Using a Bond Yield Curve to Discount Risky Cash Flows

Summary

The note addresses whether a bond yield curve can supply discount factors that incorporate credit risk, instead of deriving default probabilities from a credit default swap curve. It says the curve can be treated as a funding curve and used to obtain risky discount factors for valuing cash flows. This approach does not require separately extracting default probabilities when the task is to discount using that bond curve.

A practical consistency check is to reprice the bonds used to build the curve and confirm that present values reproduce their observed dirty prices. Interpolation choices require care, and the instruments used to construct or apply a curve should be economically comparable. In particular, securities with different recovery or collateral characteristics should not be mixed merely because their default probabilities appear similar. The answer is concise and offers no detailed bootstrapping procedure, interpolation method, or empirical comparison with CDS-based discounting.

Key ideas

• A bond yield curve can be used to derive risky discount factors for cash flows.
• Repricing the input bonds should recover their observed dirty prices.
• Interpolation choices affect the resulting discount factors and require care.
• Curve instruments should have compatible recovery and collateral characteristics.

Tags

# Answer by Dimitri Vulis (score 1)


# What is the way to calculate "Risky PV (Present Value)" (discounting including the probability of default) from bond yield curve?












Instead of using CDS spread to do risky discounting, I would like to use the bond yield curve. Can I directly use the discounting factors from the bond yield curve or do I need to figure out the probabilities of default like in a CDS curve and use them for the risky discounting?

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/65859

Yes, you can consider a bond yield curve to be like any funding curve, and in particular get risky discount factors from it, and use them, for example, to discount cash flows.

Test that if you pv the bonds used to build the yield curve, you get back the input dirty price. Be careful how you interpolate. Don't mix different kinds of instruments (e.g. zero-recovery and highly collateralized, even if they have the same probability of default).

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