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Usually a standard FVA example starts with an uncollateralized netting set that is hedged via a collateralized netting set, and because we have costs/benefits from the collateral, we say the FVA originates from the uncollateralized netting set. The uncollateralized netting set will have FVA but the perfectly collateralized netting set will have FVA=0 if perfectly collateralized. Intuitively, this is clear.

Let's assume a counterexample. A hypothetical trading company which has on its portflio only one netting set (i.e. it does no hedging with other cpties) and this netting set is fully collateralized (perfect collateralization). What would be the FVA in this case? In the first example, the FVA for a perfectly collateralized netting set would be 0 but in this case we still have the collateral funding costs but we don't have the "original" netting set that we are hedging.

My question more broadly is: does the economic context matter for FVA (which would imply we have FVA in the "counterexample"), or we just "blindly" apply the same formula, regardless of the context (we would have no FVA in the "counterexample")?

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  • $\begingroup$ FVA is effectively the drag on a hedged book due to asymmetry between collateral on the original trades and the hedging trades. In your example, the hedges would have to be with the original counterparty which would zero out the portfolio and thus FVA = 0. $\endgroup$
    – river_rat
    Dec 16, 2023 at 22:31
  • $\begingroup$ See here: quant.stackexchange.com/a/76672/29443 $\endgroup$
    – Attack68
    Dec 16, 2023 at 22:52
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    $\begingroup$ A trade is valued against its economic value. If the trade is collateralised then its flows are valued relative to the discount curve associated with the remuneration of that collateral. If that collateral happens to align with the numeraire of the market there is no difference. When that collateral does not align with the numeraire (say its GBP@RFR instead of USD@RFR) then the difference between the two might be classed as one type of valuation adjustment e.g. CollVA, if it is not collateralised (unfunded) the difference might be classed as a funding valuation adjustment, e.g FVA $\endgroup$
    – Attack68
    Dec 16, 2023 at 23:02

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