A "par curve" shows how people used to trade CDS with zero upfront fee before the 2009 Big Bang. But no one trades CDS like that any more. They trade with standard running spread, like 100 bps, and upfront fee. For convenience, most names are quoted as the conventional spread, which is very close to the par spread. But a few very high yield names (like Venezuela before the default :) are quoted as upfront. See, for example, BIS Quarterly Review, December 2010 p 65, and MarkIt, The CDS Big Bang: Understanding the Changes to the Global CDS Contract and North American Conventions (2009)
In my opinion, no one should be using par spreads anymore, except for backward compatability with bad legacy libraries and IT systems. If you have the conventional spread (market standard quote), use it and disregard the par spread.
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