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?