Counterparty risk is a subclass of, or type of, credit risk. So, it's okay to say "counterparty risk is credit risk" but not really okay to say "credit risk is counterparty risk" b/c we tend to treat credit risk as an umbrella that contains sub classes, e.g., downgrade risk, recovery risk, default correlation
It *connotes* a bilateral contract where one party has counterparty exposure to the other in a two-way trade;
e.g., say you invest in a Corporate XYZ bond. Here you have classic "credit risk" (which parses into default and downgrade/deterioration risk). At this point, you have "unilateral" credit risk (exposure) on that bond investment and we don't typically refer here to any counterparty risk.
But then say you buy credit protection from me (i.e., i sell you a credit default swap on your bond). If the bond defaults, I am supposed to "make you whole" but you have counterparty risk to me: I may default on my obligation. The CDS is a bilateral contract...
Due to this bilateral nature (e.g., the value of a CDS or interest rate swap can swing positive to negative over time), it is considered more difficult to figure that the unilateral "credit risk" in other words:
you pay $100 for a bond, that's roughly your exposure
you enter into bilateral contract with me (e.g. swap, CDS), you may pay nothing up front, you have counterparty exposure to me, but more difficult to figure.
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