# Choosing a proxy for asset credit event correlations

I'm interested in modeling the joint likelihood for rating changes and default events across a portfolio of bonds.

To estimate the correlation between these assets, I can use a third-party factor model (BarraOne) to simulate:

A) the returns for each bond's underlying issuer equity

B) the returns of the bonds themselves

A default event or ratings downgrade would occur when the simulated P&L in a trial falls below a certain threshold.

The returns for the bonds themselves (option B) are a function of simulated changes in term structure, swap spread and credit spread factors. Equity returns are a factor model incorporating simulated changes in various factors such as value, equity market, size etc.

If I am only interested in the joint likelihood of ratings up/downgrades and default, which option would give me a more accurate proxy for the correlation of credit events?

• You're facing two different problems: (1) default probability; (2) default correlation. As per (2) I would suggest to use (B) with a proper threshold estimator like tail dependence coefficient. This finds the correlation in tail risk scenarios, which is what you're looking for. Another possible approach would make use of copula correlation: scale your bonds' returns to have pseudo observations and fit a copula with tail dependence to data (t-Copula is fine). The output magic number is another possible measure of tail dependency, which translates into default correlation. Commented May 8, 2019 at 9:21

In portfolio models there are not included the correlation of credit events but the correlation of the returns of each issuer. Is that the same that you are searching for? If yes, then you can calculate the the correlation as a parameter of the model and you do not need a proxy. If you have the parameters you can get the whole distribution with a monte carlo simulation.

A default would typically entail the market cap of a company hitting 0 and its actual equity going negative. So for defaults I‘d go for option A. Downgrades are bit less straightforward, but for consistency I‘d probably go for that as well, because you map the equity prices more easily to distance-to-default metrics which you can use for setting the thresholds.