# Parametric VaR of a portfolio including a swap

I am calcualting the parametric VaR of a portfolio that includes among other things an IRS swap that begins in the exact same day the valuation is done. Therefore, its NPV is 0 and I do not which weight to assign to it in order to calculate the aggregated VaR of the portfolio. I have calculated every other asset's weight as the total value of the position relative to the total value of the portfolio, however since the NPV of the Swap is exactly 0, I cannot apply this approach. I have tried, and I think is the correct way, using the DV01 of the swap to calculate something as its total exposure, but everything I have tried gives results that are completely unreasonable. Could anybody give me some idea on how to weight this swap in the portfolio?

Treat it like a fixed rate bond with the same maturity date. The principal amount of the fixed rate bond is equivalent to the notional of the swap.

• Thanks for your answer, but once I have calculated its individual VAR, how could I calculate which is its contribution to the portfolio VAR. Should I use the notional of the Swap? To be as concrete as possible, to calculate the contribution to the portfolio volatility of a stock I weigh its volatility using as weight the relative value of the position in the stock over the value of the portfolio. However, in the case of this swap its NPV is 0, so the value of the position is 0. Then, how should I weigh the volatility of the swap rate, to include it in the volatility of the portfolio? Apr 3, 2016 at 19:29
• I am suggesting you use the notional of the swap as the weight
– dm63
Apr 3, 2016 at 19:57
• Ok, but when I use it as you say I obtain a extremely high VAR, which does not fit with the values obtained using a historical or monte carlo approach. It seems that the swap is overweighted. Any further suggestions? Thanks! Apr 4, 2016 at 17:03
• That doesnt make much sense. The Std dev of 100mm 10yr swap should be about \$6mm annually whereas the std dev of the s+p index is around three times as much.
– dm63
Apr 6, 2016 at 4:50

Similar to dm63's answer: if you are the fixed payer in the swap:

• add a long fixed rate bond with coupon equal to the fixed rate and notional equal to the notional of the swap.
• add a short Floater with the coupons linked to the floating rate of the swap. The notional is the same as of the fixed rate bond.

DV01, duration, risk should all be well captures doing this.