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is the credit spread you are referring the credit default swap spread? if so then there's already a functional relationship binding probabily of default (cumulative probability curve) and credit default swap spread, and it is through this equation, PV premium leg = PV contingent payment leg. So if you have either info (i.e. cumulative default probability curve or term structure of cds spread), you are derive the other one. Note that you also need the yield curve to discount the cash flows.