Why Quoted and Par CDS Spreads Can Differ at the First Published Tenor
Summary
The discussion distinguishes par CDS spreads, which are bootstrapped together to infer a piecewise hazard curve, from quoted spreads, which are interpreted using a flat hazard curve for an individual tenor. It also defines quoted upfront as the value matching a CDS with a fixed coupon under that flat-curve convention. The question is why the shortest visible tenor in historical data does not show matching par and quoted spreads, despite an expectation that the first interval should align.
The proposed explanation is that the data source may include a shorter three-month spread in its calculations even when it does not publish that tenor. The par and quoted values can coincide at that hidden first point, while the published six-month and longer values differ because the bootstrap incorporates the shorter input. This is a data-convention explanation tied to the described source; the discussion does not establish that the same hidden tenor is present in every dataset or market feed.
Key ideas
- Par spreads jointly determine a piecewise hazard curve, while quoted spreads use a flat curve tenor by tenor.
- Quoted upfront values correspond to a fixed coupon under the quoted-spread convention.
- An unpublished shorter tenor in the source data can explain a difference at the first visible tenor.
- The explanation depends on the source’s conventions and should be checked against the specific dataset.
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Full text
# CDS Quote Conversion - Quoted vs Par # 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? ## Answer by Phil-ZXX (score 3, accepted) https://quant.stackexchange.com/a/53311 The reason the spreads were off is that the data came from MARKIT, and MARKIT often includes a 3M spread (but does not always publish it). So the 3M Quoted Spread and 3M Par Spread are exactly the same (but unfortunately invisible). And therefore Par and Quoted for >3M will not be exactly the same.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.