Estimating Physical Default Risk Beyond CDS-Implied Probabilities
Summary
The document distinguishes risk-neutral default probabilities inferred from credit default swap spreads from physical probabilities intended to describe real-world default frequency. It cautions that a spread-implied probability depends on a recovery assumption and incorporates market pricing, so it should not be presented as an objective forecast without qualification. The question asks how to estimate the market price of default risk empirically, but the response redirects attention toward estimating physical default likelihood from historical corporate outcomes.
The suggested approach groups companies by fundamental characteristics, such as ratios used in Altman’s Z-score, and measures how often comparable firms defaulted historically. The response notes that later models may also account for industry and macroeconomic conditions, and that recovery after default can be estimated separately from default probability using historical analogues. These methods require suitable company and default data; the exchange does not provide an estimation procedure for the Girsanov risk premium or explain how to reconcile physical estimates with CDS pricing.
Key ideas
- CDS spreads imply risk-neutral default probabilities rather than direct real-world frequencies.
- The implied probability depends on the recovery assumption.
- Historical defaults among firms with similar fundamentals can inform physical default estimates.
- Industry and macroeconomic conditions may refine comparisons between firms.
- Recovery after default is a separate quantity that can also be estimated from historical data.
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Full text
# Objective probability of default from CDS spread # Objective probability of default from CDS spread I have the risk neutral probability of default extrapolated from the market data of the CDS spreads. How can I empirically estimate the market risk price of the objective probability of default (i.e. PD in the real world) with my dataset? I know that from Girsanov theorem the price of risk it's $\int_0^t(\Lambda_s)ds$ in > $$W_t^Q=W_t^P+\int_0^t(\Lambda_s)ds$$ But I don't know how to estimate it empirically. Thanks. ## Answer by Dimitri Vulis (score 4, accepted) https://quant.stackexchange.com/a/58822 (Bloomberg and Reuters News are fond is reporting that some name is trading at some such CDS spread, "which implies N% probability of default". They neglect to mention what recovery assumption they used, and that this is risk-neutral probability, not physical.) For corporate names, Ed Altman published the well-known paper on Z-score. His basic idea is: look at some fundamental ratios, and see what percentage of corporations with similar ratios defaulted historically. It is easy to reproduce if you have the data. There are several newer versions by various people that also consider the macroeconomic regime and the industry. Some examples of commercially available databases of physical probabilities of default based on versions of Z-score are from KMV (Moody's bought them) EDF (Expected Default Frequency) and Citigroup/Yieldbook HPD (Hybrid Probability of Default). This paper by Sobehart and Keenan has a good overview. Not much has changed since it was published, despite advances in data mining. In addition to probability of default, Moody's (and probably others) has a prediction for the recovery - what a defaulted bond will be worth after the default - based on similar historical data analysis.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.