Inferring Zero-Recovery Cash Flows from Credit Spreads
Summary
The document outlines a way to value cash flows that pay nothing upon default, using bond and credit default swap information. Assume a recovery rate for the relevant senior debt, then infer risk-neutral survival probabilities from market quotes. Multiply those probabilities by risk-free discount factors and the zero-recovery cash flows to obtain their present value, which can be expressed as a risky discount curve.
The method depends on assumptions. Recovery is not directly observable, so alternative recovery scenarios can produce different survival estimates and valuations. The debt ranking of the cash flows also matters: if they are more subordinated than the bonds and CDS reference obligations, they may have lower survival probabilities, requiring an adjustment. The response warns that the resulting value can be particularly sensitive to recovery assumptions and suggests reserving for that uncertainty. It gives a conceptual framework rather than a worked example or calibration procedure.
Key ideas
- Infer risk-neutral survival probabilities from bond and CDS market data after choosing a recovery assumption.
- Value zero-recovery cash flows by weighting them with survival probabilities and risk-free discount factors.
- Recovery assumptions are unobservable and can materially change the estimated value.
- Cash flows with lower debt seniority may require lower survival probabilities than senior reference obligations.
- Consider valuation reserves because zero-recovery cash flows can be sensitive to recovery estimates.
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# Calculate zero recovery discount curve from bond yields and cds prices? # Calculate zero recovery discount curve from bond yields and cds prices? 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? ## Answer by Dimitri Vulis (score 0, accepted) https://quant.stackexchange.com/a/59859 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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