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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.

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(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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    $\begingroup$ Another, somewhat ad hoc method is to calibrate a 'market price of default risk' to historical credit spreads and historical cumulative default probabilities. You may then derive phyiscal PDs from credit default swaps. Of course, this does not help with the recovery assumption; and in the end it is a very rough, model driven change-of-measure. We have used this method to get a (very) rough guess for PD upswings under P given a surge in CDS rates... $\endgroup$
    – Kermittfrog
    Commented Oct 20, 2020 at 13:51
  • $\begingroup$ in the Argie article above, the risk-neutral PD depends a lot on the recovery assumption (25 or 40). Also CDS reacts to news much faster than physical PD services , who (except for equity price and iv) use mostly quarterly fundamental data with long lag. If you have both history of some physical and risk-neutral PDs, you can estimate Radon-Nikodym derivative and for trading strategy ponder why it has been what it is, and whether CDS trade can take a view on that. $\endgroup$
    – Dimitri Vulis
    Commented Oct 20, 2020 at 14:37

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