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Why a Sovereign CDS Contract Can Have a Negative Price

Article Quant Q&A · Author: Fidelio
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Summary

The document discusses a sovereign credit default swap pricing formula that produces negative values when the market spread is below the contract’s fixed coupon. The question focuses on contracts with a stated coupon, for which this outcome occurs often, and asks whether the formula needs adjustment.

The response explains the sign economically: when the coupon paid on the fixed leg exceeds the prevailing spread, a protection buyer may obtain equivalent insurance more cheaply in the market. A negative value can therefore represent an unfavorable contract position rather than a pricing error. This is a brief conceptual answer, with no derivation, calibration details, or empirical comparison of pricing methods. Its interpretation depends on the contract perspective and sign convention used in the formula.

Key ideas

  • A CDS formula can return a negative value when its fixed coupon exceeds the market spread.
  • A negative value may reflect the economics of an above-market contract rather than a calculation mistake.
  • Protection buyers may find cheaper coverage at the prevailing spread.
  • The answer gives no formula derivation or discussion of valuation conventions.

Tags

Fixed incomeDerivatives pricing
Full text
# CDS Pricing formula leads to negative prices


# CDS Pricing formula leads to negative prices












I'm using this formula to price sovereign CDSs according to CDS Returns, Augustin, Saleh and Xu (2020), Journal of Economic Dynamics and Control.

As you can see, the highlighted part will become negative in the case the spread is lower than the coupon. I'm looking at 25bp coupon contracts, therefore prices often go negative.

How can I get around this?

## Answer by Achrbot (score 1)

https://quant.stackexchange.com/a/75735

If the coupon c on the fixed leg, is higher than the spread, then the buyer could find cheaper insurance in the market. So it's entirely reasonable that the price would be negative.

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.