VaR is usually calculated with the covariance matrix E -- the portfolio variance is w'Ew, and then you scale up the square root of that by some coefficient to get portfolio VaR (95%, 99%, 1 day, 10 day, etc).
The derivative of this portfolio variance is a vector 2Ew, which should be the vector of marginal variances from each position. From there you work back to marginal VaRs.

For single name credit default swaps or asset swaps, the covariance matrix method is not used as much. Monte Carlo is another way to get VaR, but it is more difficult to get marginal contributions -- you can run 2 portfolios on the same random paths, one portfolio with, and one without, the swap, and the VaR difference might be considered "incremental VaR" of the swap. But that is pretty costly for such a number.

Thanks Pat.
Actually, this is TRS that deals with JP Morgan. I am using historical VaR instead of Delta Normal or MC now. So you are saying the actually risk is the same as holding underlying ? :wall

 

[PatM]

It depends on the payment formula. For a 1 day 99% VaR, take the formula for the floating payout and figure how much you would have made/lost on the swap every day over the past X years. Then take the 99% worst day.