CDS Curve Inversions and Monotonic Implied Default Probabilities

Summary

The document asks whether a sharply inverted credit default swap curve can create arbitrage. Its example compares protection at two maturities: buying longer-dated protection and selling shorter-dated protection may appear to leave a positive premium balance while preserving protection against later default. The key test offered in the response is to infer cumulative default probabilities from CDS spreads across maturities. Probabilities of default by time T should not decline as T increases; a violation would indicate an arbitrage opportunity under the model used to extract them.

The argument is a diagnostic principle, not a complete spread threshold or a trade construction recipe. It depends on translating spreads into default probabilities and on assumptions about recovery and contract valuation. In particular, CDS counterparty default risk can undermine a risk-free arbitrage interpretation, so an apparent attractive payoff may still involve material credit exposure.

Key ideas

• Implied cumulative default probabilities should be nondecreasing with maturity.
• A decreasing inferred probability across maturities signals an inconsistency that may indicate arbitrage under the pricing assumptions.
• A steeply inverted spread curve alone does not specify a universal threshold for mispricing.
• Counterparty default risk in the CDS contract can prevent an apparent trade from being a true arbitrage.

Tags

# When do CDS curves yield arbitrage opportunities?


# When do CDS curves yield arbitrage opportunities?












In CDS markets we can sometimes observe inverted CDS curves or unusually steep curves. I am just wondering at what level certain curves become non-realistic.

E.g. if we have 500bp for the 1-Year tenor and 100bp for the 2-Year tenor we could buy a 2-Year CDS and sell a 1-Year CDS both on the same notional. If there is a default between Year 0 and Year 1 the two CDS cancel out. If the default is between Year 1 and Year 2, then we receive (1-Recovery)*Notional. Regardless of when/if default happens, the P&L of our fees (only pay 100bp over two years, receive 500bp over one year) will always be positive.

This seems like an arbitrage scenario for when curves are too strongly inverted. But are there any actual mathematical conditions for when given curves are not realistic anymore?

## Answer by Mark Joshi (score 7, accepted)

https://quant.stackexchange.com/a/16587

well you can use CDS spreads to strip out implied default probabilities for default before time $T.$ These had better be increasing as a function of $T$ or you have an arbitrage opportunity.

However, there is an assumption here that there is no default risk on the CDS swap itself once you take that into account there may be a good chance of profit but no real arbitrage.

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