For a swap thats fully collateralised once a day, i suppose that the cva measures risk only for the intraday chance of counterparty default? Surely thats tiny enough to be neglible, or am i missing something?
Collateral imperfections: the CVA cover the expected exposure in the event that the counterparty defaults. When the trade is collateralized and subject to variation margin. This exposure will come only from the imperfection of the collateral. Because posting and receiving collateral actually has a cost, usually the collateral agreement will be a threshold amount (bellow which no collateral is posted / received), and a minimum transfer amount.
The Margin period of risk: Also, when computing the CVA, you are concerned with the case where the counterparty defaults, and in this case before the default, the counterparty would usually stop posting collateral for a given period (called margin period of risk), usually around 10 days. In this period, the value of the swap can move with the market and diverge from the collateral balance.
The initial margin: The IM is supposed to cover these market values moves during the MPOR, it's a quantile like PFE, but it not the same as PFE is a quantile of the credit exposure = max(MV(t), 0) whereas the initial margin is a quantile of the market value variation over the margin period of risk = MV(t + MPOR) - MV(t).
I would say it is negligible, the only times have ever had to compute that on standalone ISDAs (with just one albeit large swap) it's really honestly been very small perhaps a few tens of k for a 500mm swap over 15 years from distant memory, even if you say for example that your period of risk is greater than a day (let's say you have a massive swap, a major deriv cprty defaults, whole market is same way around so you can't replace your market risk hedge as quickly as you'd like - inconceivable in vanilla swaps but bear in mind regulatory hedge replacement windows typically assume 7 days or similar).
This is even in the context of wrong way credit rates correlation - if you model credit intensity and rates as correlated brownians you just aren't going to get a material one day move. As a caveat I would say however if you have a large long dated swap book that is very one way vs a counterparty (let's say you are receiving fixed and assume low rates <-> wide credit), then obviously it will add up. So as in many problems, it's worth looking at with conservative assumptions on period of risk and correlation, to allow you decide if you can afford to ignore it on your portfolio. Regulators as mentioned do demand a marghin period of risk, but unless am wrong for certain banks, this does not generally make it into economic CVA calculations and hedging decisions.
i think that cva is meant to cover Expected credit losses and PFE x% covers Unexpected credit losses and so gap risk would be more covered by PFE
i think initial margin for ccp cleared trades is more like a charge for PFE than for cva
So, i still dont really fully get where the demand for cva is coming from