I'm wondering how to account for a CCP basis (like EUREX vs. LCH) in a trading system. Two ways that immediately come to my mind are making the forward or the discount curve CCP-specific. As the par swap rate is not very sensitive against the discount curve*, I personally tend towards having a CCP-specific forward curve. But at the same time this gives me a bit of a headache as in theory different forwards can only be justified by differences in collateral rate. But at least for the VM the collateral rate for e.g. LCH and EUREX is the same, isn't it? And if it were different then wouldn't this imply that the discount curve of the 2 CCPs can't be the same?
What are your thoughts on that?
* at the moment a 1bp difference in the 10Y EUR swap rate could only be explained by a 100bp parallel shift of the €STR curve (when keeping the forward the same)