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?