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Using CDS Spreads to Approximate Counterparty Default Risk for CVA

Article Quant Q&A · Author: Carlos F.
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Summary

The document asks how to use a counterparty’s credit default swap spread when estimating credit valuation adjustment. The response illustrates a simplified one-period relationship: if the protection premium is paid upfront, the spread is equated to expected loss, calculated as default probability times loss given default. Under those assumptions, the implied default probability is the spread divided by one minus the recovery rate.

This is a conceptual starting point rather than a complete CVA procedure. It does not explain how to select CDS notional or maturity for a particular derivative, and it supplies no exposure profile or CVA calculation. The conversion also relies on simplifying assumptions: market CDS spreads are not generally direct default probabilities, and practical estimates require a term structure and treatment of premium timing, discounting, and other credit risks.

Key ideas

  • In a simplified one-period setup, the CDS premium can be equated to expected protection loss.
  • The implied default probability depends on both the spread and the assumed recovery rate.
  • A counterparty CDS spread alone does not determine CVA or the required CDS contract terms.
  • Practical spread-to-default estimates need assumptions beyond the simplified relationship.

Tags

Derivatives pricingRisk managementFixed income
Full text
# How to estimate CVA by valuing a CDS of the counterparty?


# How to estimate CVA by valuing a CDS of the counterparty?












I'm trying to estimate CVA of one of my derivatives by valuing a credit default swap (CDS) of my counterparty. However, I don't know how to set up the CDS deal (notional amount, maturity, etc.).

Thanks!

## Answer by MattR (score 1)

https://quant.stackexchange.com/a/15639

Well, you should use the spread as the default probability.

For example, A CDS spread of 593 bp for five-year Brazilian debt means that default insurance for a notion al amount of USD 1 m costs USD 59,300 p.a.

Consider a 1-year CDS contract and assume that the total premium is paid up front. Let S: CDS spread (premium), p: default probability, R: recovery rate. The protection buyer expects to pay: S. His expected pay-off is (1-R)p. When two parties enter a CDS trade, S is set so that the value of the swap transaction is zero, i.e. S=(1-R)p ↔ S/(1-R)=p.

If R=25%, a spread of 500 bptranslates into p =6.6%. If R=0, we have S=p=5%.

I found this wikipedia article very enlightening. Price and Valuation

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.