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Measuring Interest Rate, Spread, and Default Risk in CDS

Article Quant Q&A · Author: user394334
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Summary

The document explains how to think about interest-rate and credit-spread risk in a credit default swap. Although CDS contracts are commonly quoted by spread, traded contracts may include a standardized running coupon and an upfront payment. To estimate interest-rate sensitivity, the answer perturbs rates, recalculates survival probabilities from the quoted spread, and reprices the contract. It cautions that changing rates while holding survival probabilities fixed may give a less representative profit-and-loss estimate.

For spread sensitivity, the quoted CDS spread is shocked, survival probabilities are recalculated, and the contract is repriced. The answer says this sensitivity is typically much larger than interest-rate sensitivity, while rate gamma is often small; spread gamma may warrant calculation. It also recommends evaluating jump-to-default exposure and risk by tenor bucket rather than assuming all maturities move together. These are qualitative risk-practice guidelines: the document supplies no pricing equations, calibration details, or numerical example, and exact sensitivities depend on the risk scenario and market conventions.

Key ideas

  • CDS contracts may combine a standard running coupon with an upfront payment even when quoted by spread.
  • Rate sensitivity is estimated by shocking rates, recalculating survival probabilities, and repricing.
  • Spread sensitivity requires recalculating survival probabilities after a quoted-spread shock.
  • Jump-to-default exposure and nonlinear spread risk are additional risk measures to consider.
  • Risk should be assessed across maturity buckets rather than assuming parallel spread moves.

Tags

Fixed incomeDerivatives pricingRisk management
Full text
# Does credit default swaps have interest rate duration and credit duration?


# Does credit default swaps have interest rate duration and credit duration?












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).

## Answer by Dimitri Vulis (score 2)

https://quant.stackexchange.com/a/66247

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.

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.