I was having a discussion with a colleague in the industry, who mentioned in passing that CVA on a cross currency swap from EUR into USD (pay EUR) is always higher than if paying USD and receiving EUR... why?
The CVA on a cross currency swap comes mostly from the final exchange (being the biggest flow). If you as an end user are paying the EUR, then the bank is receiving the EUR a d paying the USD. They will see that this position is a net receivable, because EUR is more valuable on a forward basis than spot. Receivables attract a higher CVA than payables. (The reason EUR is valued more highly on forward dates is due to the interest rate differential between EUR and USD. See covered interest rate parity ).
If by paying EUR you mean on the initial exchange you are short USD vs long EUR i.e. you're short USD forward, then a simple explanation might be the higher CVA is coming from the fact that the EUR/USD basis is generally negative (i.e. USD demand exceeds EUR demand). Hence the expected exposure is more material to the short USD position on notional exchange (offsetting any effect of the higher rate payer's position).