When pricing a XCCY basis on RFR (assuming USD CSA so under SOFR), for example ESTER versus SOFR (USD leg resettable) : I observed that the PV / Risk and also FX Delta are close to zero.
I have been told this is because a SOFR leg with notional exchanges discounted at SOFR have a near null PV and risk. Same as when IBOR XCCY were discounted at IBOR before the 2008 crisis.
Apparently the notional exchange which is discounted at SOFR can be seen as a SOFR floating leg in the opposite direction.
I don’t quite understand that explanation.
Can someone please shed some light on why we expect zero PV/Risk/FX Delta with a more intuitive explanation or even a mathematic proof?