Why CDS Spreads Do Not Reliably Approximate Cash Bond Spreads

# Convert CDS spread into a bond spread


# Convert CDS spread into a bond spread












I am reading, that there are two main methods for converting a CDS spread into a bond spread: a simple method (rule of thumb) and a more complex, rigorous method.

- The rigorous method being to bootstrap hazard rates from CDS spreads (as premium leg = protection leg), derive survival probabilities, and derive the bond price as:

bond value = no default leg (integrate over coupons and face value paid weighted by survival probabilities discounted to PV at RF) +

default leg (integrate accrued interest and recovery both adjusted by hazard rate and survival probability discounted to PV)

- The approximation method, I am confused I read that CDS spread approximates to z spread, I spread, asset swap spread, or even that CDS spread/LGD = I spread, different theories on the internet, i understand that there is at least liquidity adjustment on top of the credit adjustment, but when i compared CDS spread or CDS spread/LGD to bond spreads I couldn't find any relation to any of the spreads Z/I/Asset swap sp.

is there any kind of approximation?

## Answer by Dimitri Vulis (score 3, accepted)

https://quant.stackexchange.com/a/81705

If you have a history of CDS quotes, and related cash bond quotes, then you see that the basis between the CDS quotes in the form of spreads, and any bond spread - Z-spread, OAS, I-spread.. can easily be $\pm 100$ bps or more, and be quite volatile.

If you only have a CDS quote, and are trying to price cash bonds, it's really not a great approximation. You'd be better off trying to look for observable quotes for other cash bonds. If you must, then simplistically assuming that Z-spread, I-spread, or some other is equal to the CDS spread is as good as you can guess. Anything more rigorous may not add value.

If you still do want to be "rigorous", look in the methodology in Bielecki, in Duffie and Singleton (1999), in Bloomberg VCDS, etc, outlined here CDS Spread sensitivity .

Further reading: Related old discussions: The difference between Credit Curve and CDS Curve , Why was CDS-bond basis close to zero before the financial crisis? , Positive base arbitrage CDS vs Asset Swap ; Moorad Choudhry. The Credit Default Swap Basis (2006) ; David Brickman, Lehman Brothers. Trading the Cash-CDS Basis in the Current Environment (2008) ; Guesmi et al. The CDS-Bond Basis (2019).