Interpreting Default Probabilities Implied by CDS Spreads

Summary

The document explains how to interpret a default probability inferred from a credit default swap spread. A quoted CDS spread is observable, while default probability, hazard rate, and recovery are not directly observable. The simple spread-over-loss-given-default relationship is therefore an approximation rather than a direct measurement of an annual default probability.

A more complete approach assumes a form for the hazard rate, often constant across the contract or piecewise constant when quotes at multiple maturities are available. Analysts then solve for rates consistent with observed CDS quotes and assumptions, with interest rates and potentially recovery terms also entering the valuation. Once calibrated, the hazard curve can produce cumulative default probability through a chosen horizon and conditional probabilities over later intervals. The answer gives no numerical example and emphasizes model dependence: the inferred probabilities are risk-neutral and vary with assumptions. Thus, a five-year quote does not by itself directly state a one-year default probability; the rough formula is associated with default before the contract maturity.

Key ideas

• CDS spreads are observable, but default probabilities and hazard rates must be inferred.
• The spread divided by loss given default is a rough approximation for default before CDS maturity.
• A constant or piecewise constant hazard-rate assumption can be calibrated to CDS quotes.
• A calibrated hazard curve yields cumulative and conditional default probabilities.
• Inferred probabilities are risk-neutral and depend on recovery and other modeling assumptions.

Tags

# What's the interpretation of the probability of default implied from CDS spreads?


# What's the interpretation of the probability of default implied from CDS spreads?












What's the time horizon of the probability of default implied from a CDS spread? Given CDS = PD*(1-R), if I use a 5yr CDS spread in the formula, is the implied PD the probability that that name defaults within the next 5 years or 1 year given it represents the annual premium?

## Answer by Dimitri Vulis (score 3)

https://quant.stackexchange.com/a/59584

CDS quotes are observable. But none of: probabilities of default, hazard rates, loss given default/recovery, etc are observable.

To get some kind of (risk-neutral) probabilities of default, many people make a lot of assumptions, in particular, that the hazard rate is constant (or if you're lucky enough to have CDS quotes at more than one tenor, then piecewise constant between quotes). Then they solve numerically for the hazard rates that explain the obsevable quotes and assumptions. Interest rates play a minor role. Some people use more sophisticated assumptions, such as term structure of recovery, or fancier curve shapes.

Once you have the hazard rates, it's easy to read off both the probability that there will be a default within $n$ years and the marginal probability that, provides there has not been a default until $n$, there will be one between $n$ and $m$.

The formula you cite is a very rough approximation of the probability that there will be a default before the maturity if the CDS.

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.