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Why CDS Spread Sensitivity Can Be Negative Before Maturity

Article Quant Q&A · Author: MFib
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Summary

The note explains why a long five-year credit default swap can lose value when spreads at maturities shorter than five years rise while the five-year spread stays unchanged. A change in those shorter spreads affects the premium leg, but it can also change the protection leg through the implied survival probability curve. Since the CDS value is the protection leg minus the premium leg, the combined effect can be negative if the protection leg falls enough.

The explanation offers intuition rather than a calculation or empirical example. The sign depends on the shape and response of the survival curve, so the result is not a universal rule for all spread curves or CDS positions. Assessing a particular sensitivity requires the model’s curve construction and valuation assumptions.

Key ideas

  • CDS value is the protection leg value minus the premium leg value.
  • Rising spreads at maturities shorter than the contract maturity can affect both legs.
  • A sufficiently large decline in protection leg value can outweigh a decline in premium leg value.
  • The sign of the sensitivity depends on the implied survival probability curve.

Tags

Fixed incomeDerivatives pricingRisk management
Full text
# How to interpret this CDS spread sensitivity pattern?


# How to interpret this CDS spread sensitivity pattern?












From page 27, Table 6:

Why are sensitivities of CDS slightly negative before the maturity of the CDS?

I do not get the intuition: if I am long a 5-year CDS, the spreads <5y increase, and the 5y spread remains constant, according to the table above I am loosing money because of the negative signs of the sensitivity. How is this possible?

## Answer by Gordon (score 2)

https://quant.stackexchange.com/a/19582

When you long a 5y CDS and the spreads <5y increase and the 5y spread remains constant, the premium leg value is decreased. It appears that the CDS value should increase, and you should have a positive sensitivity. However, depending on the shape of the survival probability curve, the protection leg value may also decreased, and then the CDS value, which is defined as the protection leg value minus the premium leg value, may decrease as well. Then you may have a negative sensitivity.

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.