Integrating Credit and Market VaR

Question

For a portfolio of fixed income, is there a framework or model for providing a VaR-type estimate that takes into account not only market risk factors, but also the loss associated with the probability of an issue defaulting or having its rating downgraded?

While I've seen some applications (eg CreditMetrics) that are successful in capturing default/issuer risk, these models tend to isolate the credit loss and do not capture market risk factors. If I wanted to have a single VaR estimate to capture the potential loss threshold from both credit and market risk factors for a very large fixed income portfolio, what papers or model would be a good starting point to look at?

Answer 1

There are many ways to do this. Some are more computationally intense than others. Some are more realistic than others.

If you want to stay in CreditMetrics universe I would jointly simulate systemic variables impacting credit AND interest rate variables. This can be done in a Gaussian setting quite easily (eg Hull White for interest rate and drift+diffusion in log systemic variables). This method would allow correlations between interest rates and variables impacting default.

The algorithm would be roughly: simulate n systemic variables and 1 Hull White interest rate variable. Conditional on these variables, find the total number of defaults in your time horizon of interest. Of the remaining, recompute their market value given the realization of the interest rate variable. Add up the final values. This will be single realization of potential future states. Repeat M times, take the 99 (or 99.9, or 99.97) percentile and thats the combined VaR.

However, this is very computationally expensive.