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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?

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  • $\begingroup$ hi Welcome to stackexchange. Just to clarify, are both legs floating: index and index+spread? And are the notionals constant until maturity or adjusted periodically? $\endgroup$ Commented May 28, 2021 at 14:11
  • $\begingroup$ I am referring to a standard basis so the convention is float/float (ESTER+spread vs SOFR flat) but the USD leg is ressetable so the USD notional is adjusted every 3months given the EURUSD FX Fixing. $\endgroup$
    – Rich.G
    Commented May 28, 2021 at 14:25
  • $\begingroup$ I am not sure about the xccy swap because I haven't delved in those products so ideally I can help you of you can write me a payoff. About a SOFR leg discounted at SOFR, you can look up the fact that a floating rate note always has a value 1. The conclusion then is trivial. $\endgroup$
    – Arshdeep
    Commented May 30, 2021 at 13:12
  • $\begingroup$ Are you talking about a XCCY swap before the initial exchange of notional? Otherwise I would expect a significant FX sensitivity. $\endgroup$
    – Ami44
    Commented May 31, 2021 at 23:25

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