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


1 Answer 1


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.

  • $\begingroup$ Thank you for answering! Just wanted to clarify if the dv01 you refer to here means pv01 (1bp change in fixed rate). I think what I mean by dv01 is how NPV will change if the curve is bumped by 1bp. Thank you! $\endgroup$
    – Mini PP
    Jun 4, 2023 at 3:45
  • $\begingroup$ It doesn't matter what measure of duration u use or what ur annuity is (swap, bond, simple cashflow etc): higher rates mean reduced duration. Forget swaps, just consider the PV of $1 to be recd in 1y with rates at 10% (this is = 1/(1+10%)). Shift rates to 11% and take the difference to obtain the duration (called it delta_1). Then compare the same case with rates at 20% (and shifted to 21% to obtain the duration, call it delta_2). You will find delta_1 > delta_2 always. Again, this is because discount factors are inversely proportional to rates. $\endgroup$
    – user35980
    Jun 4, 2023 at 11:22
  • 2
    $\begingroup$ The question might be asking how the dv01 of a swap changes as a function of its coupon, whilst leaving market rates constant. In that case indeed the dv01 grows with coupon, since there is just more cash flow. $\endgroup$
    – dm63
    Jul 3, 2023 at 9:28
  • $\begingroup$ Agreed with @dm63, an IRS with an off market coupon can be considered as an IRS with an ATM coupon plus a fixed annuity. The fixed annuity will have additional delta risk. $\endgroup$
    – Attack68
    Oct 31, 2023 at 13:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.