Representing a Par-Value Interest Rate Swap in Parametric VaR
Summary
The document addresses a weighting problem in parametric value-at-risk when a newly starting interest rate swap has zero net present value. Since market-value portfolio weights assign no weight to a par swap, using position value alone misses its rate exposure. The proposed representation is to treat the swap as bond positions with the same maturity and notional.
For a fixed payer, one answer decomposes the swap into a long fixed-rate bond, with a coupon matching the swap’s fixed rate, and a short floater linked to the floating rate. Both legs use the swap notional. The responses state that this bond-and-floater representation captures DV01, duration, and risk more appropriately than weighting the swap by its zero NPV. The document gives no worked VaR calculation, and the representation assumes the stated swap direction and matching cash-flow terms.
Key ideas
- A par swap can have zero NPV while still carrying interest-rate risk.
- Representing the swap as bond exposures allows its risk to enter a portfolio VaR calculation.
- For a fixed payer, the suggested decomposition is long a fixed-rate bond and short a floating-rate note.
- Use the swap notional for both bond legs, with their cash flows linked to the swap terms.
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Full text
# Parametric VaR of a portfolio including a swap # 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? ## Answer by dm63 (score 0, accepted) https://quant.stackexchange.com/a/25217 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. ## Answer by Richi Wa (score 0) https://quant.stackexchange.com/a/27954 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.
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