Default Probability Curves from Credit Spreads and Proxies

# Term structure of default probabilities without market data


# Term structure of default probabilities without market data












With the forthcoming new regulations, IFRS9, financial institutions will be required to model life time expected credit losses. Consequently, it is necessary to model the term structure of default probabilities for different products/counter-parties. How can one successfully implement such a model?

In current literature one finds a variety of approaches to model the term structure of default probabilities. Most often, these approaches utilize market data to extract implied default probabilities over a certain horizon, for instance using bonds or credit default swaps. However, these methods are only applicable when such data is available. The term structure of default probabilities for non-listed enterprises (for instance) will be much more cumbersome to determine. Also, many models does not rigorously incorporate default correlations which is necessary for the application of a portfolio. Presumably one will only be able to use historical data of credit migrations.

In accordance with Bluhm and Overbeck (2007) one find the model credit migrations using Markov chains, and from there find each rating grades term structure.

Have anyone come across other interesting literature which allows one to model term structures of default probabilities only using historical credit migration data?

## Answer by user3264325 (score 4)

https://quant.stackexchange.com/a/16340

Firstly it's good to straighten out our goal.

You correctly say, that IFRS9 requires analysis of expected losses.

There are two components of expected losses.

1) Expected probability of a default event 2) Expected recovery rate

So, not only do we need the probability but also the recovery rate.

Luckily, both are approximated by the credit spread, which as you say is readily available from CDS or Bonds.

As for market data, note that CDS are available for many more names than you would usually find in the listed equity markets. A function of the the fixed income market being magnitudes larger.

In the event that you cannot find the data the industry practice is to proxy with a spread from a related CDX or company. Some funds also use several proxy schemes, to flesh out different scenarios.

Correlations are not necessary. You see this when you price a CDX for example. You do need correlations when you price CDX tranches - because the interplay between names then becomes important, but no for vanilla CDX (which are a portfolio of names essentially).

I'll happily look around for some literature, if you want something specific - suspect you can Google around easy enough for extra information though.