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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?

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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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