May 2nd, 2020, 1:51 pm
This is a subtle issue, but here goes with the bare bones.
You should be able to convince yourself that the correct rate to discount future cashflows, in generality, is your effective cost of funding. But what is this?
1) for perfectly collateralised trades, it is a fact (not especially obvious at first glance, I concede) that on an expectation value basis all cash required or generated for a position is supplied/absorbed by the transfer of collateral. So your effective cost of funding is whatever rate on posted collateral is specified in the CSA, which is usually (approximately) OIS. So that's the curve you want.
2) for uncollateralised positions, you have a choice.
(a) you can say sod it, our systems are set up to PV along OIS curves, so we will stick with that even though we know it's wrong... and then manually adjust for the wrongness with XVA adjustments.
(b) you could try and build a correct zero curve... if you think 3M Euribor is a decent approximation to your desk's cost of funding (frankly, I doubt it), you can use that [it has the advantage of being a very convenient fiction, which is why it was market standard until about 2009]; or if you're feeling brave you could try and build your own bespoke funding curve.
Most people vote for (a), or a variation of it ('CSA discounting'). But it does lead you into the murky depths of XVA, so it's by no means an easy option.