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Interpreting Pay-Fixed and Receive-Fixed Swap DV01

Article Quant Q&A · Author: user75638
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Summary

The explanation clarifies that interest rate swap pay and receive conventions refer to the fixed leg. A pay-fixed position has positive DV01 under the convention described: when market rates rise, the fixed payments become relatively less costly than current rates, so the position gains value. A receive-fixed position has the opposite exposure and benefits when rates fall.

It offers a borrowing-and-lending analogy to make the sign intuitive. Paying fixed resembles borrowing at a fixed rate, while receiving fixed resembles lending at a fixed rate. The analogy also connects swaps to bonds: selling a fixed-coupon bond is economically similar to borrowing, while buying one resembles lending. These sign descriptions depend on the stated DV01 convention and position perspective, so practitioners should confirm desk conventions when comparing reports or systems.

Key ideas

  • Swap pay and receive terminology refers to the fixed rate leg.
  • A pay-fixed swap position gains value when rates rise and has positive DV01 under the convention described.
  • A receive-fixed position gains when rates fall and has negative DV01 under that convention.
  • Thinking in terms of borrowing and lending helps connect swap exposures with fixed-coupon bond positions.

Tags

Fixed incomeDerivatives pricingRisk management
Full text
# Paid and Received IR PV01 (+ve or -ve)


# Paid and Received IR PV01 (+ve or -ve)












Can someone explain why paid IR DV01 is +ve, and why received IR DV01 is -ve?

Is "paid" referring to the fixed rate, (so receive floating) hence if IR goes up, we gain from the floating rate being higher.

And is "received" referring to the fixed rate, (so pay floating) hence if IR goes up, we lose value from paying higher rate.

## Answer by user35980 (score 2)

https://quant.stackexchange.com/a/83595

Correct, pay/receive is always wrt the fixed rate (when you're talking about IR swaps). If you are paying fixed and rates go up, you gain from the fact that you are paying fixed at a rate lower than where rates have now moved to. This is why your dv01 is positive for a you-pay-fixed position.

I think it's much better to think of things in terms of "borrowed" or "lent": $$\text{you are borrowed}\equiv\text{you pay fixed}\equiv\text{your dv01 is positive}\equiv\text{you gain when rates rise}$$ $$\text{you are lent}\equiv\text{you rec fixed}\equiv\text{your dv01 is negative}\equiv\text{you gain when rates fall}.$$

The upside of this terminology is that it covers bonds as well as swaps (cause conventionally the former is quoted in price and the latter in yield - and bond traders use terms like long/short which convolutes things further). It comes from the following: let's say you sell a bond with a fixed coupon, this means you're borrowing money and you're paying a fixed rate. Rates rise = value of bond you sold falls = gain; or equivalently: rates rise = you're paying fixed = gain. And vice versa when buy a bond (you lend money).

Edit: modified response based on Quintuple's feedback

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.