Why Swap DV01 Falls as Discount Rates Rise

Summary

The document explains the relationship between the par fixed rate of a spot-starting fixed-for-floating interest rate swap and its DV01. It gives the par-rate expression as one minus the final discount factor divided by the swap DV01, and expresses DV01 as the sum of payment accrual fractions weighted by their discount factors. This makes DV01 closely related to the present value of the fixed-leg payment schedule.

As rates rise, discount factors generally decline, reducing the weighted sum and therefore the swap’s DV01. The response corrects the premise that a higher fixed coupon itself causes higher DV01: for a given maturity and schedule, the rate environment that produces a higher par coupon generally has lower DV01. The explanation is a simplified one for a spot-starting swap, with no detailed treatment of curve shifts, conventions, or changes in swap terms.

Key ideas

• Swap DV01 is calculated from discounted fixed-leg accrual payments.
• For a given payment schedule, DV01 is closely tied to the sum of discount factors.
• Higher interest rates generally correspond to lower discount factors and lower DV01.
• A higher par coupon does not by itself imply higher DV01.
• The explanation assumes a spot-starting swap and omits detailed convention effects.

Tags

# Higher coupon on interest rate swap has higher DV01


# Higher coupon on interest rate swap has higher DV01












Why the higher the fixed rate of a swap is, the higher the DV01 will be?

## Answer by user35980 (score 1)

https://quant.stackexchange.com/a/75757

It won't.

The par fixed rate $c$ of a fixed/float $N$-year spot starting IRS is $$ c=\frac{1-df_N}{dv01} $$ with $dv01=\sum_i^N \delta_i \cdot df_i$ where $df_i$ are discount factors and $\delta_i$ are day count fractions. Hence $dv01$ is essentially just the sum of discount factors.

The higher rates are the lower the $dv01$ because discount factors are inversely proportional to rates.

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.