# CDS Quote Conversion - Quoted vs Par

Just to be on the same page, let me start with some nomenclature:

• Par Spread = Coupon for which the CDS has NPV=0, assuming a piece-wise constant hazard curve (considered in conjunction with all other par spreads); also called Running Spread
• Quoted Spread = Coupon for which the CDS has NPV=0, assuming a flat hazard curve (considered in isolation to all other quoted spreads); also called Conventional Spread
• Quoted Upfront = Value that matches the NPV of a CDS with a fixed coupon (500p in this example), assuming a flat hazard curve (considered in isolation to all other spreads)

So all pars spreads are used to bootstrap a single hazard curve. Whereas quoted spreads have a flat hazard curve each (used to convert to an upfront amount), and vice versa.

Now, I am working with some data, where I am given historic CDS spread quotes. For example:

Tenor  Recovery  Par Spread  Quoted Spread  Quoted Upfront  Coupon  CCY  Spread Diff
6M       0.4     2524.79        2488.64        0.078750     500  USD       -36.15
1Y       0.4     1891.85        1849.35        0.108750     500  USD       -42.50
2Y       0.4     1587.36        1547.65        0.156875     ...


Given the approaches above, I'd expect the very first spreads (6M in this example) to be 100% equal. The reason being, that the par hazard curve is piece-wise constant from 0-6M and the flat hazard curve is constant everywhere anyway. So the the implied "fair spread" for the first 6M contract should be the same with both curves, but they are off ~36bp.

My data shows many such examples, it's not just this name/date. Am I missing anything?

• Even though the first spread is held constant when building the hazard curve, the ISDA model specifies an interest rate (swap) curve that starts with 1M rates. Remember the payments are quarterly on these contracts so the rates before 6m do matter. I believe that is the cause of your difference- the interest rate is not kept completely "flat" from 0-6m so therefore par != quoted spread. – Bond wiz Jun 18 at 15:48
• @Bondwiz I agree the ISDA rates curve has deposit instruments prior to the 6M point, but the hazard curve's first instrument is the 6M CDS. Assuming I use the same rates curve, I should therefore have the same hazard curve for the period 0-6M, no? – Phil-ZXX Jun 18 at 16:02
• I believe for Quoted Spread, rates are also kept flat which would account for the difference here. The curve (term structure) is used for Par Spread. research-doc.credit-suisse.com/… "Broadly speaking, the RPV01 function for par spreads uses a term structure of interest rates and default probabilities that is calibrated to the market, whereas the RPV01* function for quoted spreads assumes a flat default term structure and different discount factors" – Bond wiz Jun 18 at 19:40