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Will a CDS have interest rate duration and credit duration?

It does seem likely that the value of the CDS would depend on the underlying interest rate, or the spread. But when I try to Google this I can't find anything.

Is interest rate duration or credit duration quated for CDS's in the real world? And if so, is there an easy way to explain how they are calculated?(doesn't need to be detailed, but more of a way to get an overview).

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Most credit default swaps are quoted as CDS spread (the fraction of the notional that the protection buyer would pay every year for a given CDS maturity). However the contract that's actually traded is more likely to have standardized running spread and an upfront fee. Moreover, some names on the verge of default are quoted as upfront.

To calculate the sensitivity of a CDS's mtm to a change in interest rates, you perturb the interest rates per your risk scenario, recalculate the survival probabilities from the quoted spread, and reprice the swap. Note that if you perturb the IR and keep the survival probabilities constant, then you'll get a number that won't be as good at predicting the PL from IR change. The IR sensitivity is relatively small. Depending on your environment, you may need to calculate it and hedge it (with ED futures or IR swaps), or may be allowed to keep it. The IR gamma of a CDS is so small that it can usually be ignored.

To calculate the sensitivity of a CDS's mtm to a change in the quoted CDS spread, you perturb the quoted CDS spread, recalculate the survival probabilities, and reprice the swap. You should get a number that is roughly a couple of orders of magnitude larger than the IR sensitivity. The gamma is large enough that you should calculate it under most circumstances.

In addition to the IR and CDS spread sensitivities, you should calculate the P&L from jump to default.

You should look at your risk by tenor bucket, i.e. not assume that CDS quotes for different maturities all move in parallel.

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  • $\begingroup$ Thank you very much, I just have one question if that is ok. I see that you do this for what you define as the CDS spread, but can you also do it for the ordinary spread? $\endgroup$
    – user394334
    Commented Jul 31, 2021 at 13:11
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    $\begingroup$ Just to add to what Dimitri said. Since around 2010, CDS contracts do not pay the CDS spread. They pay a fixed coupon (running spread) based on their credit quality which is typically 50, 100 or 500 bps. So they have an initial value that is non-zero. The CDS spread is the market quoted spread for a contract that would have zero initial value and that is what you bump. The coupon on the CDS is fixed. $\endgroup$
    – Dom
    Commented Jul 31, 2021 at 18:51
  • $\begingroup$ @Dom Thank you, so do you settle the differnce between the coupon and the CDS spread at the beginning? $\endgroup$
    – user394334
    Commented Aug 1, 2021 at 1:53
  • $\begingroup$ Thanks @Dom! Also I should have mentioned that if a name is being quoted on upfront, then you may have practical difficulty backing out and bumping a CDS spread in order to calculate the mtm's spread sensitivity, so the risk measure you'd likely use instead for such names is just the mtm's sensitivity to the upfront%. $\endgroup$
    – Dimitri Vulis
    Commented Aug 1, 2021 at 14:15
  • $\begingroup$ Yes. Or if you really need to you can try to imply out a CDS curve from the upfront and bump that. $\endgroup$
    – Dom
    Commented Aug 3, 2021 at 7:30

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