# How to define and measure liquidity or funding premium in credit markets?

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?

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The paper by Tavi Ronen is interesting in its analysis of the liquidity and price discovery.

As I pointed out above a simple measure is the one by Boa et al in their

• "Illiquidity of corporate bonds" (see link in my comment to Brian's answer)

For a very different take on what being illiquid means, the paper by Rossi is very interesting

Even if it is not clear from the title, the gist of it is that from the low liquidity something can inferred about the value of the current misplacing in corporate bonds (simply put, the trading costs are larger than the mispricings).

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I just reviewed the paper Corporate Bond Liquidity Before and After the Onset of the Subprime Crisis by Dick-Nielsen, Feldhütter and Lando. They define a liquidity measure $\lambda$ as a conglomerate of

• price impact (Amihud) and its variability
• spread covariance (Roll) and its variability
• turnover
• imputed roundtrip cost (Feldhütter)
Having defined $\lambda$, they run some statistics to work out liquidity premia, including setting confidence bands using a "wild cluster bootstrap" which I am going to have study just because of the awesome name.