I am a newbie and was after a simple explanation on how VaR is calculated for a portfolio of IRS's.
Here is one very simple approach. However the devil is in the details.
Choose some benchmark tenors (market factors), e.g. 1Y, 2Y... 30Y swap rates.
For each tenor, calculate the P&L if the interest rate at this tenor moves 1 basis point, ceteris paribus. This gives you the vector of sensitivities to market factors.
Calculate the covariance matrix for your market factors, based on a few years of their historical changes.
Perform a matrix muliplication. Multiply the result of the matrix multiplication by the Z value for the desired probability.
(This is very similar to what you would do for a VaR of a portfolio consisting of spot positions in several foreign currencies. I wrote in detail about that here recalculate VaR from one currency to another )
This would be "good enough" for a simple portfolio. However most firms large enough to trade interest rate swaps usually do something more complicated for their VaR.