Combining Credit and Interest Rate Risk in Portfolio VaR
Summary
The document outlines a simulation framework for estimating fixed income portfolio value at risk while accounting for both credit events and interest rate movements. It proposes jointly simulating systemic variables that influence credit outcomes and an interest rate factor, with correlations allowed between them. Conditional on each simulated state, the method determines defaults over the chosen horizon and reprices surviving positions using the simulated rate. Repeating this process produces portfolio outcomes from which a selected loss percentile can be taken as the combined VaR.
The approach adapts a CreditMetrics-style framework and suggests Hull–White dynamics for rates alongside drift and diffusion for credit related systemic variables. It describes the method conceptually but provides no empirical results or implementation detail. The document cautions that the simulation can be computationally expensive, and its Gaussian assumptions may limit realism; model choice and calibration remain important.
Key ideas
- Jointly simulate systemic credit drivers and interest rates to capture their dependence.
- Determine defaults conditional on each simulated state, then revalue the surviving bonds.
- Repeat the portfolio valuation across many scenarios and use a chosen loss percentile as VaR.
- The method offers a single measure of credit and market risk but can require substantial computation.
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Full text
# Integrating Credit and Market VaR # Integrating Credit and Market VaR 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 by user9403 (score 1, accepted) https://quant.stackexchange.com/a/33813 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.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.