Clarifying the below:

Given the prices of bonds that are not trading in distress as yet (so yields are meaningful), and data on the CDS spreads, I’ve been looking for some approaches for estimating a zero-recovery discount rate for the bond’s cash flows. The goal is to be able to estimate a sort of zero-recovery implied risky discount curve.

In other words, both the bond and CDS are pricing in some nonzero recovery rate, and the prices contain some probability of default that is not substantial enough to pull the bond price towards that recovery value. The question is whether I can find some “zero-recovery” cds curve that is consistent with the bond pricing in the market.

The idea is to use this “risky” discount curve to discount a related stream of cash flows. In other words, I’m looking to derive a credit curve that assumes 0 recovery rate. Any papers to recommend?

  • $\begingroup$ Sorry, can you clarify your question please? You have some prices of bonds that are trading close to the recovery assumpion (have defaulted, or are about to default). The remaining cash flows aren't expected to happen, so yield doesn;t make any sense. CDS quotes (upronts) are really the view on the recovery, rather than the probability of default. Risk-free interest rates have no material effect and can't be backed out. Can you please clarify what you mean by zero-recovery discount curve? $\endgroup$ – Dimitri Vulis Dec 8 '20 at 23:15
  • $\begingroup$ Given your updated question: What others have done is to use CDSs on different deb types (senior, subordinated... where available...), e.g. this paper greta.it/credit/credit2010/PAPERS/Posters/…. Others use information from the stock market, e.g. fdic.gov/analysis/cfr/2009/wp2009/2009-05.pdf. I have not yet applied these methods, though... $\endgroup$ – Kermittfrog Dec 9 '20 at 13:43

Now that your question makes much more sense:

Let's suppose the bonds are senior unsecured, and are the reference obligations for the CDS. You can make some assumptions about the recovery (say, 40%) and solve for risk-neutral survival probabilities (the calculation for getting probabilities from bonds and CDS quotes is no different from getting probabilities from CDS quotes alone). Your recovery assumption is unobservable (level 3 in accounting-spreak of Topic 820 / FASB 157). You can calculate many survival probabilities: recovery assumption 1% down, 1% up, very low (like Lehman), very high (like the GSEs).

The zero-recovery cash flows that you're trying to price may not be in the same tier of debt as the bonds and CDS. E.g. they can be subordinated. Generally, subordinated debt is rated 1 notch below senior debt. The issuer may be able to default on subordinated debt without triggering a cross-default on senior tiers. In this case, the survival probabilities from the previous paragraph are only an upper bound, and you should further lower the survival probabilties by the equivalent of 1 rating notch or more.

To compute the mark to market, you just multiply the zero-recovery cash flows by the survival probabilities and by the risk-free discount factors. This product is the discount curve that you're looking for.

Observe that this zero-recovery mark to market will be much more sensitive to your recovery assumption than, for example, the mark to market of the CDS. You will probably need to set up reserves for the possibility that the recovery is very low or very high.

A good paper (probably an overkill) is Duffie-Singleton (1999).


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