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Estimating PD and LGD for Low-Default Credit Portfolios

Article Quant Q&A · Author: QuantK
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Summary

The document discusses credit risk estimation when a portfolio has few or no observed defaults, making ordinary regression approaches difficult to fit. It points readers to texts on credit risk parameters, rating-based probability of default (PD) estimation, low-default portfolios, validation, and stress testing. The central practical methods described are shadow ratings and market-based estimates.

A shadow-rating approach uses available external ratings, calibrates rating grades to estimated PDs, and maps those grades onto an internal scale. A market-based approach draws on issuer CDS, bond, or equity prices, but can produce more volatile estimates and depends on market data; the response notes that coverage may be limited for private firms. For loss given default (LGD), it mentions balance-sheet valuation and further reading, while acknowledging that a complete reference is not offered. The recommendations are general: method selection depends on issuer type, purpose, and data availability, and the cited books predate current regulatory updates.

Key ideas

  • Low default counts can make standard regression methods difficult to estimate.
  • Shadow ratings can map external rating grades to calibrated PD estimates.
  • Market-based PD estimates use issuer securities but may be volatile and data limited.
  • Method choice depends on issuer type, analytical purpose, and available data.
  • The response gives only limited guidance on LGD estimation and notes that its references are dated.

Tags

Fixed incomeStatisticsRisk management
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# References for PD / LGD estimates of low-default portfolios


# References for PD / LGD estimates of low-default portfolios












Any recommendations or reading sources for estimating individual PDs and LGDs for a set of low-default assets (souvereigns, investment grade corporates)?

Since observing no defaults at all, regular probability regressions (linear, logit, probit,...) are not feasible.

## Answer by Quantopik (score 6)

https://quant.stackexchange.com/a/17680

I cannot suggest some reference particularly, since the field is going to develop day by day, but, generally, you could take a look to:

> Engelmann, Bernd, and Robert Rauhmeier, eds. The Basel II risk parameters: estimation, validation, and stress testing. Springer Science & Business Media, 2006.

Particularly, look at the chapter 4 and 5; the chapter 4 shows how to compute the PD using the shadow rating approach, while, the 5 one shows you how to apply the PD estimation models to the LD portfolios.

As you probably noted looking at the book, it is not updated to Basel III regulation; this is due to the fact it is not so recent (2006 edition), but the credit risk models described are explained really well and the same to ones used currently. If you're interested in the Basel regulations updates I suggest you to read:

> Sironi, Andrea, and Andrea Resti. Risk management and shareholders' value in banking: from risk measurement models to capital allocation policies. Vol. 417. John Wiley & Sons, 2007.

Again, it is not updated to the current regulation, but it is better (and more updated) than the other.

Anyway, I can suggest you some approaches used by practitioners other than those books. Those are:

- Shadow Rating Approach: it is typically employed when default events have to be considered rare events and the external ratings (provided by the main rating agencies) data are available for the most of the portfolio; using this approach, the external rating grades have to be calibrated such that, for instance, the PD is attached to them and the external grades can be mapped to the model scale.

- Market-based approach: it is based on CDS securities, bonds or stock quotes relative to the sovereign or corporate issuer and is more documented than the first approach (look at google scholar results), but, less used too, because of 2 main drawbacks: larger volatility in the PD measurement and few information about corporate issuer (you can compute a PD only for the public company).

The particular references about this field depends on what you have to do, for what kind of issuer, on the data suitability and availability.

As regards the LGD estimation model, there does not exist a complete reference to suggest you; the only one model I know is the Balance Sheet Valuation (similar to the Fitch Ratings one), but is proprietary. Anyway, in the first reference you could find some information about LGD models in chapters 8 and 9.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.