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What is the relationship between a CDS credit spread (as set by the CDS issuer) and the instantaneous default probability (as estimated by the CDS issuer)? I hear they are similar but not the same.

How are CDS's usually agreed: do they have a fixed coupon or does the coupon vary with credit spread? (If it varies, then how?)

thanks.

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CDS spreads are set by the markets (the people who trade CDSs), not by the issuer of the reference obligation.

CDS spreads reflect the market participants' view of both probability of default and an assumption about the recovery - what the defaulted debt would be worth after the default. The recovery assumption grows more important as the CDS spread widens, and the perceived probability of default increases.

CDS spread is not the same as probability of default because one also needs a recovery assumption in order to convert between CDS spread and probability of default.

Usually CDS are quoted as a spread ("market standard quote"). When the spread is really wide, the "name" (credit, reference entity) is quoted as upfront fee instead. However standard CDS is traded with an upfront fee, and a running spread that is 100 bps (1% of the notional) for most names; when the MSQ is much wider than 100, running spread is sometimes 500 bps, or some other percentage of the notional.

The running spread does not change during the life of the CDS contract, even if the CDS spread in the market changes a lot since inception. However there is a very seldom traded variant of CDS called Constant-maturity CDS, where the protection payment for each period can change if the spread changes in the market.

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