I you are calculating VaR because of some regulatory requirement (which is usually the case), you should follow the approach prescribed by the regulator. Otherwise it really depends on the nature of the bonds, in particular how much credit risk they are exposed to. If it’s a government bond portfolio I’d probably start with the first couple of principal components of the relevant yield curve. If credit risky I would add at least one factor to capture systematic spread risk. And then I would scratch my head over how to treat the contribution to tail risk from actual defaults. I don’t really see any simple application of “price VaR”, although I might just be confused about what that is.
Your comment about the contribution of calculating the VAR of actual defaults reminds of the very contrived counterexample
involving bonds with default probabilities less than the confidence limit of the VAR measure, produced to demonstrate the
non-subadditivity of VAR (e.g. here, footnote on p10
The idea that you can get a risk measure which measures zero for a very broad parameter range only goes to show VAR is
useless for such risks. It seems inevitably to be one of those worrisome situations where calculations of VAR based of market implied parameters
(default prob etc.), rather than the historical ones the textbooks demand, leads to much bigger values than the historical VAR measures.