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")?
