Even companies with just a single non-callable corporate bond outstanding will often have CDS quote spreads that differ from the bond quote spread. During the 2008 crisis, there were dozens of cases where true arbitrages were available.
You could argue these arbitrages were due to forced selling of bond inventory (a funding premium), aversion to bond trading (looks like a liquidity premium) or depression of CDS spreads due to counterparty risk.
If I want to risk model what may happen in another crisis, I would like a model of where such liquidity/funding spreads might go again. To do that, I can look at history, but first I need to separate a price $V$ out into a "true" price $V_T$ plus liquidity and/or funding components $V_L$ and $V_F$.
Has anybody found reasonable definitions and functional forms of these? If you have, what was the influence of recovery rates on their stability?